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Probing the Interface of a Phase-Separated State in a Repulsive Bose-Fermi Mixture
Abstract
We probe the interface between a phase-separated Bose-Fermi mixture consisting of a small BEC of K residing in a large Fermi sea of Li. We quantify the residual spatial overlap between the two components by measuring three-body recombination losses for variable strength of the interspecies repulsion. A comparison with a numerical mean-field model highlights the importance of the kinetic energy term for the condensed bosons in maintaining the thin interface far into the phase-separated regime. Our results demonstrate a corresponding smoothing of the phase transition in a system of finite size.
... as an additional length scale, where m r denotes the reduced mass and δµ represents the differential magnetic moment between the molecular state (closed channel) underlying the resonance and the atomic scattering state (entrance channel). Using this definition, the binding energy of the molecular state can be modeled as [29,30] ...
... A differential polarizability between the entrance channel (atom pair state) and the closed channel (molecular state) in the infrared optical trap may cause a lightinduced shift in the position of a Feshbach resonance. We have observed such an effect in the 6 Li-40 K Fermi-Fermi mixture [37] and the 6 Li-41 K Fermi-Bose mixture [30]. Taking this shift into account turned out to be essential for accurate interaction tuning, and also proved to be a very useful tool to implement extremely fast changes of the interaction strength [38]. ...
... The orange dashed line represents the linear fit B 0 = ξU K + B zero , which yields the pole position without light shift, B zero = 7.295(3) G, and the linear slope ξ=1.6(5)×10 −4 G/µK. This value for the slope ξ is about one order magnitude smaller than that of Li-K at the 335-G resonance [30]. Such a small slope implies that the light shift effect is negligible for the shallow traps used in our experiment. ...
We report on the observation of Feshbach resonances at low magnetic field strength (below 10 G) in the Fermi-Fermi mixture of Dy and K. We characterize five resonances by measurements of interspecies thermalization rates and molecular binding energies. As a case of particular interest for applications, we consider a resonance near 7.29 G, which combines accurate magnetic tunability and access to the universal regime of interactions with experimental simplicity. We show that lifetimes of a few 100 ms can be achieved for the optically trapped, resonantly interacting mixture. We also demonstrate the hydrodynamic expansion of the mixture in the strongly interacting regime and the formation of DyK Feshbach molecules. Our work opens up new experimental possibilities in view of mass-imbalanced superfluids and related phenomena.
... Before delving into the analysis of mechanical stability, we present the results for the thermodynamic parameters B , F , 0 obtained by solving the set of Eqs. (15)(16)(17). The results for these quantities have already been presented in [52]. ...
... In order to compute the stability matrix (32) and the related stability conditions (33), a straightforward finite difference evaluation of the first-order derivatives appearing in (32) is performed: the input densities B and F are slightly changed one at a time and the shifted values of B and F are obtained by solving Eqs. (15)(16)(17) accordingly. ...
We investigate the mechanical stability of Bose-Fermi mixtures at zero temperature in the presence of a tunable Feshbach resonance, which induces a competition between boson condensation and boson-fermion pairing when the boson density is smaller than the fermion density. Using a many-body diagrammatic approach validated by fixed-node Quantum Monte Carlo calculations and supported by recent experimental observations, we determine the minimal amount of boson-boson repulsion required to guarantee the stability of the mixture across the entire range of boson-fermion interactions from weak to strong coupling. Our stability phase diagrams indicate that mixtures with boson-to-fermion mass ratios near two, such as the Rb-K system, exhibit optimal stability conditions. Moreover, by applying our results to a recent experiment with a Na-K mixture, we find that the boson-boson repulsion was insufficient to ensure stability, suggesting that the experimental timescale was short enough to avoid mechanical collapse. On the other hand, we also show that even in the absence of boson-boson repulsion, Bose-Fermi mixtures become intrinsically stable beyond a certain coupling strength, preceding the quantum phase transition associated with the vanishing of the bosonic condensate. We thus propose an experimental protocol for observing this quantum phase transition in a mechanically stable configuration.
... Also, a larger number of fermions leads to a stronger bound composite system, implying that the impurities can manipulate the strength of the ensuing bound state. Specifically, a phase separation [44] between the fermions and the droplet occurs for repulsive intercomponent interactions. Importantly, for attractive couplings the fermions delocalize within the droplet and feature a gradual localization for larger attractions, a process reminiscent of the self-pinning transition known in 1D gases [45,46]. ...
... At the same time the droplet density is largely unchanged. The phase separation process of repulsively interacting Bose-Fermi mixtures has also been previously observed in the case of the bosonic component being in the gaseous phase [44,55,56]. It should also be noted that in both the decoupled and the repulsive intercomponent interaction regions, the density overlap between the fermions and the droplet is influenced by finite-size effects which vanish as the box size is enlarged. ...
We unravel the ground state properties and emergent nonequilibrium dynamics of a mixture consisting of a few spin-polarized fermions embedded in a two-dimensional bosonic quantum droplet. For an increasingly attractive droplet-fermion interaction we find a transition from a spatially delocalized fermion configuration to a state where the fermions are highly localized and isolated. This process is accompanied by the rise of induced fermion-fermion interactions mediated by the droplet. Additionally, for increasing attractive droplet-fermion coupling, undulations in the droplet density occur in the vicinity of the fermions manifesting the back-action of the latter. Following interaction quenches from strong to weaker attractive droplet-fermion couplings reveals the spontaneous nucleation of complex excitation patterns in the fermion density such as ring- and cross-shaped structures. These stem from the enhanced interference of the fermions that remain trapped within the droplet, which emulates, to a good degree, an effective potential for the fermions. The non-negligible back-action of the droplet manifests itself in the fact that the effective potential predictions are less accurate at the level of the many-body wave function. Our results provide a paradigm for physics beyond the reduced single-component droplet model, unveiling the role of back-action in droplets and the effect of induced mediated interactions.
Published by the American Physical Society 2024
... Also, a larger number of fermions leads to a stronger bound composite system implying that the impurities can manipulate the strength of the ensuing bound state. Specifically, a phase-separation [44] between the fermions and the droplet occurs for repulsive intercomponent interactions. Importantly, for attractive couplings the fermions delocalize within the droplet and feature a gradual localization for larger attractions, a process reminiscent of the self-pinning transition known in 1D gases [45,46]. ...
... At the same time the droplet density is largely unchanged. The phase separation process of repulsively interacting Bose-Fermi mixtures has also been previously observed in the case of the bosonic component being in the gaseous phase [44,55,56]. It should also be noted that in both the decoupled and the repulsive intercomponent interaction regions, the density overlap between the fermions and the droplet is influenced by finite size effects which vanish as the box size is enlarged. ...
We unravel the ground state properties and emergent non-equilibrium dynamics of a mixture consisting of a few spin-polarized fermions embedded in a two-dimensional bosonic quantum droplet. For an increasingly attractive droplet-fermion interaction we find a transition from a spatially delocalized fermion configuration to a state where the fermions are highly localized and isolated. This process is accompanied by the rise of induced fermion-fermion interactions mediated by the droplet. Additionally, for increasing attractive droplet-fermion coupling, undulations in the droplet density occur in the vicinity of the fermions manifesting the back-action of the latter. Following interaction quenches from strong attractive to weaker droplet-fermion couplings reveals the spontaneous nucleation of complex excitation patterns in the fermion density such as ring and cross shaped structures. These stem from the enhanced interference of the fermions that remain trapped within the droplet, which emulates, to a good degree, an effective potential for the fermions. The non-negligible back-action of the droplet manifests itself in the fact that the effective potential predictions are less accurate at the level of the many-body wave function. Our results provide a paradigm for physics beyond the reduced single-component droplet model, unveiling the role of back-action in droplets and the effect of induced mediated interactions.
... The formation of Feshbach molecules is here prohibited by the repulsive nature of the interactions. However, the problem of instability persists: sufficiently large repulsive boson-fermion interactions lead the system towards phase separation [8,[30][31][32]. ...
... For increasing interaction, although the QMC results qualitatively follow Eq. (32), some discrepancy between the perturbative predictions and the QMC points is manifest. This might be due to a not sufficiently accurate nodal surface, which could be improved by introducing backflow correlations. ...
We derive analytically the leading beyond-mean field contributions to the zero-temperature equation of state and to the fermionic quasi-particle residue and effective mass of a dilute Bose-Fermi mixture in two dimensions. In the repulsive case, we perform quantum Monte Carlo simulations for two representative bosonic concentrations and equal masses, extending a method for correcting finite-size effects in fermionic gases to Bose-Fermi mixtures. We find good agreement between analytic expressions and numerical results for weak interactions, while significant discrepancies appear in the regime close to mechanical instability, above which we provide evidence of phase separation of the bosonic component.
... Since then, there have been numerous experimental studies which deal with these types of mixtures, where the usual methodology is to use combinations of specific isotopes from the same or different atoms in order to produce disparate statistics between components . Furthermore, controlling both the number of carriers from each species and the interactions between them has allowed finding novel and fascinating phenomena such as phase separation [38], a Bose-Fermi superfluid mixture [39], and even effective interactions between bosons mediated by fermions. ...
... With the second quantization tool at hand we now look at our specific problem. Consider a system of scalar bosons and two-color fermions, where we can see interesting phenomena due to both the different particle statistics and the imbalance in the spin population [38,39,90]. We want first to restrict the system to a one-dimensional geometry, for that it is enough to consider a parabolic potential where the trapping frequency in the x, y plane ω ⊥ is much larger than the trapping frequency in the z direction ω ∥ . ...
We study a one-dimensional mixture of two-color fermions and scalar bosons at the hard-core limit, focusing on the effect that the next-neighbor interaction between particles of the same species has on the zero-temperature ground state of the system for different fillings of each carrier. Exploring the parameters of the problem, we observed that the non-local interaction modifies the well-known mixed and spin-selective Mott insulators, and we also found the emergence of three unusual insulating states with peculiar charge density wave orderings, a fully out-of-phase density of carriers for bosonic half-filling, an insulator with the same bosonic and fermionic fillings, and a different spin-selective insulator where the bosonic filling matches the density of one kind of fermion. Modern cold-atom setups correspond to the ideal experimental setting where these incommensurable insulators can be observed. An article based on this work can be found published on arXiv.2309.05594 and is currently under review for publication.
... Since the inter-species interaction can be tuned in an atomic Bose-Fermi mixture, the first fundamental question concerns its stability and miscibility [21][22][23][24][25][26][27][28][29][30][31][32][33]. For a weakly interacting Bose-Einstein condensate (BEC) mixed with a single-component Fermi gas, perturbation theory predicts that a sufficiently large Bose-Fermi scattering length will lead to the collapse of the system on the attractive side [22,24,27] and to phase separation on the repulsive side [26,29,31,32]. ...
... Since the inter-species interaction can be tuned in an atomic Bose-Fermi mixture, the first fundamental question concerns its stability and miscibility [21][22][23][24][25][26][27][28][29][30][31][32][33]. For a weakly interacting Bose-Einstein condensate (BEC) mixed with a single-component Fermi gas, perturbation theory predicts that a sufficiently large Bose-Fermi scattering length will lead to the collapse of the system on the attractive side [22,24,27] and to phase separation on the repulsive side [26,29,31,32]. At typical atomic gas densities, the predicted critical values of the scattering length are quite small such that perturbation theory is expected to be valid. ...
Motivated by recent surprising experimental findings, we develop a strong-coupling theory for Bose-Fermi mixtures capable of treating resonant inter-species interactions while satisfying the compressibility sum rule. We show that the mixture can be stable at large interaction strengths close to resonance, in agreement with the experiment but at odds with the widely used perturbation theory. We also calculate the sound velocity of the Bose gas in the Cs-Li mixture, again finding good agreement with the experimental observations both at weak and strong interactions. A central ingredient of our theory is the generalization of a fermion mediated interaction to strong Bose-Fermi scatterings and to finite frequencies. This further leads to a predicted hybridization of the sound modes of the Bose and Fermi gases, which can be directly observed using Bragg spectroscopy.
... Developments of last few decades in a field of cooling atoms of different species of alkalis [5,6], together with the possibility to control the parameters of their two-body potentials by means of the Feshbach resonances [7] have lead to the creation of the gaseous Bose-Fermi mixtures with an arbitrary strong interparticle interaction [8,9]. Although a simple perturbative analysis of the thermodynamic stability of these systems at a weak coupling was carried out long ago by Saam [10], and in more recent times of realization of ultracold quantum gases in [11][12][13][14][15], the interest to the topic still does not go down [16][17][18][19][20][21][22] in the community. ...
... 16) ...
We discuss an equilibrium mean-field properties of mixtures consisting of bosons and spin-polarized fermionic atoms with a point-like interaction in an arbitrary dimension . Particularly, besides the standard weak-coupling limit of the system with slightly depleted Bose condensate and almost ideal Fermi gas, we discuss the (meta)stable phase with dimers composed exactly of one boson and one fermion. The peculiarities of the fermion-dimer and the boson-dimer three-body effective interactions and their impact on the thermodynamic stability of the dilute Bose-Fermi mixtures are elucidated.
... Clean realizations of fully controllable systems are scarce. Ultracold atomic gases offer an ideal platform to experimentally investigate Bose-Fermi mixtures, as the species concentration and interaction strengths can be freely tuned [10][11][12][13][14][15][16][17][18][19][20][21][22][23]. Here, we study the collective oscillations of a spin-polarized Fermi gas immersed in a Bose-Einstein condensate (BEC) as a function of the boson-fermion interaction strength and temperature. ...
... Ultracold atomic gases provide arguably the purest realizations of Bose-Fermi mixtures, featuring precisely understood, tunable short-range interactions and a high degree of experimental control, offering a direct comparison to theoretical models. In recent years, atomic Bose-Fermi mixtures enabled the study of dual superfluids [32][33][34][35][36], the onset of phase separation [14,15,21,37], and the observation of strong-coupling Bose polarons [38,39]. ...
Interacting mixtures of bosons and fermions are ubiquitous in nature. They form the backbone of the standard model of physics, provide a framework for understanding quantum materials such as unconventional superconductors and two-dimensional electronic systems, and are of technological importance in He/He dilution refrigerators. Bose-Fermi mixtures are predicted to exhibit an intricate phase diagram featuring coexisting liquids, supersolids, composite fermions, coupled superfluids, and quantum phase transitions in between. However, their coupled thermodynamics and collective behavior challenge our understanding, in particular for strong boson-fermion interactions. Clean realizations of fully controllable systems are scarce. Ultracold atomic gases offer an ideal platform to experimentally investigate Bose-Fermi mixtures, as the species concentration and interaction strengths can be freely tuned. Here, we study the collective oscillations of a spin-polarized Fermi gas immersed in a Bose-Einstein condensate (BEC) as a function of the boson-fermion interaction strength and temperature. Remarkably, for strong interspecies interactions the fermionic collective excitations evolve to perfectly mimic the bosonic superfluid collective modes, and fermion flow becomes dissipationless. With increasing number of thermal excitations in the Bose gas, the fermions' dynamics exhibit a crossover from the collisionless to the hydrodynamic regime, reminiscent of the emergence of hydrodynamics in two-dimensional electron fluids. Our findings open the door towards understanding non-equilibrium dynamics of strongly interacting Bose-Fermi mixtures.
... Ultra-cold atomic gases provide an exceptionally versatile platform for the simulation of quantum matter [5]. In the case of Bose-Fermi (BF) atomic mixtures, several realizations have allowed exploration of a wide range of phenomena like phase separation [22], polarons [13,17,23,26,31], dual superfluidity [15,16,19,20], collective excitations [34,39], mediated interactions [28,[35][36][37], and Feshbach molecules [6,8,10,25,30,33]. ...
We consider a mixture of bosons and spin-polarized fermions in two dimensions at zero temperature with a tunable Bose-Fermi attraction. By adopting a diagrammatic T T -matrix approach, we analyze the behavior of several thermodynamic quantities for the two species as a function of the density ratio and coupling strength, including the chemical potentials, the momentum distribution functions, the boson condensate density, and the Tan’s contact parameter. By increasing the Bose-Fermi attraction, we find that the condensate is progressively depleted and Bose-Fermi pairs form, with a small fraction of condensed bosons surviving even for strong Bose-Fermi attraction. This small condensate proves sufficient to hybridize molecular and atomic states, producing quasi-particles with unusual Fermi liquid features. A nearly universal behavior of the condensate fraction, the bosonic momentum distribution, and Tan’s contact parameter with respect to the density ratio is also found.
... The interspecies interaction allows the sympathetic cooling [10,11,[16][17][18], and can change the dynamics in each components [19]. issues in the study of Bose-Fermi mixtures include their stability and miscibility [15,[20][21][22][23][24][25][26], transport properties [27][28][29], and the possible applications in quantum simulations to achieve supersymmetry [30][31][32][33][34][35][36][37]. The supersymmetry, which assigns a superpartener (a particle with the same mass but opposite statistics) to each elementary particle, appears to be broken when there is an explicit mass or chemical potential imbalance between the two components. ...
The Goldstino, which is a fermionic Nambu-Goldstone mode, has been predicted in a Bose-Fermi mixture when the supersymmetry is broken. To detect this excitation mode, we theoretically investigate the shot noise of the supersymmetry-like tunneling current in a repulsively interacting ultracold Bose-Fermi mixture. The Fano factor, which is defined by the noise-to-current ratio, reflect the elementary carriers of the tunneling process. The change of the Fano factor microscopically as the density changes evinces a crossover from the quasiparticle transport to multiparticle (Goldstino) transport. The tunneling channel can also be changed by tuning the potential barrier.
... Historically, such systems were first studied in the context of 3 He - 4 He mixtures, which now find application in dilution refrigerators [36][37][38]. In contemporary physics, Bose-Fermi mixtures have been used to study a wide array of physical phenomena, including anomalous pairing [39][40][41][42][43][44], phase separation [45,46], molecule formation [47][48][49], mediated interactions and sound propagation [50][51][52][53][54][55], polarons [56,57], and mixed superfluidity [58,59]. ...
Theoretical treatments of nonequilibrium dynamics in strongly interacting Bose-Fermi mixtures are complicated by the inherent non-Gaussian nature of the vacuum two-body physics, invalidating the typical Hartree-Fock-Bogoliubov approximation. Here we apply the cumulant expansion to study nonequilibrium Bose-Fermi mixtures, which allows us to explicitly include the missing non-Gaussian quantum correlations, leading to a consistent dynamical theory of a Bose-Fermi mixture near an interspecies Feshbach resonance. We first apply our theory to a study of atom-pair coherence in the gas, which is significantly enhanced by the competing influences of the Fermi sea and Bose-Einstein condensation, in agreement with analytical calculations. Then we study the depletion of a degenerate Bose-Fermi mixture following a quench to the unitary regime, characterizing the resulting depletion of the Bose-Einstein condensate, the deformation of the Fermi surface, and the production of molecules. We find that at early times, the population dynamics scale quadratically with the hold time, and define an associated characteristic timescale set by the parameters of the mixture and the width of the Feshbach resonance.
Published by the American Physical Society 2024
... Note that in the repulsively interacting regime, bosons and fermions tend to be spatially separated beyond a critical interaction strength [59,60]. Such phase separation has recently been studied in mass-imbalanced mixtures, where the phase separation occurs at the repulsive branch when tuning the a bf from a small positive value to resonance [61][62][63]. This process is similar to the Stoner ferromagnetic phase transition in a two-spin-component Fermi gases [64,65]. ...
... Historically, such systems were first studied in the context of 3 He- 4 He mixtures, which now find application in dilution refrigerators [36][37][38]. In contemporary physics, Bose-Fermi mixtures have been used to study a wide array of physical phenomena, including anomalous pairing [39][40][41][42][43][44], phase separation [45,46], molecule formation [47][48][49], mediated interactions and sound propagation [50][51][52][53][54][55], polarons [56,57], and mixed superfluidity [58,59]. ...
Theoretical treatments of non-equilibrium dynamics in strongly interacting Bose-Fermi mixtures are complicated by the inherent non-Gaussian nature of the vacuum two-body physics, invalidating the typical Hartree-Fock-Bogoliubov approximation. Here, we apply the cumulant expansion to study non-equilibrium Bose-Fermi mixtures, which allows us to explicitly include the missing non-Gaussian quantum correlations, leading to a consistent dynamical theory of a Bose-Fermi mixture near an interspecies Feshbach resonance. We first apply our theory to a study of atom-pair coherence in the gas, which is significantly enhanced by the competing influences of the Fermi sea and Bose-Einstein condensation, in agreement with analytical calculations. Then, we study the depletion of a degenerate Bose-Fermi mixture following a quench to the unitary regime, characterizing the resulting depletion of the Bose-Einstein condensate, the deformation of the Fermi surface, and the production of molecules. We find that at early times, the population dynamics scale quadratically with the hold time, and define an associated characteristic timescale set by the parameters of the mixture and the width of the Feshbach resonance.
... Ultracold atomic gases provide arguably the purest realizations of Bose-Fermi mixtures, featuring precisely understood, tunable short-range interactions and a high degree of experimental control 8-21 , offering a direct comparison with theoretical models [22][23][24][25][26] . In recent years, atomic Bose-Fermi mixtures enabled the study of dual superfluids 27-31 , the onset of phase separation and mean-field collapse 12,13,19,32,33 , and the observation of strong-coupling Bose polarons 34,35 . ...
Interacting mixtures of bosons and fermions are ubiquitous in nature. They form the backbone of the standard model of physics, provide a framework for understanding quantum materials and are of technological importance in helium dilution refrigerators. However, the description of their coupled thermodynamics and collective behaviour is challenging. Bose–Fermi mixtures of ultracold atoms provide a platform to investigate their properties in a highly controllable environment, where the species concentration and interaction strength can be tuned at will. Here we characterize the collective oscillations of spin-polarized fermionic impurities immersed in a Bose–Einstein condensate as a function of the interaction strength and temperature. For strong interactions, the Fermi gas perfectly mimics the superfluid hydrodynamic modes of the condensate, from low-energy quadrupole modes to high-order Faraday excitations. With an increasing number of bosonic thermal excitations, the dynamics of the impurities cross over from the collisionless to the hydrodynamic regime, reminiscent of the emergence of hydrodynamics in two-dimensional electron fluids.
... The influence of fermions onto bosons has been researched in different mixtures, for example in 4 He− 3 He [34,35], 87 Rb− 40 K [36,37], 41 K− 6 Li [38], 87 Rb− 40 K [39], 170 Yb− 173 Yb, 174 Yb− 173 Yb [40]. Other Bose-Fermi mixtures (BFM) that have been experimentally reported are 7 Li− 6 Li [41], 39 K− 40 K and 41 K− 40 K [42]. ...
The time evolution of probability density, the ground-state fidelity and the entanglement of a Bose-Fermi mixture in a 1D double well potential, are studied through the two-mode approximation. We found that the behavior of the quantum return probability shows three distinct regions. The first region is characterized by a complete miscibility, and correlated tunneling of bosons and fermion. The second region is characterized by correlated sequential tunneling and in the last region we found an increase in the tunneling frequency of the two species. Through the Von Neumann entropy, we found that the boson-fermion coupling allows a maximum entanglement of quantum correlations of bosons and fermions in the same value. Finally, Considering variations in the interaction between pairs of fermions λ FF , pairs of bosons λ BB , and variations in the interaction between particles of different species λ BF , we calculated the fidelity in the λ FF − λ BF and λ BB − λ BF planes and we found that the drop of the two fidelities becomes deeper and deeper as the boson-fermion interaction decreases.
... These quasiparticles arise from the interaction between individual impurities and the low-energy excitations of the quantum gas. Experimental realization of both Bose [5][6][7][8][9] and Fermi polarons [10][11][12][13][14] has been achieved using alkaline atomic species employing spectroscopy and interferometric protocols to characterize these quasiparticles in cold atoms-setups [15]. ...
Charged quasiparticles dressed by the low excitations of an electron gas, constitute one of the fundamental pillars for understanding quantum many-body effects in some materials. Quantum simulation of quasiparticles arising from atom-ion hybrid systems may shed light on solid-state uncharted regimes. Here we investigate the ionic Fermi polaron consisting of a charged impurity interacting with a polarized Fermi bath. Employing state-of-the-art quantum Monte Carlo techniques tailored for strongly correlated systems, we characterize the charged quasiparticle by computing the energy spectrum, quasiparticle residue, and effective mass, as well as the structural properties of the system. Our findings in the weak coupling regime agree with field-theory predictions within the ladder approximation. However, stark deviations emerge in the strongly interacting regime attributed to the vastly large density inhomogeneity around the ion, resulting in strong correlations for distances on the order of the atom-ion potential range. Moreover, we find a smooth polaron-molecule transition for strong coupling, in contrast with the neutral case, where the transition smoothens only for finite temperature and finite impurity density. This study may provide valuable insights into alternative solid-state systems such as Fermi excitons polarons in atomically thin semiconductors beyond the short-range limit. Introduction-Impurities interacting with a quantum many-body environment lead to the formation of quasiparticles termed polarons as the mobile impurity entangles with virtual quantum excitations in the medium. The concept of a quasi-particle is one of the milestones in Landau's Fermi-liquid theory [1-3], originally introduced by Landau and further developed by Pekar [4] in the context of electrons embedded in polar crystals. In a very different energy scale, the high level of controllability in ultra-cold degenerate quantum mixtures has theoretically and experimentally inspired the study of a quantum analog of the solid-state polaron. These quasiparticles arise from the interaction between individual impurities and the low-energy excitations of the quantum gas. Experimental realization of both Bose [5-9] and Fermi polarons [10-14] has been achieved using alkaline atomic species employing spec-troscopy and interferometric protocols to characterize these quasiparticles in cold atoms-setups [15].
... where B 0 represents the resonance centre, Δ denotes the magnetic width and a bg is the background scattering length. For the 41 K- 6 Li resonance (FB case), the relevant parameter values are as follows 21,46 : B 0 = 335.080(1) G, Δ = 0.9487 G and a bg = 60.865a ...
The notion of quasi-particles is essential for understanding the behaviour of complex many-body systems. A prototypical example of a quasi-particle is a polaron, formed by an impurity strongly interacting with a surrounding medium. Fermi polarons, created in a Fermi sea, provide a paradigmatic realization of this concept. Importantly, such quasi-particles interact with each other via the modulation of the medium. However, although quantum simulation experiments with ultracold atoms have substantially improved our understanding of individual polarons, the detection of their interactions has so far remained elusive. Here we report the observation of mediated interactions between Fermi polarons consisting of K impurities embedded in a Fermi sea of Li atoms. Our results confirm two predictions of Landau’s Fermi-liquid theory: the shift in polaron energy due to mediated interactions, which is linear in the concentration of impurities; and its sign inversion with impurity quantum statistics. For weak-to-moderate interactions between the impurities and the medium, our results agree with the static predictions of Fermi-liquid theory. For stronger impurity–medium interactions, we show that the observed behaviour at negative energies can be explained by a more refined many-body treatment including retardation and dressed molecule formation.
... In our case, a negative detuning gives a positive scattering length and corresponds to the magnetic field region where the pair can bind into a molecule. Knowing B 0 , δB * , and δμ, the energy of the molecular state relative to the atomic pair state (negative binding energy) can be calculated as [54,57] ...
We report on the preparation of a pure ultracold sample of bosonic DyK Feshbach molecules, composed of the fermionic isotopes Dy161 and K40. By sweeping a magnetic field across a resonance located near 7.3 G, we generate up to 5000 molecules at a temperature of approximately 50 nK. To purify the sample from remaining atoms, we employ a Stern-Gerlach technique that relies on magnetic levitation of the molecules in a very weak optical dipole trap. With the trapped molecules we finally reach a high phase-space density of about 0.1. We investigate the magnetic field dependence of the molecular binding energy and the magnetic moment, refining our knowledge of the resonance parameters. We also demonstrate a peculiar anisotropic expansion effect observed when the molecules are released from the trap and expand freely in the magnetic levitation field. Furthermore, we identify an important lifetime limitation that is imposed by the 1064-nm infrared trap light itself and not by inelastic collisions. The light-induced decay rate is found to be proportional to the trap light intensity and the closed-channel fraction of the Feshbach molecule. These observations suggest a one-photon coupling to electronically excited states to limit the lifetime and point to the prospect of loss suppression by optimizing the wavelength of the trapping light. Our results offer crucial insights and experimental progress towards achieving quantum-degenerate samples of DyK molecules and novel superfluids based on mass-imbalanced fermion mixtures.
... The immiscibility of two-component BECs are completely tunable in experiments. Phase separation effect induces rich physics in quantum gases, such as the formation of vector solitons and vortex-soliton structures, coherent spin dynamics, and pattern formations [11][12][13][14][15][16][17][18][19]. ...
In a trapped spin-1/2 Bose-Einstein condensate with miscible interactions, a two-dimensional spin-orbit coupling can introduce an unconventional spatial separation between the two components. We reveal the physical mechanism of such a spin-orbit-coupling-induced phase separation. Detailed features of the phase separation are identified in a trapped Bose-Einstein condensate. We further analyze differences of phase separation in Rashba and anisotropic spin-orbit-coupled Bose gases. An adiabatic splitting dynamics is proposed as an application of the phase separation.
... where B 0 represents the resonance center, ∆ denotes the width, and a bg is the background scattering length. For the 41 K-6 Li resonance (FB case), the relevant parameter values are [21,45]: B 0 = 335.080(1) G, ∆ = 0.9487 G, and a bg = 60.865 a 0 . ...
The notion of quasi-particles is essential for understanding the behaviour of complex many-body systems. A prototypical example of a quasi-particle, a polaron, is an impurity strongly interacting with a surrounding medium. Fermi polarons, created in a Fermi sea, provide a paradigmatic realization of this concept. As an inherent and important property such quasi-particles interact with each other via modulation of the medium. While quantum simulation experiments with ultracold atoms have significantly improved our understanding of individual polarons, the detection of their interactions has remained elusive in these systems. Here, we report the unambiguous observation of mediated interactions between Fermi polarons consisting of K impurities embedded in a Fermi sea of Li atoms. Our results confirm two landmark predictions of Landau's Fermi-liquid theory: the shift of the polaron energy due to mediated interactions, linear in the concentration of impurities, and its sign inversion with impurity quantum statistics. For weak to moderate interactions between the impurities and the medium, we find excellent agreement with the static (zero-momentum and energy) predictions of Fermi-liquid theory. For stronger impurity-medium interactions, we show that the observed behaviour at negative energies can be explained by a more refined many-body treatment including retardation and molecule formation
... In our case, a negative detuning gives a positive scattering length and corresponds to the magnetic field region where the pair can bind into a molecule. Knowing B 0 , δB * and δµ, the energy of the molecular state relative to the atomic pair state (negative binding energy) can be calculated as [53,56] The differential magnetic moment of the molecules is related to the binding energy via the differential relation ...
We report on the preparation of a pure ultracold sample of bosonic DyK Feshbach molecules, which are composed of the fermionic isotopes 161Dy and 40K. Employing a magnetic sweep across a resonance located near 7.3 G, we produce up to 5000 molecules at a temperature of about 50 nK. For purification from the remaining atoms, we apply a Stern-Gerlach technique based on magnetic levitation of the molecules in a very weak optical dipole trap. With the trapped molecules we finally reach a high phase-space density of about 0.1. We measure the magnetic field dependence of the molecular binding energy and the magnetic moment, refining our knowledge of the resonance parameters. We also demonstrate a peculiar anisotropic expansion effect observed when the molecules are released from the trap and expand freely in the magnetic levitation field. Moreover, we identify an important lifetime limitation that is imposed by the 1064-nm infrared trap light itself and not by inelastic collisions. The light-induced decay rate is found to be proportional to the trap light intensity and the closed-channel fraction of the Feshbach molecule. These observations suggest a one-photon coupling to electronically excited states to limit the lifetime and point to the prospect of loss suppression by optimizing the wavelength of the trapping light. Our results represent important insights and experimental steps on the way to achieve quantum-degenerate samples of DyK molecules and novel superfluids based on mass-imbalanced fermion mixtures.
... Topological phases and topological protected excitations: Majorana zero modes with non-Abelian exchange statistics [47] in superfluid BFMs, have been less investigated. Apart from giving rise to the exhibition of fully phase-separated states [48], the interaction between bosons and fermions also causes robust self-induced density modulations, and incidental phase interfaces might host Majorana zero modes. Therefore, it is a natural step to bring these two exciting developments together and consider BFMs of ultracold atomic gases with SO coupling. ...
We investigate a fermionic superfluid with Raman-induced spin-orbit coupling immersed in a Bose-Einstein condensate. By minimizing the total free energy, we find that, with moderate repulsive interspecies interaction, a phase separation occurs where the otherwise nontopological uniform phase is divided into two parts: a purely fermionic one and a Bose-Fermi mix characterized by nontrivial topology with the winding number W=1. We verify that Majorana zero modes emerge at the phase interfaces by numerical simulations of the coupled Bogoliubov–de Gennes and Gross–Pitaevskii equations in real space. The tunability of the phase interfaces enables a direct manipulation of the predicted Majorana zero modes.
... Mixing fermionic and bosonic isotopes of the same or different atoms, experimentalists have created unimaginable mixtures, controlling the number of each kind of carrier, the interspecies and intraspecies interactions (Truscott et al., 2001;Schreck et al., 2001;Hadzibabic et al., 2002;Roati et al., 2002;Ott et al., 2004;Silber et al., 2005;Günter et al., 2006;Ospelkaus et al., 2006;Zaccanti et al., 2006;McNamara et al., 2006;Best et al., 2009;Fukuhara et al., 2009;Deh et al., 2010;Tey et al., 2010;Sugawa et al., 2011;Schuster et al., 2012;Tung et al., 2013;Ferrier-Barbut et al., 2014;Delehaye et al., 2015;Vaidya et al., 2015;Yao et al., 2016;Onofrio, 2016;Wu et al., 2017;Roy et al., 2017;Schäfer et al., 2018). As expected, new and exciting phenomena have emerged, such as a Bose-Fermi superfluid m ixture ( Trautmann e t a l., 2018), phase separation (Lous et al., 2018), and attractive interaction between bosons mediated by fermions (DeSalvo et al., 2019). ...
Estados aislantes de espín selectivo surgen en sistemas compuestos de fermiones con dos grados de libertad internos y otro tipo de portador, que puede ser fermiónioco o bosónico. Estos aislantes se caracterizan por un estado sin gap para un tipo de fermiones y un estado aislante para los otros, donde los últimos satsfacen una relación de commensurabilidad que involucra al otro tipo de portafor. Nosotros revismos los diferentes escenarios donde estos particulares aislantes surgen, enfocandonos en las mezclas Bose-Fermi, que son el más reciente y promisor escenaro para observar estos aislantes en los montajes de átomos fríos.
... Although a simple perturbative analysis of the thermodynamic stability of these systems at a weak coupling was carried out long ago by Saam [10], and in more recent times of realization of ultracold quantum gases in Refs. [11][12][13][14][15], the interest to the topic still does not go down [16][17][18][19][20][21][22] in the community. ...
We discuss an equilibrium mean-field properties of mixtures consisting of bosons and spin-polarized fermionic atoms with a point-like interaction in an arbitrary dimension . Particularly, we discuss except the standard weak-coupling limit of the system with slightly depleted Bose condensate and almost ideal Fermi gas, the (meta)stable phase with dimers composed exactly of one boson and one fermion. The peculiarities of the fermion-dimer and the boson-dimer three-body effective interactions and their impact on the thermodynamic stability of the dilute Bose-Fermi mixtures are elucidated.
... The study of ultracold atomic mixtures offers the possibility to explore a wide scope of quantum phenomena ranging from few-body to many-body physics [1,2]. Such mixtures provide the starting point for a variety of systems, from immersed impurities [3][4][5][6][7] to Efimov states [8][9][10], groundstate molecules [11][12][13][14], and degenerate Bose-Fermi mixtures [15][16][17][18]. A prominent example in the field of many-body physics is the observation of dual Bose-Fermi superfluidity, which was achieved for the first time using an ultracold mixture of lithium-6 ( 6 Li) and lithium-7 ( 7 Li) isotopes [19], unlocking a new area of ultracold physics. ...
We report on the simultaneous sub-Doppler laser cooling of Li6 and Li7 isotopes using gray molasses operating on their respective D1 atomic transitions. For Li7 we show that the sub-Doppler cooling can be achieved with two distinct Λ-type transitions, where the upper level can be either of the two 22P1/2 hyperfine states. We obtain temperatures of ∼85μK, with atom numbers of ∼108, and phase-space densities in the range of 10−6−10−5 for both isotopes. These conditions provide a good starting point for loading the mixture into an optical dipole trap and performing evaporative cooling to quantum degeneracy. Our work provides a valuable simplification for the preparation of ultracold Li6−Li7 mixtures, which were proven to be a successful system for the study of impurity physics and Bose-Fermi superfluids.
... Second, the bosonic component is highly compressible, so that the density distributions can vary rapidly before and after the "injection". Indeed, for repulsive Bose-Fermi interactions, the mixture is highly unstable towards phase-separation [117,122,123]. On the other hand, the absence of Pauli blocking in the minority component means that it is possible to create mixtures featuring large local concentrations of impurities. ...
Polaron quasiparticles are formed when a mobile impurity is coupled to the elementary excitations of a many-particle background. In the field of ultracold atoms, the study of the associated impurity problem has attracted a growing interest over the last fifteen years. Polaron quasiparticle properties are essential to our understanding of a variety of paradigmatic quantum many-body systems realized in ultracold atomic gases and in the solid state, from imbalanced Bose–Fermi and Fermi–Fermi mixtures to fermionic Hubbard models. In this topical review, we focus on the so-called repulsive polaron branch, which emerges as an excited many-body state in systems with underlying attractive interactions such as ultracold atomic mixtures, and is characterized by an effective repulsion between the impurity and the surrounding medium. We give a brief account of the current theoretical and experimental understanding of repulsive polaron properties, for impurities embedded in both fermionic and bosonic media, and we highlight open issues deserving future investigations.
... On the theoretical side, our work motivates the exploration of DQPTs from different phases, e.g. superconducting or BOW states, and in richer models such as Bose-Fermi mixtures, which are experimentally available [123][124][125] and efficiently simulable [126,127]. Resonant driving could be also exploited, since its effective Hamiltonian, being quite different to the original [128], seems appealing to induce alternative Floquet DQPTs. ...
We study the emergence of dynamical quantum phase transitions (DQPTs) in a half-filled one-dimensional lattice described by the extended Fermi–Hubbard model, based on tensor network simulations. Considering different initial states, namely noninteracting, metallic, insulating spin and charge density waves, we identify several types of sudden interaction quenches which lead to DQPTs. Furthermore, clear connections to particular properties of observables, specifically the mean double occupation or charge imbalance, are established in two main regimes, and scenarios in which such correspondence is degraded and lost are discussed. Dynamical transitions resulting solely from high-frequency time-periodic modulation are also found, which are well described by a Floquet effective Hamiltonian. State-of-the-art cold-atom quantum simulators constitute ideal platforms to implement several reported DQPTs experimentally.
... Second, the bosonic component is highly compressible, so that the density distributions can vary rapidly before and after the "injection". Indeed, for repulsive Bose-Fermi interactions, the mixture is highly unstable towards phase-separation [114,119,120]. On the other hand, the absence of Pauli blocking in the minority component means that it is possible to create mixtures featuring large local concentrations of impurities. ...
Polaron quasiparticles are formed when a mobile impurity is coupled to the elementary excitations of a many-particle background. In the field of ultracold atoms, the study of the associated impurity problem has attracted a growing interest over the last fifteen years. Polaron quasiparticle properties are essential to our understanding of a variety of paradigmatic quantum many-body systems realized in ultracold atomic gases and in the solid state, from imbalanced Bose-Fermi and Fermi-Fermi mixtures to fermionic Hubbard models. In this topical review, we focus on the so-called repulsive polaron branch, which emerges as an excited many-body state in systems with underlying attractive interactions such as ultracold atomic mixtures, and is characterized by an effective repulsion between the impurity and the surrounding medium. We give a brief account of the current theoretical and experimental understanding of repulsive polaron properties, for impurities embedded in both fermionic and bosonic media, and we highlight open issues deserving future investigations.
... Ultracold mixtures of bosonic and fermionic atoms provide a powerful platform to explore the physics of Bose-Fermi mixtures. Degenerate mixtures have been produced to investigate phase separation [1], superfluidity [2], polarons [3][4][5], and fermion-mediated interactions [6,7]. Although various phases have been predicted for strongly interacting mixtures, ranging from supersolid charge density wave states [8,9] to boson-mediated s=pwave fermion pairing [10][11][12], experimental investigation is hindered by the strong three-body recombination loss between the atoms [13][14][15][16]. ...
We study three-body loss in an ultracold mixture of a thermal Bose gas and a degenerate Fermi gas. We find that at unitarity, where the interspecies scattering length diverges, the usual inverse-square temperature scaling of the three-body loss found in nondegenerate systems is strongly modified and reduced with the increasing degeneracy of the Fermi gas. While the reduction of loss is qualitatively explained within the few-body scattering framework, a remaining suppression provides evidence for the long-range Ruderman-Kittel-Kasuya-Yosida (RKKY) interactions mediated by fermions between bosons. Our model based on RKKY interactions quantitatively reproduces the data without free parameters, and predicts one order of magnitude reduction of the three-body loss coefficient in the deeply Fermi-degenerate regime.
Atom-ion hybrid systems are promising platforms for the quantum simulation of polaron physics in certain quantum materials. Here, we investigate the ionic Fermi polaron, a charged impurity in a polarized Fermi bath, at zero temperature using quantum Monte Carlo techniques. We compute the energy spectrum, residue, effective mass, and structural properties. Significant deviations from field-theory prediction occur in the strong coupling regime due to large density inhomogeneities around the ion. We observe a smooth polaron-molecule transition in contrast with the neutral case. This study provides insights into solid-state systems like Fermi exciton polarons in thin semiconductors and quantum technologies based on atom-ion platforms.
We present a theoretical analysis of phase separations between two repulsively interacting components in an ultracold fermionic gas, occurring at the dimensional crossover in a harmonic trap with varying aspect ratios. A tailored kinetic energy functional is derived and combined with a density-potential functional approach to develop a framework that is benchmarked with the orbital-based method. We investigate the changes in the density profile of the phase-separated gas under different interaction strengths and geometries. The analysis reveals the existence of small, partially polarized domains in certain parameter regimes, which is similar to the purely two-dimensional limit. However, the density profile is further enriched by a shell structure found in anisotropic traps. We also track the transitions that can be driven by a change in either interaction strength or trap geometry. The developed framework is noted to have applications for other systems with repulsive interactions that combine continuous and discrete degrees of freedom.
We theoretically investigate the tunneling transport in a repulsively interacting ultracold Bose-Fermi mixture. A two-terminal model is applied to such a mixture, and the supersymmetry-like tunneling current through the junction can be induced by the bias of the fermion chemical potential between two reservoirs. The goldstino, which is the Nambu-Goldstone fermionic mode associated with the spontaneous sypersymmetry breaking and appears as a gapped mode in the presence of the explicit supersymmetry breaking in existing Bose-Fermi mixtures, is found to contribute to the tunneling transport as a supercharge exchanging process. Our study provides a potential way to detect the goldstino transport in cold atom experiments.
In this study, we conducted a detailed investigation into the time evolution of the probability density within a 1D double-well potential hosting a Bose-Fermi mixture. This system comprised spinless bosons and spin one-half fermions with weak repulsive contact interactions. Notably, even at very low effective coupling constants, periodic probabilities were observed, indicating correlated tunneling of both bosons and fermions, leading to complete miscibility, which disappears when an external electric field is turned on. The electric field accentuated fermion-fermion interactions due to the Pauli exclusion principle, altering both boson density and interactions and leading to spatial redistribution of particles. These findings underscore the complex interplay between interactions, external fields, and spatial distributions within confined quantum systems. Our exploration of higher interaction strengths revealed conditions under which probability density functions are decoupled. Furthermore, we observed that increased fermion interaction, driven by the electric field, led to higher tunneling frequencies for both species because of the repulsive nature of the boson-fermion interaction. Conversely, increased boson-boson interaction resulted in complete tunneling of both species, especially when boson density was high, leading to effective fermion repulsion. Expanding our analysis to scenarios involving four bosons demonstrated that higher interaction values corresponded to increased oscillation frequencies in tunneling probabilities. Finally, by manipulating interaction parameters and activating the electric field, we achieved complete tunneling of both species, further increasing oscillation frequencies and resulting in intervals characterized by overlapping probability functions.
We derive analytically the leading beyond-mean-field contributions to the zero-temperature equation of state and to the fermionic quasiparticle residue and effective mass of a dilute Bose-Fermi mixture in two dimensions. In the repulsive case, we perform quantum Monte Carlo simulations for two representative bosonic concentrations and equal masses, extending a method for correcting finite-size effects in fermionic gases to Bose-Fermi mixtures. We find good agreement between analytic expressions and numerical results for weak interactions, while significant discrepancies appear in the regime close to mechanical instability, above which we provide evidence of phase separation of the bosonic component.
Motivated by recent surprising experimental findings, we develop a strong-coupling theory for Bose-Fermi mixtures capable of treating resonant interspecies interactions while satisfying the compressibility sum rule. We show that the mixture can be stable at large interaction strengths close to resonance, in agreement with the experiment, but at odds with the widely used perturbation theory. We also calculate the sound velocity of the Bose gas in the Cs133−Li6 mixture, again finding good agreement with the experimental observations both at weak and strong interactions. A central ingredient of our theory is the generalization of a fermion mediated interaction to strong Bose-Fermi scatterings and to finite frequencies. This further leads to a predicted hybridization of the sound modes of the Bose and Fermi gases, which can be directly observed using Bragg spectroscopy.
In a trapped spin-1/2 Bose-Einstein condensate with miscible interactions, a two-dimensional spin-orbit coupling can introduce an unconventional spatial separation between the two components. We reveal the physical mechanism of such a spin-orbit-coupling-induced phase separation. Detailed features of the phase separation are identified in a trapped Bose-Einstein condensate. We further analyze differences of phase separation in Rashba and anisotropic spin-orbit-coupled Bose gases. An adiabatic splitting dynamics is proposed as an application of the phase separation.
Particlelike excitations, or quasiparticles, emerging from interacting fermionic and bosonic quantum fields underlie many intriguing quantum phenomena in high energy and condensed matter systems. Computation of the properties of these excitations is frequently intractable in the strong interaction regime. Quantum degenerate Bose-Fermi mixtures offer promising prospects to elucidate the physics of such quasiparticles. In this work, we investigate phonon propagation in an atomic Bose-Einstein condensate immersed in a degenerate Fermi gas with interspecies scattering length aBF tuned by a Feshbach resonance. We observe sound mode softening with moderate attractive interactions. For even greater attraction, surprisingly, stable sound propagation reemerges and persists across the resonance. The stability of phonons with resonant interactions opens up opportunities to investigate novel Bose-Fermi liquids and fermionic pairing in the strong interaction regime.
Atomic gases confined in curved geometries display distinctive features that are absent in their flat counterparts, such as periodic boundaries, local curvature, and nontrivial topologies. The recent experiments with shell-shaped quantum gases and the study of one dimensional rings point out that the manifold of a quantum gas could soon become a controllable feature, thus allowing to address the fundamental study of curved many-body quantum systems. Here, we review the main geometries realized in the experiments, analyzing the theoretical and experimental status on their phase transitions and on the superfluid dynamics. In perspective, we delineate the study of vortices, the few-body physics, and the search for analog models in various curved geometries as the most promising research areas.
We investigate one-dimensional three-body systems composed of two identical bosons and one mass-imbalanced atom (impurity) with attractive two-body and three-body zero-range interactions. In the absence of three-body interaction, we give a complete phase diagram of the number of three-body bound states in the whole region of mass ratio and the ratio of intra- and intercomponent interaction strength via direct calculation of Skornyakov-Ter-Martirosyan equations. We demonstrate that other low-lying three-body bound states emerge when the mass of the impurity particle is different from other two identical particles. We obtain the binding energies together with the corresponding wave functions. When the mass of impurity atom is very large, there are at most three three-body bound states. In the presence of three-body zero-range interaction, we reveal that weak three-body interaction will not always induce one more three-body bound state. At some special parameter points, arbitrary small three-body interaction can generate one more three-body bound state. This corresponds to the transition of the number of three-body bound states induced only by two-body attractive interaction.
Dynamical properties of two-component mass-imbalanced few-fermion systems confined in a one-dimensional harmonic trap following a sudden quench of interactions are studied. It is assumed that initially the system is prepared in the non-interacting ground state and then, after a sudden quench of interactions, the unitary evolution is governed by interacting many-body Hamiltonian. By careful analysis of the evolution of the Loschmidt echo, density distributions of the components, and entanglement entropy between them, the role of mass imbalance and particle number imbalance on the system’s evolution stability are investigated. All the quantities studied manifest a dramatic dependence on the number of heavy and lighter fermions in each component at a given quench strength. The results may have implications for upcoming experiments on fermionic mixtures with a well-defined and small number of particles.
We report on the observation of Feshbach resonances at low magnetic-field strength (below 10 G) in the Fermi-Fermi mixture of Dy161 and K40. We characterize five resonances by measurements of interspecies thermalization rates and molecular binding energies. As a case of particular interest for future experiments, we consider a resonance at 7.29 G, which combines accurate magnetic tunability and access to the universal regime of interactions with experimental simplicity. We show that lifetimes of a few hundred milliseconds can be achieved for the optically trapped, resonantly interacting mixture. We also demonstrate the hydrodynamic expansion of the mixture in the strongly interacting regime and the formation of DyK Feshbach molecules. Our work opens up experimental possibilities in view of mass-imbalanced superfluids and related phenomena.
Monolayer transition metal dichalcogenides (TMDs) host deeply bound excitons interacting with itinerant electrons, and as such they represent an exciting new quantum many-body Bose-Fermi mixture. Here, we demonstrate that electrons interacting with a Bose-Einstein condensate (BEC) of exciton-polaritons can realize a two-dimensional topological px+ipy superconductor. Using strong coupling Eliashberg theory, we show that this is caused by an attractive interaction mediated by the BEC, which overcompensates the repulsive Coulomb interaction between the electrons. The hybrid light-matter nature of the BEC is crucial for achieving this, since it can be used to reduce retardation effects and increase the mediated interaction in regimes important for pairing. We finally show how the great flexibility of TMDs allows one to tune the critical temperature of the topological superconducting phase to be within experimental reach.
Within Gross-Pitaevskii (GP) theory we derive the interface potential V(ℓ) which describes the interaction between the interface separating two demixed Bose-condensed gases and an optical hard wall at a distance ℓ. Previous work revealed that this interaction gives rise to extraordinary wetting and prewetting phenomena. Calculations that explore nonequilibrium properties by using ℓ as a constraint provide a thorough explanation for this behavior. We find that at bulk two-phase coexistence, V(ℓ) for both complete wetting and partial wetting is monotonic with exponential decay. Remarkably, at the first-order wetting phase transition, V(ℓ) is independent of ℓ. This anomaly explains the infinite continuous degeneracy of the grand potential reported earlier. As a physical application, using V(ℓ) we study the three-phase contact line where the interface meets the wall under a contact angle θ. Employing an interface displacement model we calculate the structure of this inhomogeneity and its line tension τ. Contrary to what happens at a usual first-order wetting transition in systems with short-range forces, τ does not approach a nonzero positive constant for θ→0, but instead approaches zero (from below) in the manner τ∝−θ as would be expected for a critical wetting transition. This hybrid character of τ is a consequence of the absence of a barrier in V(ℓ) at wetting. For a typical V(ℓ)=Sexp(−ℓ/ξ), with S the spreading coefficient and ξ a decay length, we conjecture that τ=−2(1−ln2)γξsinθ is exact within GP theory, with γ the interfacial tension and 0≤θ≤π.
Experiments with ultracold atoms involve interatomic interactions, which are essential for cooling the atoms. The s-wave interaction between atoms can be tuned via the Feshbach resonance, potentially enabling the creation of a noninteracting system when the interaction reaches its vanishing limit. Although feasible at zero temperature, eliminating the interaction at a finite temperature in an isolated system prevents the system from reaching equilibrium. In this study, we used a Bose-Fermi mixture to create equilibrated noninteracting Bose gas at a finite temperature. First, we used the Bose-Fermi superfluid mixture of a dilute lithium gas in an optical dipole trap to determine the zero crossing of the boson-boson interaction at near-zero temperature. Thereafter, we showed that the noninteracting Bose gas created at a finite temperature represents an ideal Bose gas under the canonical description. The results of this study provides an avenue for experimental investigations of the fundamental properties of an ideal Bose gas in a harmonic trap.
This review elaborates pedagogically on the fundamental concept, basic theory, expected properties, and materials realizations of topological superconductors. The relation between topological superconductivity and Majorana fermions are explained, and the difference between dispersive Majorana fermions and a localized Majorana zero mode is emphasized. A variety of routes to topological superconductivity are explained with an emphasis on the roles of spin-orbit coupling. Present experimental situations and possible signatures of topological superconductivity are summarized with an emphasis on intrinsic topological superconductors.
Ultracold two-component Fermi gases with a tunable population imbalance have provided an excellent opportunity for studying the exotic Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) states, which have been of great interest in condensed matter physics. However, the FFLO states have not been observed experimentally in Fermi gases in three dimensions (3D), possibly due to their small phase space volume and extremely low temperature required for an equal-mass Fermi gas. Here we explore possible effects of mass imbalance, mainly in a ⁶Li–⁴⁰K mixture, on the one-plane-wave FFLO phases for a 3D homogeneous case at the mean-field level. We present various phase diagrams related to the FFLO states at both zero and finite temperatures, throughout the BCS-BEC crossover, and show that a large mass ratio may enhance substantially FFLO type of pairing.
The miscibility of two interacting quantum systems is an important testing ground for the understanding of complex quantum systems. Two-component Bose-Einstein condensates enable the investigation of this scenario in a particularly well controlled setting. In a homogeneous system, the transition between mixed and separated phases is fully characterised by a `miscibility parameter', based on the ratio of intra- to inter-species interaction strengths. Here we show, however, that this parameter is no longer the optimal one for trapped gases, for which the location of the phase boundary depends critically on atom numbers. We demonstrate how monitoring of damping rates and frequencies of dipole oscillations enables the experimental mapping of the phase diagram by numerical implementation of a fully self-consistent finite-temperature kinetic theory for binary condensates. The change in damping rate is explained in terms of surface oscillation in the immiscible regime, and counterflow instability in the miscible regime, with collisions becoming only important in the long time evolution.
We study the sensitivity of coupled condensate formation dynamics on the history of initial stochastic domain formation in the context of instantaneously quenched elongated harmonically trapped immiscible two-component atomic Bose gases. The spontaneous generation of defects in the fastest condensing component, and subsequent coarse-graining dynamics, can lead to a deep oscillating microtrap into which the other component condenses, thereby establishing a long-lived composite defect in the form of a dark-bright solitary wave. We numerically map out diverse key aspects of these competing growth dynamics, focusing on the role of shot-to-shot fluctuations and global parameter changes (initial state choices, quench parameters, and condensate growth rates), with our findings also qualitatively confirmed by realistic finite-duration quenches. We conclude that phase-separated structures observable on experimental time scales are likely to be metastable states whose form is influenced by the stability and dynamics of the spontaneously emerging dark-bright solitary wave.
We have realized a dual-species Bose-Einstein condensate (BEC) of Na
and Rb atoms and observed their immiscibility. Because of the favorable
background intra- and inter-species scattering lengths, stable condensates can
be obtained via efficient evaporative cooling and sympathetic cooling without
the need for fine tuning of the interactions. Our system thus provides a clean
platform for studying inter-species interactions driven effects in superfluid
mixtures. With a Feshbach resonance, we have successfully created double BECs
with largely tunable inter-species interactions and studied the
miscible-immiscible phase transition.
We investigate separations of trapped balanced two-component atomic Fermi
gases with repulsive contact interaction. Candidates for ground-state densities
are obtained from the imaginary-time evolution of a nonlinear
pseudo-Schr\"odinger equation in three dimensions, rather than from the
cumbersome variational equations. With the underlying hydrodynamical approach,
gradient corrections to the Thomas-Fermi approximation are conveniently
included and are shown to be vital for reliable density profiles. We provide
critical repulsion strengths that mark the onset of phase transitions in a
harmonic trap. We present transitions from identical density profiles of the
two fermion species towards isotropic and anisotropic separations for various
confinements, including harmonic and double-well-type traps. Our proposed
method is suited for arbitrary trap geometries and can be straightforwardly
extended to study dynamics in the light of ongoing experiments on degenerate
Fermi gases.
We analyse a Bose-Einstein condensate (BEC) mixed with a superfluid
two-component Fermi gas in the whole BCS-BEC cross-over. Using a quasiparticle
random phase approximation combined with Beliaev theory to describe the Fermi
superfluid and the BEC respectively, we show that the single particle and
collective excitations of the Fermi gas give rise to an induced interaction
between the bosons, which varies strongly with momentum and frequency. The
induced interaction diverges at the sound mode of the Fermi superfluid,
resulting in a discontinuous jump in the excitation spectrum of the BEC. In
addition, the excitation of quasiparticles in the Fermi superfluid leads to
damping of the excitations in the BEC. Besides studying induced interactions
themselves, these prominent effects can be used to systematically probe the
strongly interacting Fermi gas.
We use a gray molasses operating on the D atomic transition to produce
degenerate quantum gases of Li with a large number of atoms. This
sub-Doppler cooling phase allows us to lower the initial temperature of 10
atoms from 500 to 40 K in 2 ms. We observe that D cooling remains
effective into a high-intensity infrared dipole trap where two-state mixtures
are evaporated to reach the degenerate regime. We produce molecular
Bose-Einstein condensates of up to 510 molecules and
weakly-interacting degenerate Fermi gases of 10 atoms at
with a typical experimental duty cycle of 11 seconds.
The investigation of nonequilibrium dynamics in interacting quantum many-body
systems has emerged as a key approach to characterize the nature of quantum
states, to study excitation spectra, and to shed light on thermalization
processes. So far, research on nonequilibrium dynamics has focused on many-body
quantum states of bosonic particles, leading to the observation of coherent
quench dynamics and the exploration of relaxation and thermalization in
isolated quantum systems. Here we report on the observation of coherent quench
dynamics in a many-body quantum state of fermionic particles. In the
experiment, we prepare a metallic state of ultracold spin-polarized fermionic
atoms in a shallow three-dimensional (3D) optical lattice. The delocalized
fermions are in contact with a Bose-Einstein condensate (BEC) that is
simultaneously loaded into the lattice. With a rapid increase of lattice depth,
we take the system out of equilibrium and induce quench dynamics that is driven
by the interactions between fermions and bosons. We observe the time evolution
of the fermionic momentum distribution, which shows long-lived coherent
oscillations for up to ten periods, both for attractive and repulsive
Fermi-Bose interactions. A theoretical model reveals that the dynamics arises
as a consequence of the delocalized nature of the initial fermionic state and
the on-site number fluctuations of the BEC. Our work demonstrates that coherent
quench dynamics constitutes a powerful technique to gain insight into the
nature of fermionic quantum many-body states and to accurately determine
Hamiltonian parameters used in their microscopic description.
We investigate a mixture of ultracold fermionic K40 atoms and weakly bound Li6K40 dimers on the repulsive side of a heteronuclear atomic Feshbach resonance. By radio-frequency spectroscopy we demonstrate that the normally repulsive atom-dimer interaction is turned into a strong attraction. The phenomenon can be understood as a three-body effect in which two heavy K40 fermions exchange the light Li6 atom, leading to attraction in odd partial-wave channels (mainly p wave). Our observations show that mass imbalance in a fermionic system can profoundly change the character of interactions as compared to the well-established mass-balanced case.
We study the breathing oscillations in Bose–Fermi mixtures of Yb isotopes in the largely prolate deformed trap, which are realized by the Kyoto group. We take three combinations of the Yb isotopes, 170Yb–171Yb , 170Yb–173Yb and 174Yb–173Yb , whose boson–fermion interactions are weakly repulsive, strongly attractive and strongly repulsive. The collective oscillations in the deformed trap are calculated in the dynamical time-development approach, which is formulated with the time-dependent Gross–Pitaevskii and Vlasov equations. We analyse the results with the intrinsic oscillation modes of the deformed system, obtained in the scaling method, and show that the damping and forced-oscillation effects of the intrinsic modes explain time-variation behaviour of oscillations, especially, in the fermion transverse mode.
We report the formation of a dual-species Bose-Einstein condensate of 87Rb and 133Cs in the same trapping potential. Our method exploits the efficient sympathetic cooling of 133Cs via elastic collisions with 87Rb, initially in a magnetic quadrupole trap and subsequently in a levitated optical trap. The two condensates each contain up to 2×104 atoms and exhibit a striking phase separation, revealing the mixture to be immiscible due to strong repulsive interspecies interactions. Sacrificing all the 87Rb during the cooling, we create single-species 133Cs condensates of up to 6×104 atoms.
The formation of bound states at surfaces of materials with an energy gap in the bulk electron spectrum is a well known physical phenomenon. At superconductor surfaces, quasiparticles with energies inside the superconducting gap Delta may be trapped in bound states in quantum wells, formed by total reflection against the vacuum and total Andreev reflection against the superconductor. Since an electron reflects as a hole and sends a Cooper pair into the superconductor, the surface states give rise to resonant transport of quasiparticle and Cooper pair currents, and may be observed in tunnelling spectra. In superconducting junctions these surface states may hybridize and form bound Andreev states, trapped between the superconducting electrodes. In d-wave superconductors, the order parameter changes sign under 90° rotation and, as a consequence, Andreev reflection may lead to the formation of zero energy quasiparticle bound states, midgap states (MGS). The formation of MGS is a robust feature of d-wave superconductivity and provides a unified framework for many important effects which will be reviewed: large Josephson current, low-temperature anomaly of the critical Josephson current, pi-junction behaviour, 0-->pi junction crossover with temperature, zero-bias conductance peaks, paramagnetic currents, time reversal symmetry breaking, spontaneous interface currents, and resonance features in subgap currents. Taken together these effects, when observed in experiments, provide proof for d-wave superconductivity in the cuprates.
We have used three-body recombination rates as a sensitive probe of the statistical correlations between atoms in Bose-Einstein condensates (BEC) and in ultracold noncondensed dilute atomic gases. We infer that density fluctuations are suppressed in the BEC samples. We measured the three-body recombination rate constants for condensates and cold noncondensates from number loss in the F = 1,mf = -1 hyperfine state of 87Rb. The ratio of these is 7.42.6 which agrees with the theoretical factor of 3! and demonstrates that condensate atoms are less bunched than noncondensate atoms.
.
We present a detailed theoretical and experimental study of Feshbach resonances in the 6Li-40K mixture.
Particular attention is given to the inelastic scattering properties, which have not been considered before. As an important
example, we thoroughly investigate both elastic and inelastic scattering properties of a resonance that occurs near 155 G.
Our theoretical predictions based on a coupled channels calculation are found in excellent agreement with the experimental
results.
We also present theoretical results on the molecular state that underlies the 155 G resonance, in particular concerning its
lifetime against spontaneous dissociation. We then present a survey of resonances in the system, fully characterizing the
corresponding elastic and inelastic scattering properties. This provides the essential information to identify optimum resonances
for applications relying on interaction control in this Fermi-Fermi mixture.
High-resolution Fourier transform spectroscopy was used to record fluorescence progressions of KLi formed in a heat pipe. Lithium isotope effects were used to derive the adiabatic correction to the Born-Oppenheimer potential for the electronic ground state over a wide range of internuclear separations. With a short extrapolation from the experimentally determined potential functions of the coupled states X 1Σ+ and a 3Σ+ toward their common atomic asymptote, we have improved the modeling of recently observed Feshbach resonances for the fermionic atom pair 6Li and 40K. Predictions for cold collisions between different isotopologues are presented using mass scaling with or without Born-Oppenheimer corrections. Predictions for Feshbach resonance positions differ by up to 0.5 G within reach of current experimental verification.
We consider a system of repulsively interacting Bose-Fermi mixtures of spin-polarized uniform atomic gases at zero temperature. We examine possible realization of p -wave superfluidity of fermions due to an effective attractive interaction via density fluctuations of Bose-Einstein condensate within mean-field approximation. We find the ground state of the system by direct energy comparison of the p -wave superfluid state in a single uniform mixed phase and normal Fermi gas state in a phase-separated phase, and suggest an occurrence of the p -wave superfluidity for a strong boson-fermion interaction regime. We study some signatures of the p -wave superfluid, such as anisotropic energy gap and quasiparticle energy in the axial state, that have not been observed in spin-unpolarized superfluid of atomic fermions. We also show that a Cooper pair is a tightly bound state, such as a diatomic molecule in the strong boson-fermion coupling regime, and suggest an observable indication of the p -wave superfluid in the real experiment.
We perform radio-frequency dissociation spectroscopy of weakly bound ^{6}Li_{2} Feshbach molecules using low-density samples of about 30 molecules in an optical dipole trap. Combined with a high magnetic field stability, this allows us to resolve the discrete trap levels in the radio-frequency dissociation spectra. This novel technique allows the binding energy of Feshbach molecules to be determined with unprecedented precision. We use these measurements as an input for a fit to the ^{6}Li scattering potential using coupled-channel calculations. From this new potential, we determine the pole positions of the broad ^{6}Li Feshbach resonances with an accuracy better than 7×10^{-4} of the resonance widths. This eliminates the dominant uncertainty for current precision measurements of the equation of state of strongly interacting Fermi gases. As an important consequence, our results imply a corrected value for the Bertsch parameter ξ measured by Ku et al. [Science 335, 563 (2012)], which is ξ=0.370(5)(8).
We study a resonant Bose-Fermi mixture at zero temperature using the
fixed-node Diffusion Monte Carlo method. We explore the system from weak to
strong boson-fermion interaction, for different concentrations of the bosons
relative to the fermion component. We focus on the case where the boson density
is smaller than the fermion density , for which a first-order
quantum phase transition is found from a state with condensed bosons immersed
in a Fermi sea, to a Fermi-Fermi mixture of composite fermions and unpaired
fermions. We obtain the equation of state and the phase diagram and we find
that the region of phase separation shrinks to zero for vanishing .
We present the essential experimental steps of our all-optical approach to prepare a double-degenerate Fermi-Fermi mixture of Li-6 and K-40 atoms, which then serves as a starting point for molecule formation. We first describe the optimized trap loading procedures, the internal-state preparation of the sample, and the combined evaporative and sympathetic cooling process. We then discuss the preparation of the sample near an interspecies Feshbach resonance, and we demonstrate the formation of heteronuclear molecules by a magnetic field ramp across the resonance.
Feshbach resonances are the essential tool to control the interaction between atoms in ultracold quantum gases. They have found numerous experimental applications, opening up the way to important breakthroughs. This review broadly covers the phenomenon of Feshbach resonances in ultracold gases and their main applications. This includes the theoretical background and models for the description of Feshbach resonances, the experimental methods to find and characterize the resonances, a discussion of the main properties of resonances in various atomic species and mixed atomic species systems, and an overview of key experiments with atomic Bose-Einstein condensates, degenerate Fermi gases, and ultracold molecules.
We present the first simultaneous trapping of two different ultracold atomic species in a conservative trap. Lithium and cesium
atoms are stored in an optical dipole trap formed by the focus of a CO2 laser. Techniques for loading both species of atoms are discussed and observations of elastic and inelastic collisions between
the two species are presented. A model for sympathetic cooling of two species with strongly different mass in the presence
of slow evaporation is developed. From the observed Cs-induced evaporation of Li atoms we estimate a cross-section for cold
elastic Li-Cs collisions.
We have measured the three-body decay of a Bose–Einstein condensate of rubidium (87Rb) atoms prepared in the doubly polarized ground state F=m
F
=2. Our data are taken for a peak atomic density in the condensate varying between 2×1014cm-3 at initial time and 7×1013cm-3, 16s later. Taking into account the influence of the uncondensed atoms on the decay of the condensate, we deduce a rate
constant for condensed atoms L=1.8 (±0.5) ×10-29cm6 s-1. For these densities we did not find a significant contribution of two-body processes such as spin dipole relaxation.
Ultracold Fermi gases with tunable interactions provide a test bed for exploring the many-body physics of strongly interacting quantum systems. Over the past decade, experiments have investigated many intriguing phenomena, and precise measurements of ground-state properties have provided benchmarks for the development of theoretical descriptions. Metastable states in Fermi gases with strong repulsive interactions represent an exciting area of development. The realization of such systems is challenging, because a strong repulsive interaction in an atomic quantum gas implies the existence of a weakly bound molecular state, which makes the system intrinsically unstable against decay. Here we use radio-frequency spectroscopy to measure the complete excitation spectrum of fermionic (40)K impurities resonantly interacting with a Fermi sea of (6)Li atoms. In particular, we show that a well-defined quasiparticle exists for strongly repulsive interactions. We measure the energy and the lifetime of this 'repulsive polaron', and probe its coherence properties by measuring the quasiparticle residue. The results are well described by a theoretical approach that takes into account the finite effective range of the interaction in our system. We find that when the effective range is of the order of the interparticle spacing, there is a substantial increase in the lifetime of the quasiparticles. The existence of such a long-lived, metastable many-body state offers intriguing prospects for the creation of exotic quantum phases in ultracold, repulsively interacting Fermi gases.
We investigate local three-body correlations for bosonic particles in three and one dimensions as a function of the interaction strength. The three-body correlation function g(3) is determined by measuring the three-body recombination rate in an ultracold gas of Cs atoms. In three dimensions, we measure the dependence of g(3) on the gas parameter in a BEC, finding good agreement with the theoretical prediction accounting for beyond-mean-field effects. In one dimension, we observe a reduction of g(3) by several orders of magnitude upon increasing interactions from the weakly interacting BEC to the strongly interacting Tonks-Girardeau regime, in good agreement with predictions from the Lieb-Liniger model for all strengths of interaction.
We study a quantum Bose-Fermi mixture near a broad Feshbach resonance at zero
temperature. Within a quantum field theoretical model a two-step Gaussian
approximation allows to capture the main features of the quantum phase diagram.
We show that a repulsive boson-boson interaction is necessary for thermodynamic
stability. The quantum phase diagram is mapped in chemical potential and
density space, and both first and second order quantum phase transitions are
found. We discuss typical characteristics of the first order transition, such
as hysteresis or a droplet formation of the condensate which may be searched
for experimentally.
We report on the expansion of a Fermi-Fermi mixture of Li-6 and K-40 atoms
under conditions of strong interactions realized near the center of an
interspecies Feshbach resonance. We observe two different phenomena of
hydrodynamic behavior. The first one is the well-known inversion of the aspect
ratio. The second one is a collective expansion, where both species stick
together and despite of their different masses expand jointly. Our work
constitutes a first step to explore the intriguing many-body physics of this
novel system.
We have created a triply quantum degenerate mixture of bosonic K and
two fermionic species K and Li. The boson is shown to be an
efficient coolant for the two fermions, spurring hopes for the observation of
fermionic superfluids with imbalanced masses. We observe multiple heteronuclear
Feshbach resonances, in particular a wide s-wave resonance for the combination
K-K, opening up studies of strongly interacting {\it isotopic}
Bose-Fermi mixtures. For large imbalance, we enter the polaronic regime of
dressed impurities immersed in a bosonic or fermionic bath.
Ferromagnetism is a manifestation of strong repulsive interactions between itinerant fermions in condensed matter. Whether short-ranged repulsion alone is sufficient to stabilize ferromagnetic correlations in the absence of other effects, such as peculiar band dispersions or orbital couplings, is, however, unclear. Here, we investigate ferromagnetism in the minimal framework of an ultracold Fermi gas with short-range repulsive interactions tuned via a Feshbach resonance. Whereas fermion pairing characterizes the ground state, our experiments provide signatures suggestive of a metastable Stoner-like ferromagnetic phase supported by strong repulsion in excited scattering states. We probe the collective spin response of a two-spin mixture engineered in a magnetic domain-wall-like configuration, and reveal a substantial increase of spin susceptibility while approaching a critical repulsion strength. Beyond this value, we observe the emergence of a time window of domain immiscibility, indicating the metastability of the initial ferromagnetic state. Our findings establish an important connection between dynamical and equilibrium properties of strongly correlated Fermi gases, pointing to the existence of a ferromagnetic instability.
We measure the temperature of a deeply degenerate Fermi gas, by using a weakly interacting sample of heavier bosonic atoms as a probe. This thermometry method relies on the thermalization between the two species and on the determination of the condensate fraction of the bosons. In our experimental implementation, a small sample of 41K atoms serves as the thermometer for a 6Li Fermi sea. We investigate the evaporative cooling of a 6Li spin mixture in a single-beam optical dipole trap and observe how the condensate fraction of the thermometry atoms depends on the final trap depth. From the condensate fraction, the temperature can be readily extracted. We show that the lowest temperature of 6.3(5)% of the Fermi temperature is obtained, when the decreasing trap depth closely approaches the Fermi energy. To understand the systematic effects that may in uence the results, we carefully investigate the role of the number of bosons and the thermalization dynamics between the two species. Our thermometry approach provides a conceptually simple, accurate, and general way to measure the temperature of deeply degenerate Fermi gases. Since the method is independent of the specific interaction conditions within the Fermi gas, it applies to both weakly and strongly interacting Fermi gases.
Efimov physics is a universal phenomenon arising in quantum three-body systems. For systems with resonant two-body interactions, Efimov predicted an infinite series of three-body bound states with geometric scaling symmetry. These Efimov states were first observed in cold Cs atoms and have since been reported in a variety of atomic systems. While theories predict non-universal behavior for narrow Feshbach resonances, experiments on Efimov resonances are so far consistent with predictions based on universal theories. Here we directly compare the Efimov spectra in a Li-Cs mixture near two Feshbach resonances which are very different in their resonance strengths but otherwise almost identical. Our result shows a clear dependence of the Efimov resonance positions on Feshbach resonance strength and a clear departure from the universal prediction for the narrow Feshbach resonance.
We present a joint experimental and theoretical investigation of the lifetime of weakly bound dimers formed near narrow interspecies Feshbach resonances in mass-imbalanced Fermi-Fermi systems, considering the specific example of a mixture of Li and K atoms. Our work addresses the central question of the increase in the stability of the dimers resulting from Pauli suppression of collisional losses, which is a well-known effect in mass-balanced fermionic systems near broad resonances. We present measurements of the spontaneous dissociation of dimers in dilute samples, and of the collisional losses in dense samples arising from both dimer-dimer processes and from atom-dimer processes. We find that all loss processes are suppressed close to the Feshbach resonance. Our general theoretical approach for fermionic mixtures near narrow Feshbach resonances provides predictions for the suppression of collisional decay as a function of the detuning from resonance, and we find excellent agreement with the experimental benchmarks provided by our Li-K system. We finally present model calculations for other Feshbach-resonant Fermi-Fermi systems, which are of interest for experiments in the near future.
Sluggish turmoil in the Fermi sea
The nonequilibrium dynamics of many-body quantum systems are tricky to study experimentally or theoretically. As an experimental setting, dilute atomic gases offer an advantage over electrons in metals. In this environment, the heavier atoms make collective processes that involve the entire Fermi sea occur at the sluggish time scale of microseconds. Cetina et al. studied these dynamics by using a small cloud of ⁴⁰ K atoms that was positioned at the center of a far larger ⁶ Li cloud. Controlling the interactions between K and Li atoms enabled a detailed look into the formation of quasiparticles associated with K “impurity” atoms.
Science , this issue p. 96
The refrigerator uses the heat of mixing at constant osmotic pressure between 3He and 4He, and has attained a temperature of 0.22°K in preliminary runs. The eight (probably) essential parts of the cycle are the condenser (C), expansion valve (V), heat exchanger (I), mixing chamber (M), superfluid duct (D), helium mixture funnel (F), evaporator (E), and circulation pump (see Fig. 1).
We study Efimov resonances via three-body loss in an ultracold two-component
gas of fermionic Li and bosonic Cs atoms close to a Feshbach
resonance at 843~G, extending results reported previously [Pires \textit{et
al.}, Phys. Rev. Lett. 112, 250404 (2014)] to temperatures around 120~nK. The
experimental scheme for reaching lower temperatures is based upon compensating
the gravity-induced spatial separation of the mass-imbalanced gases with
bichromatic optical dipole traps. We observe the first and second excited
Li-Cs-Cs Efimov resonance in the magnetic field dependence of the three-body
event rate constant, in good agreement with the universal zero-range theory at
finite temperature [Petrov and Werner, Phys. Rev. A 92, 022704 (2015)].
Deviations are found for the Efimov ground state, and the inelasticity
parameter is found to be significantly larger than those for
single-species systems.
We present the production of dual-species Bose-Einstein condensates of
and . Preparation of both species in the
state enabled us to exploit a total of three
Fesh\-bach resonances which allows for simultaneous Feshbach tuning of the
intraspecies and the -
interspecies scattering length. Thus dual-species Bose-Einstein condensates
were produced by sympathetic cooling of with
. A dark spontaneous force optical trap was used for
, to reduce the losses in due to
light-assisted collisions in the optical trapping phase, which can be of
benefit for other dual-species experiments. The tunability of the scattering
length was used to perform precision spectroscopy of the interspecies Feshbach
resonance located at and to determine the width of the
resonance to by rethermalization measurements. The
transition region from miscible to immiscible dual-species condensates was
investigated and the interspecies background scattering length was determined
to using an empirical model. This paves the way for
dual-species experiments with and BECs
ranging from molecular physics to precision metrology.
We report on the observation of unusually strong interactions in a thermal mixture of ultracold atoms which cause a significant modification of the spatial distribution. A mixture of Rb87 and Yb174 with a temperature of a few muK is prepared in a hybrid trap consisting of a bichromatic optical potential superimposed on a magnetic trap. For suitable trap parameters and temperatures, a spatial separation of the two species is observed. We infer that the separation is driven by a large interaction strength between Yb174 and Rb87 accompanied by a large three-body recombination rate. Based on this assumption we have developed a diffusion model which reproduces our observations.
We have measured the surface tension of liquid He4 down to 0.35°, using the capillary-rise method. The results are consistent with the theory that this temperature variation is mainly due to the excitation of surface modes similar to capillary waves. However, the results do not exclude an alternative theory, due to Singh, which considers the effect of the surface on the wave functions of an ideal degenerate Bose-Einstein gas. At the lambda point, we observed a discontinuity (or at least a very rapid variation) of the first derivative with respect to temperature.
We consider the T = 0 ground state of mixtures of bosons and fermions. Applying the Thomas-Fermi approximation we show that, depending on the strength of boson-boson and boson-fermion interactions, the Fermi gas may constitute a ``shell'' around or a ``core'' inside the Bose condensate, or even both.
Following a suggestion due to Frenkel, the normal modes of a liquid helium surface are taken to be surface tension waves. The free energy associated with these modes is estimated and is found to give a major contribution to the temperature dependence of the surface tension of liquid helium II. The zero-point energy of the modes is shown to be an appreciable fraction of the total surface energy at 0°K.
Following the bichromatic sub-Doppler cooling scheme on the D1 line of 40K
recently demonstrated in (Fernandes et al. 2012), we introduce a similar
technique for 7Li atoms and obtain temperatures of 60 uK while capturing all of
the 5x10^8 atoms present from the previous stage. We investigate the influence
of the detuning between the the two cooling frequencies and observe a threefold
decrease of the temperature when the Raman condition is fulfilled. We interpret
this effect as arising from extra cooling due to long-lived coherences between
hyperfine states. Solving the optical Bloch equations for a simplified,
\Lambda-type three-level system we identify the presence of an efficient
cooling force near the Raman condition. After transfer into a quadrupole
magnetic trap, we measure a phase space density of ~10^-5. This laser cooling
offers a promising route for fast evaporation of lithium atoms to quantum
degeneracy in optical or magnetic traps.
We obtain the threshold laws for three-body recombination of particles interacting via short-range potentials, taking into account all combinations of particle symmetry. In particular, we show that the recombination rate is constant at zero energy unless indistinguishable fermions are present. In this case, the rate is suppressed by either a factor of E or for two or three indistinguishable fermions, respectively. In addition, we present the threshold law for collision-induced dissociation.
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Spinor Bose gases form a family of quantum fluids manifesting both magnetic
order and superfluidity. This article reviews experimental and theoretical
progress in understanding the static and dynamic properties of these fluids.
The connection between system properties and the rotational symmetry properties
of the atomic states and their interactions are investigated. Following a
review of the experimental techniques used for characterizing spinor gases,
their mean-field and many-body ground states, both in isolation and under the
application of symmetry-breaking external fields, are discussed. These states
serve as the starting point for understanding low-energy dynamics, spin
textures and topological defects, effects of magnetic dipole interactions, and
various non-equilibrium collective spin-mixing phenomena. The paper aims to
form connections and establish coherence among the vast range of works on
spinor Bose gases, so as to point to open questions and future research
opportunities.
The low temperature thermodynamic properties of dilute solutions of 3He in 4He are reviewed. The main emphasis is on experiments and theoretical work performed since the discovery that some 3He remains in solution even at T = 0. The experiments include measurements of the heat capacity, phase-separation, equation of state, osmotic pressure, heat of mixing, nuclear magnetic susceptibility and first- and second-sound velocities. The discussion is limited to 3He concentrations below about 15% and temperatures small enough (T ⪅0.6 K) that the contributions from thermal phonons and rotons are neglible. The dependence of the various properties on temperature, concentration and, where data exist, pressure is described and analyzed in terms of various simple theories of helium solutions. The original theory is that of Landau and Pomeranchuk in which the 3He impurities are supposed to behave as free Fermi excitations of effective mass m where m depends only on the pressure. The “Fermi entropy model”, which is useful in the analysis of thermodynamic data at finite temperature, is an empirical generalization of the Landau-Pomeranchuk theory in which the entropy is still given by the ideal Fermi gas formula, but the effective mass is allowed to depend on concentration as well as pressure. The most accurate theory (“dilute solution theory”) includes the effects of interactions between 3He excitations, and it is developed here as an expansion of the ‘osmotic energy’, U − N4μ4, in terms of the 3He quasi-particle distribution function. Various theories of the effective interaction potential and its relation to the transport properties are reviewed. The results of the experiments are compared with the predictions of the theory, based on the most recent conjectures for the interaction potential, only in the limit of T → 0 at zero pressure. The one exception is the normal mass density of the 3He component ϱn for which the theory is compared with the results of second sound experiments at all temperatures such that the effects of thermal phonons and rotons are neglible. Finally, application of the solution thermodynamics is made to the theory of dilution refrigerators.
We develop a systematic approach to the calculations of finite size effects in phase transitions. The method consists of constructing an effective hamiltonian for the homogeneous modes, obtained by tracing out all other degrees of freedom. These modes are obtained by averaging the order parameter over the finite dimensions of the system. These techniques, together with the renormalization group, lead to explicit calculations of universal finite size scaling functions, under the form of (2+ϵ) or singular (4-ϵ) expansions. Some simple universal results above the upper critical dimension are presented. Simple and universal properties of the rounding of first order transitions are derived.
Using thermodynamic fluctuation theory, we study the finite-size rounding
of anomalies occurring at first-order phase transitions of the corresponding
infinite system. Explicit expressions for thermodynamic functions
are derived both for "'symmetric transitions"' (such as the jump
of the spontaneous magnetization in the Ising model from +Msp to
-Msp as the field changes from 0+ to 0-) as well as for asymmetric
cases, but restricting attention to (hyper)cubic system shapes. As
an explicit example for the usefulness of these considerations in
Monte Carlo simulations where it may be a problem to (i) locate a
phase transition and (ii) distinguish first-order from second-order
transitions, we present numerical results for the two-dimensional
nearest-neighbor Ising ferromagnet in a field, both below the critical
temperature Tc and at Tc. The numerical results are found to be in
very good agreement with the phenomenological theory and it is shown
that one may extract the magnitudes of jumps occurring at first-order
phase transitions in a well-defined and accurate way.