L. Mathey

George Mason University, Fairfax, VA, United States

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Publications (46)113.72 Total impact

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    ABSTRACT: We propose to detect quadrupole interactions of neutral ultra-cold atoms via their induced mean-field shift. We consider a Mott insulator state of spin-polarized atoms in a two-dimensional optical square lattice. The quadrupole moments of the atoms are aligned by an external magnetic field. As the alignment angle is varied, the mean-field shift shows a characteristic angular dependence, which constitutes the defining signature of the quadrupole interaction. For the $^{3}P_{2}$ states of Yb and Sr atoms, we find a frequency shift of the order of tens of Hertz, which can be realistically detected in experiment with current technology. We compare our results to the mean-field shift of a spin-polarized quasi-2D Fermi gas in continuum.
    02/2014;
  • Physical Review Letters 12/2013; · 7.94 Impact Factor
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    Wen-Min Huang, M. Lahrz, L. Mathey
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    ABSTRACT: Following the recent proposal to create quadrupolar gases[S.G. Bhongale et al., Phys. Rev. Lett. 110, 155301 (2013)], we investigate what quantum phases can be created in these systems in one dimension. We consider a geometry of two coupled one-dimensional systems, and derive the quantum phase diagram of ultra-cold fermionic atoms interacting via quadrupole-quadrupole interaction within a Tomonaga-Luttinger-liquid framework. We map out the phase diagram as a function of the distance between the two tubes and the angle between the direction of the tubes and the quadrupolar moments. The latter can be controlled by an external field. We show that there are two magic angles $\theta^{c}_{B,1}$ and $\theta^{c}_{B,2}$ between $0$ to $\pi/2$, where the intratube quadrupolar interactions vanish and change signs. Adopting a pseudo-spin language with regards to the two 1D systems, the system undergoes a spin-gap transition and displays a zig-zag density pattern, above $\theta^{c}_{B,2}$ and below $\theta^{c}_{B,1}$. Between the two magic angles, we show that polarized triplet superfluidity and a planar spin-density wave order compete with each other. The latter corresponds to a bond order solid in higher dimensions. We demonstrate that this order can be further stabilized by applying a commensurate periodic potential along the tubes.
    11/2013;
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    ABSTRACT: Magnetism plays a key role in modern science and technology, but still many open questions arise from the interplay of magnetic many-body interactions. Deeper insight into complex magnetic behaviour and the nature of magnetic phase transitions can be obtained from, for example, model systems of coupled XY and Ising spins. Here, we report on the experimental realization of such a coupled system with ultracold atoms in triangular optical lattices. This is accomplished by imposing an artificial gauge field on the neutral atoms, which acts on them as a magnetic field does on charged particles. As a result, the atoms show persistent circular currents, the direction of which provides an Ising variable. On this, the tunable staggered gauge field, generated by a periodic driving of the lattice, acts as a longitudinal field. Further, the superfluid ground state presents strong analogies with the paradigm example of the fully frustrated XY model on a triangular lattice.
    Nature Physics 09/2013; 9(9):2750. · 19.35 Impact Factor
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    ABSTRACT: We propose a method to reach the antiferromagnetic state of two-dimensional Fermi gases trapped in optical lattices: Independent subsystems are prepared in suitable initial states and then connected by a sudden or slow quench of the tunneling between the subsystems. Examples of suitable low-entropy subsystems are double wells or plaquettes, which can be experimentally realized in Mott insulating shells using optical super-lattices. We estimate the effective temperature T* of the system after the quench by calculating the distribution of excitations created using the spin wave approximation in a Heisenberg model. We investigate the effect of an initial staggered magnetic field and find that for an optimal polarization of the initial state the effective temperature can be significantly reduced from T* approximately T_c at zero polarization to T*<0.65 T_c, where T_c is the crossover temperature to the antiferromagnetic state. The temperature can be further reduced by using a finite quench time. We also show that T* decreases logarithmically with the linear size of the subsystem.
    08/2013;
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    ABSTRACT: Emulation of gauge fields for ultracold atoms provides access to a class of exotic states arising in strong magnetic fields. Here we report on the experimental realisation of tunable staggered gauge fields in a periodically driven triangular lattice. For maximal staggered magnetic fluxes, the doubly degenerate superfluid ground state breaks both a discrete Z2 (Ising) symmetry and a continuous U(1) symmetry. By measuring an Ising order parameter, we observe a thermally driven phase transition from an ordered antiferromagnetic to an unordered paramagnetic state and textbook-like magnetisation curves. Both the experimental and theoretical analysis of the coherence properties of the ultracold gas demonstrate the strong influence of the Z2 symmetry onto the condensed phase.
    arXiv. 04/2013;
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    ABSTRACT: We report on the experimental observation of an analog to a persistent alternating photocurrent in an ultracold gas of fermionic atoms in an optical lattice. The dynamics is induced and sustained by an external harmonic confinement. While particles in the excited band exhibit long-lived oscillations with a momentum-dependent frequency, a strikingly different behavior is observed for holes in the lowest band. An initial fast collapse is followed by subsequent periodic revivals. Both observations are fully explained by mapping the system onto a nonlinear pendulum.
    Physical Review Letters 02/2013; 110(8):085302. · 7.94 Impact Factor
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    ABSTRACT: We introduce a new platform for quantum simulation of many-body systems based on nonspherical atoms or molecules with zero dipole moment but possessing a significant value of electric quadrupole moment. We consider a quadrupolar Fermi gas trapped in a 2D square optical lattice, and show that the peculiar symmetry and broad tunability of the quadrupole-quadrupole interaction results in a rich phase diagram encompassing unconventional BCS and charge density wave phases, and opens up a perspective to create topological superfluid. Quadrupolar species, such as metastable alkaline-earth atoms and homonuclear molecules, are stable against chemical reactions and collapse and are readily available in experiment at high densities.
    Physical Review Letters 11/2012; 110(15). · 7.94 Impact Factor
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    ABSTRACT: The conventional spin density wave (SDW) phase (Overhauser, 1962), as found in antiferromagnetic metal for example (Fawcett 1988), can be described as a condensate of particle-hole pairs with zero angular momentum, $\ell=0$, analogous to a condensate of particle-particle pairs in conventional superconductors. While many unconventional superconductors with Cooper pairs of finite $\ell$ have been discovered, their counterparts, density waves with non-zero angular momenta, have only been hypothesized in two-dimensional electron systems (Nayak, 2000). Using an unbiased functional renormalization group analysis, we here show that spin-triplet particle-hole condensates with $\ell=1$ emerge generically in dipolar Fermi gases of atoms (Lu, Burdick, and Lev, 2012) or molecules (Ospelkaus et al., 2008; Wu et al.) on optical lattice. The order parameter of these exotic SDWs is a vector quantity in spin space, and, moreover, is defined on lattice bonds rather than on lattice sites. We determine the rich quantum phase diagram of dipolar fermions at half-filling as a function of the dipolar orientation, and discuss how these SDWs arise amidst competition with superfluid and charge density wave phases.
    Physical Review A 09/2012; 87(4). · 3.04 Impact Factor
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    ABSTRACT: Using a numerical implementation of the truncated Wigner approximation, we simulate the experiment reported by Ramanathan et al. in Phys. Rev. Lett. 106, 130401 (2011), in which a Bose-Einstein condensate is created in a toroidal trap and set into rotation via a Gauss-Laguerre beam. A potential barrier is then placed in the trap to study the decay of the superflow. We find that the current decays via thermally activated phase slips, which can also be visualized as vortices crossing the barrier region in radial direction. Adopting the notion of critical velocity used in the experiment, we determine it to be lower than the local speed of sound at the barrier. This result is in agreement with the experimental findings, but in contradiction to the predictions of the Gross-Pitaevskii equation. This emphasizes the importance of thermal fluctuations in the experiment.
    07/2012;
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    ABSTRACT: Cold atoms provide a promising platform to solve problems that, although computationally infeasible, are of immense importance to condensed matter physics and material science. Ultra-cold bosonic atoms have been quite successful in emulating the Bose-Hubbard model. Experiments are now underway towards mapping out the unknown phase diagram of the Fermi-Hubbard model. Recent experimental advances in cooling dipolar gases to quantum degeneracy provide an unprecedented opportunity to engineer Hubbard-like models with long range interactions. Here we show that two new and exotic types of order emerge generically in dipolar fermion systems: bond order solids of p- and d-wave symmetry. Similar, but manifestly different, phases of two-dimensional correlated electronic systems have previously only been hypothesized. Our results suggest that these phases can be constructed flexibly with dipolar fermions, using currently available experimental techniques, providing detectable experimental signatures.
    06/2012;
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    Ippei Danshita, L. Mathey
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    ABSTRACT: We study the quantum phases of one-dimensional Bose-Fermi mixtures in optical lattices. Assuming repulsive interparticle interactions, equal mass, and unit total filling, we calculate the ground-state phase diagram by means of both Tomonaga-Luttinger liquid theory and time-evolving block decimation method. We demonstrate the existence of a counterflow superfluid (CFSF) phase of polaron pairs, which are composite particles consisting of two fermions and two bosonic holes, in a broad range of the parameter space. We find that this phase naturally emerges in $^{174}$Yb-$^{173}$Yb mixtures, realized in recent experiments, at low temperatures.
    Physical Review A 04/2012; 87(2). · 3.04 Impact Factor
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    ABSTRACT: The recent experimental realization of dipolar Fermi gases near or below quantum degeneracy provides an opportunity to engineer Hubbard-like models with long-range interactions. Motivated by these experiments, we chart out the theoretical phase diagram of interacting dipolar fermions on the square lattice at zero temperature and half filling. We show that, in addition to p-wave superfluid and charge density wave order, two new and exotic types of bond order emerge generically in dipolar fermion systems. These phases feature homogeneous density but periodic modulations of the kinetic hopping energy between nearest or next-nearest neighbors. Similar, but manifestly different, phases of two-dimensional correlated electrons have previously only been hypothesized and termed "density waves of nonzero angular momentum." Our results suggest that these phases can be constructed flexibly with dipolar fermions, using currently available experimental techniques.
    Physical Review Letters 04/2012; 108(14):145301. · 7.94 Impact Factor
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    ABSTRACT: We propose a realistic experiment to demonstrate a dynamic Kosterlitz-Thouless transition in ultra-cold atomic gases in two dimensions. With a numerical implementation of the Truncated Wigner Approximation we simulate the time evolution of several correlation functions, which can be measured via matter wave interference. We demonstrate that the relaxational dynamics is well-described by a real-time renormalization group approach, and argue that these experiments can guide the development of a theoretical framework for the understanding of critical dynamics.
    12/2011;
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    ABSTRACT: Recent trapped atom experiments are able to generate an ultra-cold gas of hetero-nuclear molecules with a sufficiently large dipole moment to allow for the occurrence of rich many-body physics leading to exotic quantum phases. A key role is played by the anisotropic and long range nature of the dipole-dipole interaction. We study a system of fermionic dipolar molecules in a 2D optical lattice. Previous studies for homogeneous configurations have revealed the possibility of s-wave CDW and the p-wave BCS phase. However, much remains to be understood. In our study we take an unbiased approach by following the functional RG technique. This method allows us to look at the flow of various channels as one approaches the Fermi surface in the RG sense. We find an intriguing interplay between the s-wave CDW and the p-wave superfluid phases.
    06/2011;
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    ABSTRACT: We suggest an experimentally feasible procedure to observe paired and counterflow superfluidity in ultra-cold atom systems. We study the time evolution of one-dimensional mixtures of bosonic atoms in an optical lattice following an abrupt displacement of an additional weak confining potential. We find that the dynamic responses of the paired superfluid phase for attractive inter-species interactions and the counterflow superfluid phase for repulsive interactions are qualitatively distinct and reflect the quasi long-range order that characterizes these states. These findings suggest a clear experimental procedure to detect these phases, and give an intuitive insight into their dynamics.
    Physical Review A 03/2011; 84(4). · 3.04 Impact Factor
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    ABSTRACT: We study the dynamic response of the paired superfluid (PSF) and counterflow superfluid (CFSF) states in a binary mixture of ultra-cold bosonic atoms following an abrupt displacement of the trapping potential. In the PSF and CFSF states, the pairing and anti-pairing orders lead to novel transport properties and distinctive dynamic responses to the abrupt displacement. The findings provide a clear experimental procedure to detect these orders and give an intuitive insight into the dynamics of paired and counterflow superfluidity.
    03/2011;
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    ABSTRACT: We study the many-body dynamics of a mixture of two hyperfine states of bosonic atoms in 2D, following a pi/2-pulse. Using both a numerical implementation of the Truncated Wigner approximation and an analytical approach, we find that a dynamic phase transition can be triggered, in which the system relaxes from a superfluid to a disordered state via vortex unbinding. This process can be dynamically suppressed, which creates a long-lived metastable supercritical state. We discuss the realization and detection of these effects.
    03/2011;
  • Amy Cassidy, Ludwig Mathey, Charles Clark
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    ABSTRACT: We study the dynamics of Bose gases following a phase imprint. Numerical results within truncated Wigner approximation, which includes both quantum and thermal fluctuations, are compared with analytical predictions. In order to emphasize the effects of fluctuations in these approximations, we also compare our results with dynamics governed by the Gross Pitaevskii equation. We study the dynamics of several observables, including the density and single-particle and density-density correlation functions, with particular focus on experimentally relevant quantities.
    03/2011;
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    ABSTRACT: We study the phase-fluctuating condensate regime of ultra-cold atoms trapped in a ring-shaped trap geometry, which has been realized in recent experiments. We first consider a simplified box geometry, in which we identify the conditions to create a state that is dominated by thermal phase-fluctuations, and then explore the experimental ring geometry. In both cases we demonstrate that the requirement for strong phase fluctuations can be expressed in terms of the total number of atoms and the geometric length scales of the trap only. For the ring-shaped trap we discuss the zero temperature limit in which a condensate is realized where the phase is fluctuating due to interactions and quantum fluctuations. We also address possible ways of detecting the phase fluctuating regime in ring condensates. Comment: 10 pages, 5 figures, minor edits
    Physical Review A 07/2010; · 3.04 Impact Factor

Publication Stats

189 Citations
274 Downloads
2k Views
113.72 Total Impact Points

Institutions

  • 2012
    • George Mason University
      • School of Physics, Astronomy, and Computational Sciences
      Fairfax, VA, United States
    • University of Hamburg
      Hamburg, Hamburg, Germany
  • 2008–2011
    • National Institute of Standards and Technology
      Maryland, United States
  • 2004–2009
    • Harvard University
      • Department of Physics
      Cambridge, Massachusetts, United States