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(a) Two-photon excitation scheme to ${{nD}}_{3/2}$ Rydberg states in Rb used at Institut d’Optique. A π-polarized 795 nm light field couples the ground state $| g\rangle =| 5{S}_{1/2},F=2,{m}_{F}=2\rangle $ prepared by optical pumping with the intermediate state $| 5{P}_{1/2},F=2,{m}_{F}=2\rangle $ with a detuning ${\rm{\Delta }}=2\pi \times 740\;{\rm{MHz}}$ . In the second excitation step a ${\sigma }^{+}$ -polarized 474 nm beam populates the Rydberg state $| r\rangle =| {{nD}}_{3/2},{m}_{j}=3/2\rangle $ . (b) Typical single-atom Rabi oscillations between the ground $| g\rangle $ and Rydberg state $| r\rangle $ .
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This review summarizes experimental works performed over the last decade by several groups on the manipulation of a few individual interacting Rydberg atoms. These studies establish arrays of single Rydberg atoms as a promising platform for quantum-state engineering, with potential applications to quantum metrology, quantum simulation and quantum i...
Citations
... One of their key advantages is their long coherence time for ground-state atoms, combined with the exceptional properties of highly excited Rydberg states. These highly excited Rydberg states not only possess an extended lifetime proportional to the third power of the principal quantum number, but also significantly interact through strong long-range Rydberg-Rydberg interactions, manifesting as Rydberg-mediated dipoledipole or van der Waals interactions [38][39][40][41][42]. The presence of these strong Rydberg-Rydberg interactions enables a phenomenon known as Rydberg blockade, where the resonant excitation of two or more atoms to the Rydberg states is hindered [43,44]. ...
... As demonstrated in Refs. [39,[81][82][83], the pair states |dd , |pf 1 , and |f 1 p exhibit nearly degenerate characteristics. Consequently, the resonant dipole-dipole (Förster resonance) interaction between the two Rydberg atoms causes a hopping transition between the Rydberg states |dd and (|pf 1 + |f 1 p )/ √ 2, with a coupling strength of √ 2J. ...
Holonomic quantum computing offers a promising paradigm for quantum computation due to its error resistance and the ability to perform universal quantum computations. Here, we propose a scheme for the rapid implementation of a holonomic swap gate in neutral atomic systems, based on the selective Rydberg pumping mechanism. By employing time-dependent soft control, we effectively mitigate the impact of off-resonant terms even at higher driving intensities compared to time-independent driving. This approach accelerates the synthesis of logic gates and passively reduces the decoherence effects. Furthermore, by introducing an additional atom and applying the appropriate driving field, our scheme can be directly extended to implement a three-qubit controlled-swap gate. This advancement makes it a valuable tool for quantum state preparation, quantum switches, and a variational quantum algorithm in neutral atom systems.
... Due to stable encoding in hyperfine atomic states and the ability to manipulate and measure qubit states with laser light [50][51][52][53], neutral atoms have emerged as a promising physical system for quantum information processing. Recently, researchers have utilized Rydberg atom arrays for quantum optimization to solve the Maximum Independent Set problem on unit disk graphs [38]. ...
In contrast to the classical optimization process required by the quantum approximate optimization algorithm, FALQON, a feedback-based algorithm for quantum optimization [A. B. Magann {\it et al.,} {\color{blue}Phys. Rev. Lett. {\bf129}, 250502 (2022)}], enables one to obtain approximate solutions to combinatorial optimization problems without any classical optimization effort. In this study, we leverage the specifications of a recent experimental platform for the neutral atom system [Z. Fu {\it et al.,} {\color{blue}Phys. Rev. A {\bf105}, 042430 (2022)}] and present a scheme to implement an optimally tuned small-angle controlled-phase gate with quantum optimal control. By examining the 2- to 4-qubit FALQON algorithms in the Max-Cut problem and considering the spontaneous emission of the neutral atomic system, we have observed that the performance of FALQON implemented with small-angle controlled-phase gates exceeds that of FALQON utilizing CZ gates. This approach has the potential to significantly simplify the logic circuit required to simulate FALQON and effectively address the Max-Cut problem, which may pave a way for the experimental implementation of near-term noisy intermediate-scale quantum algorithms with neutral-atom systems.
... Several years ago, arrays of trapped molecules and Rydberg atoms were proposed [26][27][28] as an alternative paradigm for exploring synthetic dimensions with strong interactions. In this approach, one starts with a dipolar spin system in which interactions naturally play a significant role [29][30][31] . Then, by introducing tailored microwaves that drive transitions between internal states in a way that mimics the hopping structure of a lattice tight-binding model, the spin system is transformed into a playground for exploring the dynamics of strongly interacting matter in a synthetic dimension. ...
Synthetic dimensions, wherein dynamics occurs in a set of internal states, have found great success in recent years in exploring topological effects in cold atoms and photonics. However, the phenomena thus far explored have largely been restricted to the non-interacting or weakly interacting regimes. Here, we extend the synthetic dimensions playbook to strongly interacting systems of Rydberg atoms prepared in optical tweezer arrays. We use precise control over driving microwave fields to introduce a tunable U(1) flux in a four-site lattice of coupled Rydberg levels. We find highly coherent dynamics, in good agreement with theory. Single atoms show oscillatory dynamics controllable by the gauge field. Small arrays of interacting atoms exhibit behavior suggestive of the emergence of ergodic and arrested dynamics in the regimes of intermediate and strong interactions, respectively. These demonstrations pave the way for future explorations of strongly interacting dynamics and many-body phases in Rydberg synthetic lattices.
... In recent years, Rydberg atoms have proved to be an ideal candidate for exploring intriguing synthetic quantum matter. [1][2][3][4] The highly flexible geometry facilitated by individual optical-tweezer trapping, [5][6][7] together with the long-range dipole-dipole interactions, [8,9] offer abundant control degrees of freedom for simulating a variety of manybody quantum models and strongly correlated phenomena, including quantum spin models, [10][11][12][13][14][15] the topological order, [16][17][18] dynamic gauge fields, [19][20][21][22][23] and quantum spin liquids. [24][25][26][27][28] Particularly, under dipolar exchange interactions, Rydberg atoms can be modeled as few-level systems in the and manifolds, with excitations in the states hopping between different atoms that are often spatially separated. ...
We demonstrate the flexible tunability of excitation transport in Rydberg atoms, under the interplay of controlled dissipation and interaction-induced synthetic flux. Considering a minimum four-site setup——a triangular configuration with an additional output site——we study the transport of a single excitation, injected into a vertex of the triangle, through the structure. While the long-range dipole-dipole interactions between the Rydberg atoms lead to geometry-dependent Peierls phases in the hopping amplitudes of excitations, we further introduce on-site dissipation to a vertex of the triangle. As a result, both the chirality and destination of the transport can be manipulated through the flux and dissipation. In particular, we illustrate a parameter regime where our Rydberg-ring structure may serve as a switch for transporting the injected excitation through to the output site. The underlying mechanism is then analyzed by studying the chiral trajectory of the excitation and the time-dependent dissipation. The switchable excitation transport reported here offers a flexible tool for quantum control in Rydberg atoms, and holds interesting potentials for applications in quantum simulation and quantum information.
... Introducing the two collective states |ψ ± = (|0r ± |r0 )/ √ 2, the collective ground state |00 is not coupled to |ψ -but coupled to |ψ + with the coupling √ 2 . Starting from |00 and applying the laser for a duration π/( √ 2 ) thus we prepares the entangled state |ψ + [19]. The Rydberg blockade can be used to construct fast quantum gates with dipolar molecules. ...
... This leads to the truth table shown in Fig. 4(c), which constructs a controlled-phase gate. The controlled-phase gate can be turned into a controlled-not (CNOT) gate using additional single-qubit gates [19]. The remarkable feature of the Rydberg gates lies in its short duration, set by the interaction energy of the two molecules. ...
We propose a new kind of qubits composed of electric dipolar molecules. The electric dipolar molecules in an external electric field will take simple harmonic oscillations, whose quantum states belonging to the two lowest energy levels act as the states |0〉\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$|0\rangle$\end{document}, |1〉\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$|1\rangle$\end{document} of a qubit. The qubits’ excited states have a very long controlled mean life time about several seconds. We can perform quantum computations by manipulating the qubits of electric dipolar molecules just like those of neutral atoms. When the qubits are used for quantum computations, the dipolar moments’ orientations will harmonically oscillate along an external electric field and they will not change the directions: along or against the electric field, so the qubits can be large-scalely manufactured in graphene system. The radius of Rydberg blockade is about 100 nm.
... For instance, in cuprous oxide, manipulation of giant Rydberg excitons with principal quantum numbers of up to n = 25 has been demonstrated 14 . The strong, long-range dipole-dipole interactions from these excitons could be used to create solid-state analogs of Rydberg atoms 15 . Unfortunately, it has been difficult to produce high crystal quality artificial cuprous oxide and the observation of such higher excited states is made possible by the comparatively large Rydberg energy of around 100 meV 14 . ...
We propose a quantum science platform utilizing the dipole-dipole coupling between donor-acceptor pairs (DAPs) in wide bandgap semiconductors to realize optically controllable, long-range interactions between defects in the solid state. We carry out calculations based on density functional theory (DFT) to investigate the electronic structure and interactions of DAPs formed by various substitutional point-defects in diamond and silicon carbide (SiC). We determine the most stable charge states and evaluate zero phonon lines using constrained DFT and compare our results with those of simple donor-acceptor pair (DAP) models. We show that polarization differences between ground and excited states lead to unusually large electric dipole moments for several DAPs in diamond and SiC. We predict photoluminescence spectra for selected substitutional atoms and show that while B-N pairs in diamond are challenging to control due to their large electron-phonon coupling, DAPs in SiC, especially Al-N pairs, are suitable candidates to realize long-range optically controllable interactions.
... In the strong interaction regime, the mean-field state is fragmented, i.e., several orbitals contribute in the dynamics. Fragmentation is the mesoscopic effect that decreases with particle number as 1 N [27][28][29][30]. Thus a lower number of particles is preferable to study the beyond mean-field effect. ...
We solve the Schrödinger equation from first principles to investigate the many-body effects in the expansion dynamics of one-dimensional repulsively interacting bosons released from a harmonic trap. We utilize the multiconfigurational time-dependent Hartree method for bosons (MCTDHB) to solve the many-body Schrödinger equation at high level of accuracy. The MCTDHB basis sets are explicitly time-dependent and optimised by variational principle. We probe the expansion dynamics by three key measures; time evolution of one-, two- and three-body densities. We observe when the mean-field theory results to unimodal expansion, the many-body calculation exhibits trimodal expansion dynamics. The many-body features how the initially fragmented bosons independently spreads out with time whereas the mean-field pictures the expansion of the whole cloud. We also present the three different time scale of dynamics of the inner core, outer core and the cloud as a whole. We analyze the key role played by the dynamical fragmentation during expansion. A Strong evidence of the many-body effects is presented in the dynamics of two- and three-body densities which exhibit correlation hole and pronounced delocalization effect.
... 4 In atomic physics, dipole-dipole interactions play a fundamental role, e.g., in optical atomic clocks 5,6 and atom-based quantum simulators. 7 Resonant dipole-dipole interactions are also important for the optical properties of atomic vapors as they contribute to shifts and broadenings of the absorption lines, including the so-called self-broadening. [8][9][10][11][12][13][14][15][16][17][18][19][20][21] In atomic vapors, different processes control the broadening mechanism and the spectroscopic response. ...
In this article, we present a simulation study of the linear and nonlinear spectroscopy of dense atomic vapors. Motivated by recent experiments, we focus on double quantum spectroscopy, which directly probes dipole–dipole interactions. By explicitly including thermal velocity, we show that temperature has an important impact on the self-broadening mechanisms of the linear and nonlinear spectra. We also provide analytical expressions for the response functions in the short time limit using the two-body approximation, which shows that double quantum spectroscopy for atomic vapors directly probes the transition amplitude of the electronic excitation between two atoms. We also propose an expression for the double quantum spectrum that includes the effect of Doppler broadening, and we discuss the effect of density on the spectrum. We show that when Doppler broadening is negligible compared to self-broadening, the double quantum spectrum scales with the atomic density, while when Doppler broadening dominates, it scales as the square of the density.
... By representing all vertices with atoms, one can encode a Maximum Independent Set of G in the ground state of an Ising Hamiltonian on Rydberg atoms [32] over the augmented graph G + : where n i = (σ z i + 1)/2 and δ j represents the local detuning applied to each atom, ensuring that the MIS is achieved when the chain is in an antiferromagnetic state. ...
In the past years, many quantum algorithms have been proposed to tackle hard combinatorial problems. In particular, the Maximum Independent Set (MIS) is a known NP-hard problem that can be naturally encoded in Rydberg atom arrays. By representing a graph with an ensemble of neutral atoms one can leverage Rydberg dynamics to naturally encode the constraints and the solution to MIS. However, the classes of graphs that can be directly mapped ``vertex-to-atom" on standard devices with 2D capabilities are currently limited to Unit-Disk graphs. In this setting, the inherent spatial locality of the graphs can be leveraged by classical polynomial-time approximation schemes (PTAS) that guarantee an $\epsilon$-approximate solution. In this work, we build upon recent progress made for using 3D arrangements of atoms to embed more complex classes of graphs. We report experimental and theoretical results which represent important steps towards tackling combinatorial tasks on quantum computers for which no classical efficient $\varepsilon$-approximation scheme exists.
... To observe the corresponding quadratic speedup on near-term devices, the algorithm must be efficiently encoded in hardware [53]. The modified QAA is amenable to direct experimental implementation via Trotterized evolution combined using hybrid digital-analog evolution [54], by generating spin-exchange interactions with excitation into S and P Rydberg states or microwave driving [55,56], and decomposing the diagonal component of H ℓ into multiqubit controlled phase gates. Local detunings can generate the diagonal component of H ℓ on certain instances with structured configuration graphs, such as when the suboptimal configurations correspond to the motion of a domain wall [57]. ...
Designing quantum algorithms with a speedup over their classical analogs is a central challenge in quantum information science. Motivated by recent experimental observations of a superlinear quantum speedup in solving the Maximum Independent Set problem on certain unit-disk graph instances [Ebadi et al., Science 376, 6598 (2022)], we develop a theoretical framework to analyze the relative performance of the optimized quantum adiabatic algorithm and a broad class of classical Markov chain Monte Carlo algorithms. We outline conditions for the quantum adiabatic algorithm to achieve a quadratic speedup on hard problem instances featuring flat low-energy landscapes and provide example instances with either a quantum speedup or slowdown. We then introduce an additional local Hamiltonian with no sign problem to the optimized adiabatic algorithm to achieve a quadratic speedup over a wide class of classical simulated annealing, parallel tempering, and quantum Monte Carlo algorithms in solving these hard problem instances. Finally, we use this framework to analyze the experimental observations.
