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arXiv:2204.08800 · Physical review. B./Physical review. B

Quantum phase transition of a two-dimensional Rydberg atom array in an optical cavity

Gao-Qi An, Yan-Hua Zhou, Tao Wang, Xue‐Feng Zhang

Published Oct 11, 2022• 9 citations
arXivHTMLPDF

Abstract

We study the two-dimensional Rydberg atom array in an optical cavity with the help of a variational method and large-scale quantum Monte Carlo simulations. The strong dipole-dipole interactions between Rydberg atoms can make the system exhibit a crystal structure, and the coupling between a two-level atom and a cavity photon mode can result in the formation of a polariton. The interplay between them provides a rich quantum phase diagram including the Mott, solid-1/2, superradiant, and superradiant solid (SRS) phases. As a two-order coexisted phase, the superradiant solid breaks both translational and U(1) symmetries. Different from the fragile SRS phase in a one-dimensional system [Zhang et al., Phys. Rev. Lett. 110, 090402 (2013)], the SRS phase stays in a larger parameter region. Thus, it is more feasible to detect a SRS phase and corresponding quantum criticality in the real system involving dissipations. Our work not only extends the understanding of the light-atom interacting system, but also provides the guidelines and benchmark for the future experiments.

DOI
10.1103/physrevb.106.134506

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We study the two-dimensional Rydberg atom array in an optical cavity with the help of a variational method and large-scale quantum Monte Carlo simulations. The strong dipole-dipole interactions between Rydberg atoms can make the system exhibit a crystal structure, and the coupling between a two-level atom and a cavity photon mode can result in the formation of a polariton. The interplay between them provides a rich quantum phase diagram including the Mott, solid-1/2, superradiant, and superradiant solid (SRS) phases. As a two-order coexisted phase, the superradiant solid breaks both translational and U(1) symmetries. Different from the fragile SRS phase in a one-dimensional system [Zhang et al., Phys. Rev. Lett. 110, 090402 (2013)], the SRS phase stays in a larger parameter region. Thus, it is more feasible to detect a SRS phase and corresponding quantum criticality in the real system involving dissipations. Our work not only extends the understanding of the light-atom interacting system, but also provides the guidelines and benchmark for the future experiments.
We study an optical cavity coupled to a lattice of Rydberg atoms, which can be represented by a generalized Dicke model. We show that the competition between the atom-atom interaction and atom-light coupling induces a rich phase diagram. A novel superradiant solid (SRS) phase is found, where both the superradiance and crystalline orders coexist. Different from the normal second order superradiance transition, here both the solid-1/2 and SRS to SR phase transitions are first order. These results are confirmed by large scale quantum Monte Carlo simulations.
Rydberg atom triangular arrays in an optical cavity serve as an ideal platform for understanding the interplay between geometric frustration and quantized photons. Using a large-scale quantum Monte Carlo method, we obtain a rich ground state phase diagram. Around half-filling, the infinite long-range light-matter interaction lifts the ground state degeneracy, resulting in a novel order-coexisted superradiant clock phase that completely destroys the fragile order-by-disorder phase observed in classical light fields. According to the Ginzburg-Landau theory, this replacement may result from the competition between threefold and sixfold clock terms. Similar to the spin supersolid, the clear first-order phase transition at the Z_{2} symmetry line is attributed to the nonzero photon density, which couples to the threefold clock term. Finally, we discuss the low-energy physics in the dimer language and propose that cavity-mediated nonlocal ring exchange interactions may play a critical role in the rich physics induced by the attachment of cavity QED. Our Letter opens a new arena of research on the emergent phenomena of quantum phase transitions in many-body quantum optics.
We study the properties of a generalized Dicke-Ising model realized with an array of Rydberg atoms, driven by microwave electric fields and coupled to an optical cavity. As this platform allows for a precisely tunable anisotropy parameter, the model exhibits a rich landscape of phase transitions and critical phenomena, induced by the interplay of rotating-wave, counter-rotating-wave, and Ising interactions. We develop an improved quantum Monte Carlo algorithm based on the stochastic series expansion that explicitly tracks the Fock state of the quantum cavity. In the superradiant (SR) phase, this allows us to determine, through data collapse, the scaling laws of the photon number. We also demonstrate the vanishing of parity symmetry in finite-size simulations and show that the Rydberg blockade leads to a significant suppression of cavity occupation. Notably, stronger quantum fluctuations induced by the counter-rotating wave terms slightly favor the superradiant solid (SRS) phase over the Solid-1/2 state. Finally, we confirm that the SR phase transition and the transition from the Solid-1/2 to the SRS are second-order. In contrast, the transitions from the Solid-1/2 or SRS to the SR phase are both first-order for any value of the normalized anisotropy parameter.
We study the superradiant phase transition of an array of Rydberg atoms in a dissipative microwave cavity. Under the interplay of the cavity field and the long-range Rydberg interaction, the steady state of the system exhibits an interaction-enhanced superradiance, with vanishing critical atom-cavity coupling rates at a discrete set of interaction strengths. We find that, while the phenomenon can be analytically understood in the case of a constant all-to-all interaction, the enhanced superradiance persists under typical experimental parameters with spatially dependent interactions, but at modified critical interaction strengths. The diverging susceptibility at these critical points is captured by emergent quantum Rabi models, each of which comprises a pair of collective atomic states with different numbers of atomic excitations. These collective states become degenerate at the critical interaction strengths, resulting in a superradiant phase for an arbitrarily small atom-cavity coupling.
Precise control of criticality in superradiant phase transitions is essential for quantum state engineering and the simulation of nonequilibrium phase transitions. Here, we investigate theoretically multicritical phenomena in a dissipative two-Rydberg-atom cavity--QED system. The intrinisic dipole--dipole interaction between the two Rydberg atoms restructures the energy-level landscape of the atomic subsystem, thereby significantly modifying the boundary of the continuous second-order superradiant phase transition, and shifting both the phase boundary and the multicritical point toward weaker atom--cavity strengths. For sufficiently strong dipole--dipole interactions, the continuous second-order phase transition and the multicritical point both disappear, leaving only a discontinuous first--order phase transition that enables the emergence of a superradiant phase even at arbitrarily weak atom--cavity coupling. This work is of fundamental interest for studying dissipative quantum phase transitions, with potential implications for quantum precision measurement and quantum sensing.
An extended Dicke model, which includes atom-atom interactions and a driving classical laser field, is established for a Bose-Einstein condensate inside an ultrahigh-finesse optical cavity. A feasible experimental setup with a strong atom-field coupling is proposed, where most parameters are easily controllable and thus the predicted a second-order superradiant-normal phase transition may be detected by measuring the ground-state atomic population. More intriguingly, second-order phase transition from the superradiant phase to the ``Mott'' phase is also revealed. In addition, a rich and exotic phase diagram is presented.