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arXiv:2304.01535 · Physical Review A

Quantum Rabi hexagonal ring in an artificial magnetic field

Linjun Li, Li-Lu Feng, Jia-Hao Dai, Yuyu Zhang

Published Oct 9, 2023• 10 citations
arXivHTMLPDF

Abstract

We present exotic quantum phases in a quantum Rabi hexagonal ring. A remarkable finding is that the application of an artificial magnetic field to the ring induces long-range interactions, yielding effective next-nearest-neighbor photon hopping in the subrings. This phenomenon gives rise to two chiral superradiant phases in addition to a ferro-superradiant and an antiferro-superradiant phase. As evidence, there appear chiral ground-state currents of photons in the subrings with opposite signs in different chiral phases. The degenerate configurations of the complex order parameters in chiral phases are similar to the in-plane magnetizations of a chiral magnetic. The critical exponents governing the excitation energy in the two chiral phases are identical to those of the Rabi triangle, which depend on the size of the subrings rather than the size of the ring. It is important to classify the universality class of the multiple chiral phase transitions as the size of Rabi ring increases. Furthermore, the implementation of the proposed system is an exciting prospect in quantum simulations for exploring intriguing quantum phases.

DOI
10.1103/physreva.108.043705

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We present exotic quantum phases in a quantum Rabi hexagonal ring. A remarkable finding is that the application of an artificial magnetic field to the ring induces long-range interactions, yielding effective next-nearest-neighbor photon hopping in the subrings. This phenomenon gives rise to two chiral superradiant phases in addition to a ferro-superradiant and an antiferro-superradiant phase. As evidence, there appear chiral ground-state currents of photons in the subrings with opposite signs in different chiral phases. The degenerate configurations of the complex order parameters in chiral phases are similar to the in-plane magnetizations of a chiral magnetic. The critical exponents governing the excitation energy in the two chiral phases are identical to those of the Rabi triangle, which depend on the size of the subrings rather than the size of the ring. It is important to classify the universality class of the multiple chiral phase transitions as the size of Rabi ring increases. Furthermore, the implementation of the proposed system is an exciting prospect in quantum simulations for exploring intriguing quantum phases.
We present the phase diagram of a one-dimensional quantum Rabi zigzag chain under an artificial gauge field, which is implemented via phase-modulated next-nearest-neighbor (NNN) hopping. For a system size of N=8N=8N=8, we analytically determine the order parameters and critical thresholds, identifying five distinct superradiant phases. For strong nearest-neighbor (NN) coupling, the system exhibits either a ferro-superradiant (FSR) or an antiferro-superradiant (AFSR) phase depending on its sign. Increasing NNN coupling induces a stripe antiferro-superradiant (sAFSR) phase with antiparallel NNN and parallel NN displacements, which is distinct from the conventional AFSR phase. Tuning the magnetic flux drives the system into chiral or antichiral superradiant phases with opposite ground-state photon currents, which are different from the conventional superradiant phases. Remarkably, geometric frustration within each triangular plaquette stabilizes chiral phases even at small magnetic flux while suppressing the sAFSR phase, which vanishes for N=6N=6N=6. Mapping the system onto an effective magnetic Hamiltonian yields an analogous phase diagram featuring distinct magnetic phases, offering insight into the anomalous superradiant phases. This equivalence establishes a quantum optical platform for simulating chiral magnetism.
We map a quantum Rabi ring, consisting of N cavities arranged in a ring geometry, into an effective magnetic model containing the XY exchange and the Dzyaloshinskii-Moriya (DM) interactions. The analog of the latter is induced by an artificial magnetic field, which modulates photon hopping between nearest-neighbor cavities with a phase. This mapping facilitates the description and understanding of the different phases in the quantum optical model through simple arguments of competing magnetic interactions. For the square geometry (N=4) the rich phase diagram exhibits three superradiant phases denoted as ferro-superradiant, antiferro-superradiant, and chiral superradiant. In particular, the DM interaction is responsible for the chiral phase in which the energetically degenerate configurations of the order parameters are similar to the in-plane magnetizations of skyrmions with different helicities. The antiferro-superradiant phase is suppressed in the triangle geometry (N=3) as geometric frustration contributes to stabilize the chiral phase even for small values of the DM interaction. The chiral phases for odd and even N show a different scaling behavior close to the phase transition. The equivalent behavior on both systems opens the possibility of simulating chiral magnetism in a few-body quantum optical platform, as well as understanding one system using the insights gained from the other.
The quantum fluctuations of a quantum Rabi triangle are investigated using an analytical method that goes beyond mean-field theory. An artificial magnetic field applied in three cavities leads to the breaking of time-reversal symmetry, which is evident in the directional transfer of photons. In contrast to previous studies, we focus on the scaling exponents of quantum fluctuations of the local photon number and the position variance near the critical point. Specifically, the fluctuations of photons do not diverge as the coupling strength approaches the critical value from below for the chiral superradiant phase transition. Attributing to geometric frustration, two distinct scaling laws arise for the frustrated cavity and the remaining cavities. Specifically, in the frustrated cavity, the scaling exponent in the chiral superradiant phase differs from that without an artificial magnetic field for the frustrated antiferromagnetic superradiant phase. The unusual scaling exponents indicate distinct universality classes in contrast to the single-cavity Rabi one. We suggest that accurate critical exponents in few-body systems are useful for identifying exotic quantum phase transitions in light-matter coupling systems.
We propose a quantum Rabi square model where both the nearest-neighbor and the next-nearest-neighbor photon hopping are allowed among four quantum Rabi systems located at the vertices of a square. By tuning the next-nearest hopping strength, we realize a first-order phase transition between the antiferromagnetic superradiant phase and the frustrated superradiant phase, as well as a second-order phase transition between the normal and the superradiant phases. To understand the emergence of such phases, we show analytically that the effect induced by next-nearest hopping is equivalent to that of an artificial gauge phase. Our findings suggest that the next-nearest-neighbor hopping can serve as an alternative for the gauge phase to realize quantum control in applications of quantum simulation and quantum materials and that our model represents a basic building block for the frustrated ${J}_{1}\text{\ensuremath{-}}{J}_{2}$ quantum spin model on square lattices.
Abstract The existence of quantum tricriticality and exotic phases are found in a tricritical Dicke triangle (TDT) where three cavities, each one containing an ensemble of three-level atoms, are connected to each other through the action of an artificial magnetic field. The conventional superradiant phase (SR) is connected to the normal phase through first- and second-order boundaries, with tricritical points located at the intersection of such boundaries. Apart from the SR phase, a chiral superradiant (CSR) phase is found by tuning the artificial magnetic field. This phase is characterized by a nonzero photon current and its boundary presents chiral tricritical points (CTCPs). Through the study of different critical exponents, we are able to differentiate the universality class of the CTCP and TCP from that of second-order critical points, as well as find distinctive critical behavior among the two different superradiant phases. The TDT can be implemented in various systems, including atoms in optical cavities as well as the circuit QED system, allowing the exploration of a great variety of critical manifolds.
We show that an NNN-site quantum Rabi ring with matched giant-atom couplings has 2N2^N2N degenerate superradiant configurations as the atomic-to-cavity frequency ratio η=Δ/ωη=Δ/ωη=Δ/ω tends to infinity. Each atom couples to two cavities two sites apart, and the photon hopping carries a phase π/2π/2π/2. Tuning the ratio of contact strengths to the photon hopping reduces the mean-field energy to a sum of single-site Rabi energies, with a common critical coupling for all momentum-pair sectors. The degeneracy survives quadratic quantum fluctuations despite a dispersive excitation spectrum. At finite ηηη, second-order processes involving the local cubic anharmonicity generate a same-sublattice Ising coupling of order ω/ηω/ηω/η, selecting ferro- and antiferro-superradiant configurations. This quantum order-by-disorder effect has no classical counterpart. Four-site calculations retaining all spin states quantitatively support the predicted energy coefficients. The separation between the induced coupling and the excitation gap allows a broad temperature interval with macroscopic photon occupation and short-range correlations between displacement signs.