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Physical Review A

Role of chiral symmetry in a kicked Jaynes-Cummings model

Pinquan Qin, Hee Chul Park

Published Jan 19, 2023• 1 citation
Publisher

Abstract

We have studied the role of chiral symmetry in a periodically kicked Jaynes--Cummings (KJC) model by freezing an initial phase. We show that commensurate kicks ($2\ensuremath{\pi}k$ periodicity with integer $k$) conserve the chiral symmetry in the KJC model under the resonant condition, while incommensurate kicks break the symmetry. The chiral symmetry preserves the phase of an initial state against phase fluctuations during the dynamical evolution, but broken chiral symmetry erases the initial phase. The frozen phase is preserved within a finite evolution time for slight deviations of the kick period from an integer multiple of $2\ensuremath{\pi}$ and small variations of detuning from the resonant condition. The chiral symmetry-protected phase information is noteworthy as it provides various uses in quantum computation and information.

DOI
10.1103/physreva.107.013712

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We have studied the role of chiral symmetry in a periodically kicked Jaynes--Cummings (KJC) model by freezing an initial phase. We show that commensurate kicks (2\ensuremathπk2\ensuremath{\pi}k2\ensuremathπk periodicity with integer kkk) conserve the chiral symmetry in the KJC model under the resonant condition, while incommensurate kicks break the symmetry. The chiral symmetry preserves the phase of an initial state against phase fluctuations during the dynamical evolution, but broken chiral symmetry erases the initial phase. The frozen phase is preserved within a finite evolution time for slight deviations of the kick period from an integer multiple of 2\ensuremathπ2\ensuremath{\pi}2\ensuremathπ and small variations of detuning from the resonant condition. The chiral symmetry-protected phase information is noteworthy as it provides various uses in quantum computation and information.
We investigate the emergence of frustrated quantum phases in a Jaynes-Cummings (JC) trimer with complex hopping amplitudes between the cavities, which represents the smallest frustrated unit in light-matter systems. The complex hopping amplitudes that can be engineered via synthetic gauge fields introduce chiral effects and geometric frustration to the system. We obtain analytic solutions in the semiclassical limit and map out the phase diagram of this model, featuring one normal and three distinct superradiant phases. Among these phases, a chirally frustrated superradiant phase emerges, characterized by broken chiral and translational symmetries and unidirectional photon flow. These results reveal how frustration and symmetry breaking can arise in JC systems with synthetic gauge fields and strong light-matter coupling.
Abstract We carefully investigate the comprehensive impact of atom-cavity interaction and artificial magnetic fields on quantum phase transitions of anti-Jaynes-Cummings triangle model in the infinite frequency limit. We discover that ground states of the optical field can be a gapped normal phase (NP) or three kinds of gapless superradiant phases with infinite degeneracy. When the atom-cavity coupling is weak, the optical field is in a NP, which is a vacuum with no photons. Otherwise, it will stay at one of the superradiant phases: a normal superradiant phase without photon currents and another two chiral superradiant phases with opposite photon currents. The former only breaks the continuous U (1) symmetry and its gapless excitations are normal Goldstone modes. Nevertheless, the latter, mainly induced by an external synthetic gauge field, break both the continuous U (1) symmetry and chiral symmetry, thereby corresponding gapless excitations are chiral Goldstone modes. In addition, we also propose a detecting scheme to distinguish these superradiant phases.
Nonreciprocity can profoundly alter the spectra and dynamics of open quantum systems, yet its impact on the long-time steady-state phases of matter has remained largely unexplored. Here we show that the interplay of nonreciprocity, symmetry defects, and spatial boundaries can generate phases beyond the standard spontaneous-symmetry-breaking paradigm. We demonstrate this mechanism by showing that sufficiently strong nonreciprocity turns boundaries into sources and drains of symmetry defects, while simultaneously endowing these defects with chiral dynamics in the bulk. As a result, the conventional uniform symmetry-broken state gives way to a domain-wall traveling-wave phase, in which symmetry defects form a persistent chiral wave. We showcase this mechanism in a bosonic model with Z2Z_{2}Z2​ symmetry, where periodic boundary conditions support only the conventional symmetric and symmetry-broken phases, whereas open boundary conditions allow the traveling-wave phase. We further show that even in the absence of symmetry breaking, the steady state can exhibit anomalous chiral relaxation: owing to the non-Hermitian skin effect in the stability matrix, local fluctuations are chirally amplified as they approach a boundary, where they eventually decay. Combining mean-field theory with truncated Wigner simulations, we characterize these phases, analyze the order parameter and Goldstone-mode fluctuations of the traveling-wave phase, and confirm its existence in three spatial dimensions.
Abstract We study the dynamical evolution and symmetry breaking of the non-Hermitian double Jaynes–Cummings model with symmetry. The results indicate that there exist symmetry maintained and breaking phase in this model, and the non-Hermitian terms lead to different behaviors in two phases. In the symmetry phase, there exists stable Rabi oscillation caused by the interaction between photons and atoms. At the exceptional point, the system shows critical property that the probabilities in each state over time tend to be equal. The system will undergo a transition from the symmetry phase to the symmetry breaking phase, as increasing the coupling constant. In the symmetry breaking phase, complex eigenvalues appear, and the probability in each state increases monotonically in an exponential form. This study can help us to understand the effect of symmetry on the interaction between photons and atoms in non-Hermitian systems.
Chiral symmetry is broken by typical interactions in lattice models, but the statistical interactions embodied in the anyon-Hubbard model are an exception. This is an example for a correlated hopping model where chiral symmetry protects a degenerate zero-energy subspace. Complementary to the traditional approach of anyon braiding in real space, we adiabatically evolve the statistical parameter and find nontrivial Berry phases and holonomies in this chiral subspace. The corresponding states possess stationary checkerboard patterns in their N-particle densities that are preserved under adiabatic manipulation. We give an explicit protocol for how these chirally protected zero-energy states can be prepared, observed, validated, and controlled.
A map from the charged Dirac oscillator on a noncommutative plane interacting with a homogeneous magnetic field onto a quantum optics model is proposed. We find that both anti-Jaynes-Cummings (AJC) and Jaynes-Cummings (JC) interactions are included in this mapped quantum optics model. A competition between AJC and JC interactions will happen when the intensity of the magnetic field changes. Contrary to previous studies, the competition is symmetrical since the phonons that take part in the competition are only associated with the excitation of the Dirac oscillator. Furthermore, this model will experience a quantum phase transition when the intensity of the magnetic field crosses the critical point. However, the critical point is different from the one in the model of the charged nonrelativistic harmonic oscillator interacting with a homogenous magnetic field on a noncommutative plane. It also deviates from its commutative counterpart because of spatial noncommutativity. Some characteristics of the quantum phase transition are studied. Then we investigate the nonrelativistic limit of this model. Our results show that its nonrelativistic counterpart inherits similar properties of the chirality quantum phase transition from the relativistic one.