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Europhysics Letters (EPL)

Quantum quench dynamics of the Jaynes-Cummings-Hubbard model with weak nearest-neighbor hopping

Qing Li, Jin-Lou Ma, Tong Huang, Lei Tan, Huai-Qiang Gu, Wu-Ming Liu

Published Apr 1, 2021• 6 citations
Publisher

Abstract

Motivated by the nonequilibrium dynamics experiment, we study the quantum quench dynamics of the JCH model with weak nearest-neighbor hopping strength by exact diagonalization. One of the crucial insights is to focus on the comparison between the time-averaged density matrix and the canonical ensemble in a wide range of values for the coupling strength between the cavity and the atom, and significant differences are found. Thus, this phenomenon can be used to infer that the system with weak nearest-neighbor hopping strength may be integrable. In order to verify our prediction, we perform the level spacing distribution of the system and find that they conform with the characteristics of the integrable system. Further, a nearly integrable system is presented by removing the degenerate energy level and fitting Brody distribution. Besides, the evolution of the momentum distribution functions of the photon and the equilibrium value predicted by the canonical ensemble are followed, which demonstrates that the system cannot be thermalized. Finally, the way how the system avoids thermalization is also discussed by the finite-size scaling of the fluctuations of the diagonal and the off-diagonal matrix elements.

DOI
10.1209/0295-5075/134/20007

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Motivated by the nonequilibrium dynamics experiment, we study the quantum quench dynamics of the JCH model with weak nearest-neighbor hopping strength by exact diagonalization. One of the crucial insights is to focus on the comparison between the time-averaged density matrix and the canonical ensemble in a wide range of values for the coupling strength between the cavity and the atom, and significant differences are found. Thus, this phenomenon can be used to infer that the system with weak nearest-neighbor hopping strength may be integrable. In order to verify our prediction, we perform the level spacing distribution of the system and find that they conform with the characteristics of the integrable system. Further, a nearly integrable system is presented by removing the degenerate energy level and fitting Brody distribution. Besides, the evolution of the momentum distribution functions of the photon and the equilibrium value predicted by the canonical ensemble are followed, which demonstrates that the system cannot be thermalized. Finally, the way how the system avoids thermalization is also discussed by the finite-size scaling of the fluctuations of the diagonal and the off-diagonal matrix elements.
In one-dimensional low-density Jaynes-Cummings Hubbard (JCH) models [Phys. Rev. E 106, 064107 (2022)2470-004510.1103/PhysRevE.106.064107], we proved that the eigenstate thermalization hypothesis (ETH) is valid when the tunneling strength and coupling strength are of the same order. Surprisingly, at the weak tunneling limit, we observed that the entanglement entropy and scaling law of kinetic energy operators also exhibit obvious quantum chaotic properties, this is an unexpected result. To substantiate these findings, we further discuss their nonequilibrium dynamics in this paper. Our analysis reveals that when the model is a weak tunneling limit after the quench and the initial state is an equilibrium state of chaos, the system reaches an equilibrium state. This observation supports the conclusion that the low-density JCH model at the weak tunneling limit is nonintegrable, corroborating our previous results [Phys. Rev. E 106, 064107 (2022)2470-004510.1103/PhysRevE.106.064107]. Additionally, by discussing the validity of the fluctuation-dissipation theorem (FDT) and the evolution behavior of entanglement entropy and fidelity, we numerically demonstrate the differences between the one-dimensional low-density JCH model and general nonintegrable systems. Specifically, in the low-density JCH model, when the Hamiltonian after the quench is integrable, the validity of FDT depends on the thermal behavior of the initial Hamiltonian, and a metastable state is observed during the evolution of entanglement entropy. Our research presents an an intriguing and unique nonintegrable model, enriching the current understanding of nonintegrable systems.
Motivated by recent experiments, we study the relaxation dynamics and thermalization in the one-dimensional Bose-Hubbard model induced by a global interaction quench. Specifically, we start from an initial state that has exactly one boson per site and is the ground state of a system with infinitely strong repulsive interactions at unit filling. Using exact diagonalization and the density-matrix renormalization-group method, we compute the time dependence of such observables as the multiple occupancy and the momentum distribution function. Typically, the relaxation to stationary values occurs over just a few tunneling times. The stationary values are identical to the so-called diagonal ensemble on the system sizes accessible to our numerical methods and we further observe that the microcanonical ensemble describes the time averages of many observables reasonably well for small and intermediate interaction strength. The expectation values of observables in the canonical ensemble agree quantitatively with the time averages obtained from the quench at small interaction strengths, and qualitatively provide a good description even in parameter regimes where the microcanonical ensemble is not applicable due to finite-size effects. We discuss our numerical results in the framework of the eigenstate thermalization hypothesis. Moreover, we also observe that the diagonal and the canonical ensembles are practically identical for our initial conditions already on the level of their respective energy distributions for small interaction strengths. Finally, we discuss implications of our results for the interpretation of a recent sudden expansion experiment [Phys. Rev. Lett. 110, 205301 (2013)], in which the same interaction quench was realized.
Abstract The eigenstate thermalization hypothesis (ETH) is a mechanism for the thermalization of quantum chaotic systems. Most researches on quantum chaotic systems involve the two-body interaction between spins, fermions, and bosons, but for the JCH model, the emergence of quantum-chaotic properties comes from the competition between the hopping strength of the photon and the photon-atom coupling strength. We use exact diagonalization to prove that the JCH system has the property of the quantum chaotic system and verify the validity of ETH ansatz both for diagonal and off-diagonal matrix elements of the photon observables with reasonable experimental parameters.
In the one-dimensional low-density Jaynes-Cummings Hubbard (JCH) model, we find that when the hopping strength is much smaller than the coupling strength, the average restricted energy gap ratio exhibits an abnormal statistical behavior that is neither a Poisson nor a Gaussian orthogonal ensemble. But the average half-chain entanglement entropy exhibits ergodicity, and the eigenstate thermalization hypothesis (ETH) is valid for the observable. These results are quite different from those of the standard JCH model. In addition, when the hopping and the coupling strengths are of the same order, quantum chaos still appears in the low-density JCH model, which is in contrast to the integrability of the one-dimensional hard-core bosons. Finally, the dipole-dipole interaction breaks the particle-hole symmetry and leads the abnormal statistical properties to be closer to those of the integrable system at the weak hopping strength limit, but the quantum chaos properties cannot be affected when the hopping strength is of the same order as the coupling strength. Our results demonstrate the counterintuitive behavior in the low-density JCH model and explain the physics behind them from the perspective of the energy spectrum.
We study quench dynamics of the Bose-Hubbard model by exact diagonalization. Initially, the system is at thermal equilibrium and of a finite temperature. The system is then quenched by changing the on-site interaction strength UUU suddenly. Both the single-quench and double-quench scenarios are considered. In the former case, the time-averaged density matrix and the real-time evolution are investigated. It is found that though the system thermalizes only in a very narrow range of the quenched value of UUU, it does equilibrate or relax well into a much larger range. Most importantly, it is proven that this is guaranteed for some typical observables in the thermodynamic limit. In order to test whether it is possible to distinguish the unitarily evolving density matrix from the time-averaged (thus time-independent), fully decohered density matrix, a second quench is considered. It turns out that the answer is affirmative or negative depending on whether the intermediate value of UUU is zero or not.
Disorder in one-dimensional (1D) many-body systems facilitates abundant phases such as many-body localization (MBL) and thermalization. However, it remains unclear regarding their existence and behavior within hybrid quantum systems. Here, based on a simple bosonic-spin hybrid model, known as the Jaynes-Cummings-Hubbard (JCH) array, we investigate the effect of disorder compared to the phenomena in the clean system with the variation of atom-photon coupling strength. By using the level-spacing ratio, entanglement entropy, and the properties of observable diagonal and off-diagonal matrix elements, we find that strong disorder results in the appearance of a MBL phase in the JCH model that strongly violates the eigenstate thermalization hypothesis (ETH), while a conditional prethermal behavior can exist in the weak disorder regime. The conditional prethermal dynamics is based on the choice of initial product states. This work systematically reveals abundant many-body phases in the 1D JCH model and clarifies the discrepancies in the thermalization properties of systems with and without disorder.