Quantum Dynamics of the Dissipative Jaynes-Cummings Model Toward Thermal Equilibrium

M. Nakatani, T. Ogawa

J. J. Sánchez-Mondragón, Joseph H. Eberly

Qing Li, Jin-Lou Ma, Lei Tan

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.

Carlos A. González-Gutiérrez, D Solís-Valles, B. M. Rodríguez-Lara

Abstract We use the microscopic derivation of the Jaynes–Cummings model master equation under field losses to study the dynamics of initial field-qubit states in the single-excitation manifold and beyond. We show that field-qubit detuning, as well as finite temperature, modify the effective decay rate of the system using measures like field-qubit purity and concurrence for the case of one-excitation, and for initial Fock states for more excitations. For initial semi-classical states of the field, we show that the microscopic approach, in phase space, provides an evolution to thermal equilibrium that is smoother than the one provided by the standard phenomenological approach.

Koushik Mandal, M. V. Satyanarayana

Rui‐Hua Xie, Gong-ou Xu