Dynamics of an open quantum system interacting with a quantum environment

TL;DR

This paper investigates the dynamics of open quantum systems with nonlinear interactions, analyzing entanglement, revival phenomena, and ergodic properties in atom-field models through entropy, photon statistics, and time series analysis.

Contribution

It provides a detailed analysis of entanglement dynamics and revival phenomena in nonlinear open quantum systems, highlighting how nonlinearity and initial coherence influence system behavior.

Findings

Revival phenomena are clearly identifiable in subsystem von Neumann entropy.

Time series analysis reveals diverse ergodic properties depending on system parameters.

Entanglement and photon statistics are significantly affected by nonlinearity and initial states.

Abstract

We examine the dynamics of subsystems of bipartite and tripartite quantum systems with nonlinear Hamiltonians. We consider two models which capture the generic features of open quantum systems: a three-level atom interacting with a single-mode radiation field, and a three-level atom interacting with two field modes which do not directly interact with each other. The entanglement of specific initially unentangled states of the atom-field system is examined through the time-varying subsystem von Neumann entropy (SVNE). The counterparts of near-revivals and fractional revivals of the initial state are clearly identifiable in the SVNE in all cases where revival phenomena occur. The Mandel $Q$ parameter corresponding to the photon number of a radiation field is obtained as a function of time in both models. In those cases where revivals are absent, a time series analysis of the mean photon number reveals a variety of ergodicity properties (as manifested in return maps, recurrence-time distributions and Lyapunov exponents), depending on the strength of the nonlinearity and the degree of coherence of the initial state of the radiation field(s).