Initial correlations in open system's dynamics: The Jaynes-Cummings model

TL;DR

This paper investigates how initial correlations affect the dynamics of an open quantum system using the Jaynes-Cummings model, revealing how these correlations influence state distinguishability over time.

Contribution

It introduces a method to quantify initial correlations via trace distance and analyzes their impact on system dynamics within the Jaynes-Cummings framework.

Findings

Initial correlations influence the distinguishability of quantum states over time.

Thermal equilibrium states contain correlations dependent on temperature and coupling.

Open system dynamics reveal features of initial correlations through time evolution.

Abstract

Employing the trace distance as a measure for the distinguishability of quantum states, we study the influence of initial correlations on the dynamics of open systems. We concentrate on the Jaynes-Cummings model for which the knowledge of the exact joint dynamics of system and reservoir allows the treatment of initial states with arbitrary correlations. As a measure for the correlations in the initial state we consider the trace distance between the system-environment state and the product of its marginal states. In particular, we examine the correlations contained in the thermal equilibrium state for the total system, analyze their dependence on the temperature and on the coupling strength, and demonstrate their connection to the entanglement properties of the eigenstates of the Hamiltonian. A detailed study of the time dependence of the distinguishability of the open system states evolving from the thermal equilibrium state and its corresponding uncorrelated product state shows that the open system dynamically uncovers typical features of the initial correlations.