A generalized fidelity amplitude for open systems

TL;DR

This paper introduces a generalized fidelity amplitude framework for open quantum systems, enabling the probing of intermediate system dynamics through measurable coherences in a coupled central system.

Contribution

It derives a master equation for the reduced dynamics of the intermediate environment, extending previous work by focusing on using central system coherences to investigate open system behavior.

Findings

Derived a master equation for the intermediate system's dynamics.

Validated analytical results with random matrix simulations.

Showed how central coherences can probe open quantum dynamics.

Abstract

We consider a central system which is coupled via dephasing to an open system, i.e. an intermediate system which in turn is coupled to another environment. Considering intermediate and far environment as one composite system, the coherences in the central system are given in the form of fidelity amplitudes for a certain perturbed echo dynamics in the composite environment. On the basis of the Born-Markov approximation, we derive a master equation for the reduction of that dynamics to the intermediate system alone. In distinction to an earlier paper [arXiv: 1502.04143 (2015)] where we discussed the stabilizing effect of the far environment on the decoherence in the central system, we focus here on the possibility to use the measurable coherences in the central system for probing the open quantum dynamics in the intermediate system. We illustrate our results for the case of chaotic dynamics in the near environment, where we compare random matrix simulations with our analytical result.