Comparison between quantum jumps and master equation in the presence of a finite environment

TL;DR

This paper demonstrates the equivalence between a finite environment quantum jump model and a master equation approach for a qubit, highlighting their agreement in work moments and differences in work moment forms.

Contribution

It derives a microscopic master equation for a qubit with a finite bosonic environment and compares it to the quantum jump model, revealing their equivalence and differences in work moments.

Findings

Master equation and quantum jump model produce identical work moments via the two-measurement protocol.

Both methods yield the same moments of work when excluding interaction energy.

Differences arise in work moments when using the power operator approach.

Abstract

We study the equivalence between the recently proposed finite environment quantum jump model and a master equation approach. We derive microscopically the master equation for a qubit coupled to a finite bosonic environment and show that the master equation is equivalent with the finite environment quantum jump model. We analytically show that both the methods produce the same moments of work when the work is defined through the two-measurement protocol excluding the interaction energy. However, when compared to the work moments computed using the power operator approach, we find a difference in the form of the work moments. To numerically verify our results, we study a qubit coupled to an environment consisting of ten two-level systems.