Exact Non-Markovian master equation for the Spin-Boson and Jaynes-Cummings models

TL;DR

This paper derives an exact non-Markovian master equation for two-level systems interacting with thermal baths, unifying previous approximations and extending to complex multi-system models like the Jaynes-Cummings model.

Contribution

It provides the first exact non-Markovian master equation for such systems, including multi-system generalizations and explicit solutions in terms of the Bloch vector.

Findings

Exact master equation for a two-level system with a thermal bath.

Previous approximations are special cases of this exact solution.

Extension of the formalism to multi-system models like Jaynes-Cummings.

Abstract

We provide the exact non-Markovian master equation for a two-level system interacting with a thermal bosonic bath, and we write the solution of such a master equation in terms of the Bloch vector. We show that previous approximated results are particular limits of our exact master equation. We generalize these results to more complex systems involving an arbitrary number of two-level systems coupled to different thermal baths, providing the exact master equations also for these systems. As an example of this general case we derive the master equation for the Jaynes-Cummings model.