Quantum Adiabatic Markovian Master Equations

TL;DR

This paper derives and compares two Markovian master equations for adiabatic quantum systems weakly coupled to a thermal bath, analyzing their predictions and applying them to an Ising spin chain to identify different evolution phases.

Contribution

It introduces two new master equations in the adiabatic limit, one with and one without the rotating wave approximation, and systematically analyzes their differences and higher order corrections.

Findings

Different predictions depending on the Lamb shift inclusion.

Identification of four distinct evolution phases in the spin chain.

Dissipation can enhance fidelity in one phase.

Abstract

We develop from first principles Markovian master equations suited for studying the time evolution of a system evolving adiabatically while coupled weakly to a thermal bath. We derive two sets of equations in the adiabatic limit, one using the rotating wave (secular) approximation that results in a master equation in Lindblad form, the other without the rotating wave approximation but not in Lindblad form. The two equations make markedly different predictions depending on whether or not the Lamb shift is included. Our analysis keeps track of the various time- and energy-scales associated with the various approximations we make, and thus allows for a systematic inclusion of higher order corrections, in particular beyond the adiabatic limit. We use our formalism to study the evolution of an Ising spin chain in a transverse field and coupled to a thermal bosonic bath, for which we identify four distinct evolution phases. While we do not expect this to be a generic feature, in one of these phases dissipation acts to increase the fidelity of the system state relative to the adiabatic ground state.