Adiabatically steered open quantum systems: Master equation and optimal phase

TL;DR

This paper presents a new derivation of the master equation for adiabatically controlled open quantum systems, emphasizing phase optimization and gauge invariance, with potential for higher-order accuracy.

Contribution

It introduces an alternative derivation method using super-adiabatic bases and discusses phase selection to minimize adiabatic parameters and ensure gauge invariance.

Findings

Derived a generalized master equation for adiabatically steered systems.

Showed how phase choices affect the adiabatic parameter and gauge invariance.

Analyzed the impact of geometric phases on the master equation.

Abstract

We introduce an alternative way to derive the generalized form of the master equation recently presented by J. P. Pekola et al. [Phys. Rev. Lett. 105, 030401 (2010)] for an adiabatically steered two-level quantum system interacting with a Markovian environment. The original derivation employed the effective Hamiltonian in the adiabatic basis with the standard interaction picture approach but without the usual secular approximation. Our approach is based on utilizing a master equation for a non-steered system in the first super-adiabatic basis. It is potentially efficient in obtaining higher-order equations. Furthermore, we show how to select the phases of the adiabatic eigenstates to minimize the local adiabatic parameter and how this selection leads to states which are invariant under a local gauge change. We also discuss the effects of the adiabatic noncyclic geometric phase on the master equation.