Dynamical invariants and nonadiabatic geometric phases in open quantum systems

TL;DR

This paper develops a framework for analyzing non-adiabatic geometric phases in open quantum systems, generalizing dynamical invariants to arbitrary evolutions and demonstrating robustness against decoherence.

Contribution

It introduces a method to define and analyze non-adiabatic geometric phases in open systems without the adiabatic approximation, using dynamical invariants and Jordan canonical forms.

Findings

Non-adiabatic geometric phases can be constructed to be robust against decoherence.

The framework applies to systems under arbitrary convolutionless master equations.

Illustrated with a two-level system showing robustness against dephasing and spontaneous emission.

Abstract

We introduce an operational framework to analyze non-adiabatic Abelian and non-Abelian, cyclic and non-cyclic, geometric phases in open quantum systems. In order to remove the adiabaticity condition, we generalize the theory of dynamical invariants to the context of open systems evolving under arbitrary convolutionless master equations. Geometric phases are then defined through the Jordan canonical form of the dynamical invariant associated with the super-operator that governs the master equation. As a by-product, we provide a sufficient condition for the robustness of the phase against a given decohering process. We illustrate our results by considering a two-level system in a Markovian interaction with the environment, where we show that the non-adiabatic geometric phase acquired by the system can be constructed in such a way that it is robust against both dephasing and spontaneous emission.