Berry phase with environment: classical versus quantum

TL;DR

This paper explores how the Berry phase in a dissipative system is affected by the environment, showing that environmental noise influences the Berry phase through its spectrum, regardless of whether the noise is classical or quantum.

Contribution

It demonstrates that the environmental correction to the Berry phase depends solely on the noise spectrum, unifying classical and quantum noise effects in a dissipative quantum system.

Findings

The correction to the Berry phase is expressed via symmetrized noise power.

The correction is insensitive to the classical or quantum nature of the noise.

Quantum and classical environments produce equivalent effects on the Berry phase.

Abstract

We discuss the concept of the Berry phase in a dissipative system. We show that one can identify a Berry phase in a weakly-dissipative system and find the respective correction to this quantity, induced by the environment. This correction is expressed in terms of the symmetrized noise power and is therefore insensitive to the nature of the noise representing the environment, namely whether it is classical or quantum mechanical. It is only the spectrum of the noise which counts. We analyze a model of a spin-half (qubit) anisotropically coupled to its environment and explicitly show the coincidence between the effect of a quantum environment and a classical one.