Geometric nature of the environment-induced Berry phase and geometric dephasing

TL;DR

This paper explores how a dissipative environment modifies the Berry phase of a spin-half system, revealing a geometric nature of the environment-induced phase and a gauge-invariant geometric dephasing effect.

Contribution

It demonstrates that environment-induced modifications to the Berry phase are geometric and introduces the concept of geometric dephasing, which is gauge invariant for open paths.

Findings

Environment modifies Berry phase with a quadrupole-like flux.

Environment-induced phase has a complex, geometric component.

Geometric dephasing is gauge invariant for open paths.

Abstract

We investigate the geometric phase or Berry phase (BP) acquired by a spin-half which is both subject to a slowly varying magnetic field and weakly-coupled to a dissipative environment (either quantum or classical). We study how this phase is modified by the environment and find that the modification is of a geometric nature. While the original BP (for an isolated system) is the flux of a monopole-field through the loop traversed by the magnetic field, the environment-induced modification of the BP is the flux of a quadrupole-like field. We find that the environment-induced phase is complex, and its imaginary part is a geometric contribution to dephasing. Its sign depends on the direction of the loop. Unlike the BP, this geometric dephasing is gauge invariant for open paths of the magnetic field.