Robustness of geometric phase under parametric noise

TL;DR

This paper investigates how the geometric phase, specifically the Dirac phase, remains robust or is affected when a particle's path is subjected to parametric noise modeled as Brownian motion, in a static magnetic field.

Contribution

It introduces a gauge-invariant definition of the Dirac phase under noisy conditions and analyzes its statistical properties, providing insights into phase robustness amidst environmental disturbances.

Findings

The Dirac phase distribution's moments are derived under parametric noise.

The study shows conditions under which the geometric phase remains stable despite noise.

Results suggest potential resilience of geometric phases in noisy quantum systems.

Abstract

We study the robustness of geometric phase in the presence of parametric noise. For that purpose we consider a simple case study, namely a semiclassical particle which moves adiabatically along a closed loop in a static magnetic field acquiring the Dirac phase. Parametric noise comes from the interaction with a classical environment which adds a Brownian component to the path followed by the particle. After defining a gauge invariant Dirac phase, we discuss the first and second moments of the distribution of the Dirac phase angle coming from the noisy trajectory.