Geometric phases under the presence of a composite environment

TL;DR

This paper investigates how a composite environment affects the geometric phase of a spin-1/2 particle, revealing that initial entanglement can enhance the phase's robustness against environmental disturbances.

Contribution

It introduces a model for computing the geometric phase of a spin-1/2 particle in a complex environment, highlighting the role of initial entanglement in preserving the phase.

Findings

Initial entanglement enhances the geometric phase's robustness.

The geometric phase is affected by the composite environment.

Entanglement can be used to protect quantum phases.

Abstract

We compute the geometric phase for a spin-1/2 particle under the presence of a composite environment, composed of an external bath (modeled by an infinite set of harmonic oscillators) and another spin-1/2 particle. We consider both cases: an initial entanglement between the spin-1/2 particles and an initial product state in order to see if the initial entanglement has an enhancement effect on the geometric phase of one of the spins. We follow the nonunitary evolution of the reduced density matrix and evaluate the geometric phase for a single two-level system. We also show that the initial entanglement enhances the sturdiness of the geometric phase under the presence of an external composite environment.