Berry phase in a non-isolated system

TL;DR

This paper studies how environmental interactions affect Berry phase measurements in a spin-half system, revealing that the phase can be observed under specific timescales but lacks a simple geometric interpretation due to dissipation.

Contribution

It demonstrates that environmental effects alter the Berry phase in a spin-half system, challenging the assumption of a straightforward geometric interpretation in realistic, dissipative settings.

Findings

Berry phase observable within specific timescales

Environmental effects modify the Berry phase from the ideal case

No simple geometric interpretation for the dissipative Berry phase

Abstract

We investigate the effect of the environment on a Berry phase measurement involving a spin-half. We model the spin+environment using a biased spin-boson Hamiltonian with a time-dependent magnetic field. We find that, contrary to naive expectations, the Berry phase acquired by the spin can be observed, but only on timescales which are neither too short nor very long. However this Berry phase is not the same as for the isolated spin-half. It does not have a simple geometric interpretation in terms of the adiabatic evolution of either bare spin-states or the dressed spin-resonances that remain once we have traced out the environment. This result is crucial for proposed Berry phase measurements in superconducting nanocircuits as dissipation there is known to be significant.