Geometric phase of a two-level system in a dissipative environment

TL;DR

This paper presents a second-quantized, gauge-invariant approach to analyze the geometric (Berry) phase of a two-level system in a dissipative environment, including nonadiabatic effects and experimental relevance.

Contribution

It introduces a unified formulation for adiabatic and nonadiabatic phases in dissipative systems, applicable to real experimental conditions like superconducting qubits.

Findings

Derived correction to the total phase in dissipative environments

Provided a transparent expression for geometry-dependent dephasing time

Analyzed the behavior of the geometric phase away from ideal adiabaticity

Abstract

The geometric (Berry) phase of a two-level system in a dissipative environment is analyzed by using the second-quantized formulation, which provides a unified and gauge-invariant treatment of adiabatic and nonadiabatic phases and is thus applicable to a quantitative analysis of transitional regions away from ideal adiabaticity. In view of the recent experimental observation of the Berry phase in a superconducting qubit, we illustrate our formulation for a concrete adiabatic case in the Ohmic dissipation. The correction to the total phase together with the geometry-dependent dephasing time is given in a transparent way. The behavior of the geometric phase away from ideal adiabaticity is also analyzed in some detail.