Geometric phase as a determinant of a qubit--environment coupling

TL;DR

This paper explores how the geometric phase of a qubit depends on different decoherence mechanisms, revealing distinct behaviors that could help identify the nature of qubit-environment interactions.

Contribution

It provides a detailed analysis of the geometric phase under dephasing and dissipative couplings using the Davies Markovian master equation, highlighting their contrasting effects.

Findings

Pure dephasing causes a monotonic and antisymmetric geometric phase variation.

Dissipative coupling results in non-monotonic geometric phase behavior with local extrema.

Geometric phase sensitivity can serve as a diagnostic tool for qubit-environment interactions.

Abstract

We investigate the qubit geometric phase and its properties in dependence on the mechanism for decoherence of a qubit weakly coupled to its environment. We consider two sources of decoherence: dephasing coupling (without exchange of energy with environment) and dissipative coupling (with exchange of energy). Reduced dynamics of the qubit is studied in terms of the rigorous Davies Markovian quantum master equation, both at zero and non--zero temperature. For pure dephasing coupling, the geometric phase varies monotonically with respect to the polar angle (in the Bloch sphere representation) parameterizing an initial state of the qubit. Moreover, it is antisymmetric about some points on the geometric phase-polar angle plane. This is in distinct contrast to the case of dissipative coupling for which the variation of the geometric phase with respect to the polar angle typically is non-monotonic, displaying local extrema and is not antisymmetric. Sensitivity of the geometric phase to details of the decoherence source can make it a tool for testing the nature of the qubit--environment interaction.