Ergotropy from Geometric Phases in a Dephasing Qubit

TL;DR

This paper explores how geometric and dynamic phases in a dephasing qubit relate to ergotropy, revealing that geometric phases encode the interplay of coherence and dissipation, and can be used to infer energy resources in quantum systems.

Contribution

It establishes a direct connection between geometric phases and ergotropy in open quantum systems, highlighting their physical distinction and potential for energy resource measurement.

Findings

Dynamic phase depends on incoherent ergotropy.

Geometric phase reflects both coherent and incoherent ergotropy.

In weak coupling, geometric phase is determined solely by incoherent ergotropy.

Abstract

We analyze the geometric phase and dynamic phase acquired by a qubit coupled to an environment through pure dephasing, establishing a direct connection between phase accumulation and ergotropy. We show that the dynamic phase depends solely on the incoherent ergotropy, reflecting its purely energetic origin. In contrast, the geometric phase exhibits a nontrivial dependence on both the coherent and incoherent contributions to the total ergotropy, encoding the interplay between coherence, dissipation, and energy extraction. By performing a perturbative expansion in the qubit-environment coupling strength, we demonstrate that, in the weak-coupling and long-time regime, the geometric phase becomes determined exclusively by the incoherent ergotropy, which coincides with the asymptotic value of the total ergotropy reached under decoherence. These results provide a clear physical distinction between dynamic and geometric phases in open quantum systems and establish geometric phases as sensitive probes of energetic resources. Furthermore,~in superconducting circuit implementations, our findings suggest that the ergotropy of a two-level system could be inferred indirectly from geometric-phase measurements using standard techniques such as quantum state tomography.