Nonunitary geometric phases: a qubit coupled to an environment with random noise

TL;DR

This paper investigates how a qubit's geometric phase is affected by non-equilibrium, noisy environments, providing analytical and numerical insights into decoherence and potential control methods for phase measurement.

Contribution

It introduces a model for non-unitary geometric phases of a qubit interacting with non-stationary, non-equilibrium environments, analyzing decoherence effects and phase behavior.

Findings

Decoherence factors exhibit a characteristic dip related to bath mode phases.

Different environments (ohmic, supra-ohmic) have distinct decoherence time-scales.

Under certain conditions, decoherence can be controlled to measure geometric phases.

Abstract

We describe the decoherence process induced on a two-level quantum system in direct interaction with a non-equilibrium environment. The non-equilibrium feature is represented by a non-stationary random function corresponding to the fluctuating transition frequency between two quantum states coupled to the surroundings. In this framework, we compute the decoherence factors which have a characteristic "dip" related to the initial phases of the bath modes. We therefore study different types of environments, namely ohmic and supra-ohmic. These environments present different decoherence time-scales than the thermal environment we used to study. As a consequence, we compute analytically and numerically the non-unitary geometric phase for the qubit in a quasi-cyclic evolution under the presence of these particular non-equilibrium environments. We show in which cases decoherence effects could, in principle, be controlled in order to perform a measurement of the geometric phase using standard procedures.