Non-Markovian effect on the geometric phase of a dissipative qubit

TL;DR

This paper investigates how non-Markovian environmental effects influence the geometric phase of a dissipative qubit, revealing conditions under which the phase is significantly affected or remains robust, with implications for quantum information processing.

Contribution

It provides an analytical and numerical analysis of the non-Markovian effects on the geometric phase of a qubit coupled to a Lorentzian environment, highlighting the conditions for significant corrections.

Findings

Large correction to geometric phase when spectral width is small

Robustness of geometric phase increases with spectral width

Non-Markovian dynamics significantly impact the geometric phase in certain regimes

Abstract

We study the geometric phase of a two-level atom coupled to an environment with Lorentzian spectral density. The non-Markovian effect on the geometric phase is explored analytically and numerically. In the weak coupling limit the lowest-order correction to the geometric phase is derived analytically and the general case is calculated numerically. It is found that the correction to the geometric phase is significantly large if the spectral width is small and in this case the non-Markovian dynamics has a significant impact to the geometric phase. When the spectral width increases, the correction to the geometric phase becomes negligible, which shows the robustness of the geometric phase to the environmental white noises. The result is significant to the quantum information processing based on the geometric phase.