Geometric phase corrected by initial system-environment correlations

TL;DR

This paper investigates how initial system-environment correlations influence the geometric phase of a two-level quantum system undergoing pure dephasing, revealing that such correlations can significantly alter and potentially stabilize the geometric phase.

Contribution

The study introduces a formalism to account for initial correlations in calculating the geometric phase, demonstrating their impact across different environments and initial states.

Findings

Initial correlations can significantly modify the geometric phase.

Accounting for correlations can enhance the robustness of the geometric phase.

The correction to the geometric phase depends on system-environment coupling strength.

Abstract

We find the geometric phase of a two-level system undergoing pure dephasing via interaction with an arbitrary environment, taking into account the effect of the initial system-environment correlations. We use our formalism to calculate the geometric phase for the two-level system in the presence of both harmonic oscillator and spin environments, and we consider the initial state of the two-level system to be prepared by a projective measurement or a unitary operation. The geometric phase is evaluated for a variety of parameters such as the system-environment coupling strength to show that the initial correlations can affect the geometric phase very significantly even for weak and moderate system-environment coupling strengths. Moreover, the correction to the geometric phase due to the system-environment coupling generally becomes smaller (and can even be zero) if initial system-environment correlations are taken into account, thus implying that the system-environment correlations can increase the robustness of the geometric phase.