Correction to the geometric phase by structured environments: the onset of non-Markovian effects

TL;DR

This paper investigates how structured environments and non-Markovian effects influence the geometric phase of a two-level quantum system, revealing environment-dependent corrections crucial for quantum information processing.

Contribution

It introduces a detailed analysis of geometric phase corrections in both Markovian and non-Markovian environments, highlighting the impact of environment structure and memory effects.

Findings

Non-Markovian environments induce significant phase corrections.

Correction mainly governed by system-environment coupling in Markovian regimes.

Memory effects in non-Markovian regimes cause notable deviations in geometric phase.

Abstract

We study the geometric phase of a two-level system under the presence of a structured environment, particularly analysing its correction with the ohmicity parameter $s$ and the onset of non-Markovianity. We firstly examine the system coupled to a set of harmonic oscillators and studied the decoherence factor as function of the environment's ohmicity parameter. Secondly, we propose the two-level system coupled to a non-equilibrium environment, and show that these environments display non-Markovian effects for all values of the ohmicity parameter. The geometric phase of the two-level system is therefore computed under the presence of both types of environment. The correction to the unitary geometric phase is analysed in both, Markovian and non-Markovian regimes. Under Markovian environments, the correction induced on the system's phase is mainly ruled by the coupling constant between the system and the environment, while in the non-Markovian regime, memory effects seem to trigger a significant correction to the unitary geometric phase. The result is significant to the quantum information processing based on the geometric phase in quantum open systems