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

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

arXiv comment7 figures. Accepted for publication in Phys. Rev. A. arXiv admin note: text overlap with arXiv:1303.4937

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• Decoherence by spontaneous emission: a single-atom analog of superradiance