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

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

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Cited by in corpus (4)

• Quantum dephasing induced by non-Markovian random telegraph noise
• Towards detecting traces of non-contact quantum friction in the corrections of the accumulated geometric phase
• Non-Abelian holonomic transformation in the presence of classical noise
• Geometry of quantum evolution in a nonequilibrium environment