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

Fernando C. Lombardo and Paula I. Villar
Phys. Rev. A 91, 042111 – Published 10 April 2015

Abstract

We study the geometric phase of a two-level system under the presence of a structured environment, particularly analyzing its correction with the ohmicity parameter s and the onset of non-Markovianity. We first examine the system coupled to a set of harmonic oscillators and study the decoherence factor as function of the environment's ohmicity parameter. Second, we propose the two-level system coupled to a nonequilibrium 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 analyzed in both the 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.

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  • Received 5 September 2014
  • Revised 18 February 2015

DOI:https://doi.org/10.1103/PhysRevA.91.042111

©2015 American Physical Society

Authors & Affiliations

Fernando C. Lombardo and Paula I. Villar

  • Departamento de Física Juan José Giambiagi, FCEyN UBA and IFIBA CONICET-UBA, Facultad de Ciencias Exactas y Naturales, Ciudad Universitaria, Pabellón I, 1428 Buenos Aires, Argentina

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Vol. 91, Iss. 4 — April 2015

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