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

FERNANDO C. LOMBARDO AND PAULA I. VILLAR

PHYSICAL REVIEW A - ATOMIC, MOLECULAR AND OPTICAL PHYSICS

AMER PHYSICAL SOC

Lugar: New York; Año: 2015 vol. 91 p. 421111 - 421118

1050-2947

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.