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arXiv:1002.3147 · Physical Review A

Environmentally induced effects on a bipartite two-level system: Geometric phase and entanglement properties

Fernando C. Lombardo, Paula I. Villar

Published Feb 16, 2010• 33 citations
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Abstract

We calculate the geometric phase of a bipartite two-level system coupled to an external environment. We analyze the reduced density matrix for an arbitrary initial state of the composite system and compute the correction to the unitary geometric phase through a kinematic approach. In all cases considered, we observe a similar structure as a function of the degree of the entanglement of the initial state. Further, we compute the entanglement entropy and concurrence of the bipartite state and analyze if there is any relation among these quantities and the geometric phase acquired during the nonunitary system's evolution. Finally, we discuss the results obtained.

DOI
10.1103/physreva.81.022115

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We calculate the geometric phase of a bipartite two-level system coupled to an external environment. We analyze the reduced density matrix for an arbitrary initial state of the composite system and compute the correction to the unitary geometric phase through a kinematic approach. In all cases considered, we observe a similar structure as a function of the degree of the entanglement of the initial state. Further, we compute the entanglement entropy and concurrence of the bipartite state and analyze if there is any relation among these quantities and the geometric phase acquired during the nonunitary system's evolution. Finally, we discuss the results obtained.
We calculate the geometric phase of a bipartite two-level system coupled to an external environment. We compute the correction to the unitary geometric phase through a kinematic approach. To this end, we analyse the reduced density matrix of the bipartite system after tracing over the environmental degrees of freedom, for arbitrary initial states of the composite system. In all cases considered, the correction to the unitary phase has a similar structure as a function of the degree of the entanglement of the initial state. In the case of a maximally entangled state (MES), the survival phase is only the topological phase, and there is no correction induced by the environments. Further, we compute the quantum discord and concurrence of the bipartite state and analyse possible relations among these quantities and the geometric phase acquired during the non-unitary system's evolution.
We compute the geometric phase for a spin-1/2 particle under the presence of a composite environment, composed of an external bath (modeled by an infinite set of harmonic oscillators) and another spin-1/2 particle. We consider both cases: an initial entanglement between the spin-1/2 particles and an initial product state in order to see if the initial entanglement has an enhancement effect on the geometric phase of one of the spins. We follow the nonunitary evolution of the reduced density matrix and evaluate the geometric phase for a single two-level system. We also show that the initial entanglement enhances the sturdiness of the geometric phase under the presence of an external composite environment.
By studying the dynamical evolution of the bipartite two-level system which interacts with external environment,we analyze the reduced density matrix for an arbitrary initial state of the bipartite two-level system.Moreover,we calculate the initial state reduced density matrix with Werner-like state.Further,we analyze quantitatively variation law of entanglement of the bipartite two-level system with the expression of Concurrence in the bosonic ohmic and bosonic supraohmic environment at zero temperature as the parameters t,r and p change.Finally,we conclude that in the same condition,entanglement sudden death time under the bosonic supraohmic environment at zero temperature is more than that under the bosonic ohmic environment at zero temperature.
We present a bipartite two-level system coupled to electromagnetic quantum vacuum fluctuations through a general dipolar coupling. We derive the master equation in the framework of an open quantum system, assuming an environment composed of (i) solely vacuum fluctuations and (ii) the vacuum fluctuations and a conducting plate located at a fixed distance from the bipartite system. For both cases considered, we study the dynamics of the bipartite system and the temporal evolution of the concurrence of an initial entangled bipartite state. We further analyze the generation of entanglement due to the vacuum structure. Finally, we study the different induced contributions to the correction of the unitary geometric phase of a bipartite quantum state so as to explore the possibility of future experimental setups by exploring the influence of boundaries conditions in vacuum.
We make a geometric study of the phases acquired by a general, pure bipartite two-level system after a cyclic unitary evolution. The geometric representation of the two particle Hilbert space makes use of Hopf fibrations. It allows for a simple description of the dynamics of the entangled state's phase during the whole evolution. The global phase after a cyclic evolution is always an entire multiple of $\ensuremath{\pi}$ for all bipartite states, a result that does not depend on the degree of entanglement. There are three different types of phases combining themselves so as to result in the $n\ensuremath{\pi}$ global phase. They can be identified as dynamical, geometrical, and topological. Each one of them can be easily identified using the presented geometric description. The interplay between them depends on the initial state and on its trajectory, and the results obtained are shown to be in connection to those on mixed state phases.