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Progress of Theoretical Physics

Quantum Decoherence and Entanglement Induced by Nonlinear Dissipative Environment

H. A. Hessian

Published Apr 1, 2012• 2 citations
Publisher

Abstract

The analytical description of the dynamics of a nonlinear atom-field system described by a diagonal f -deformed Jaynes-Cummings model for a chosen initial state is obtained. The purity loss of the global system, and the atomic and field subsystems are discussed. Information on entanglement between the field and matter is studied by comparing the results for mutual entropy, which is a measure of the total correlation, and the negativity as a measure of the amount of entanglement. It is found that the nonlinearity of the dissipation tends to accelerate the decoherence of the global, field, and atomic states. In addition, we find that the so-called entanglement sudden death can occur when both of the nonlinearity couplings between the cavity field and the dissipation are combined. Subject Index: 061

DOI
10.1143/ptp.127.631

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The analytical description of the dynamics of a nonlinear atom-field system described by a diagonal f -deformed Jaynes-Cummings model for a chosen initial state is obtained. The purity loss of the global system, and the atomic and field subsystems are discussed. Information on entanglement between the field and matter is studied by comparing the results for mutual entropy, which is a measure of the total correlation, and the negativity as a measure of the amount of entanglement. It is found that the nonlinearity of the dissipation tends to accelerate the decoherence of the global, field, and atomic states. In addition, we find that the so-called entanglement sudden death can occur when both of the nonlinearity couplings between the cavity field and the dissipation are combined. Subject Index: 061
We give a fully analytical description of the dynamics of an atom dispersively coupled to a field mode in a dissipative environment fed by an external source. The competition between the unitary atom field (which leads to entanglement) and the dissipative field-environment couplings are investigated in detail. We find the time evolution of the global atom-field system for any intial state and we show that the atom-field steady state is, at most, classically correlated. For a chosen initial state, we evaluate the purity loss of the global system and of atomic and field subsystems as a function of time. We find that the source will tend to compensate for the dissipation of the field intensity and to accelerate decoherence of the global and atomic states. A result pertinent to quantum information is the quantification of concurrence during the dissipative dynamics. An analytical expression for the time evolution of the concurrence is given.
We give a fully description of the dynamics of an atom dispersively coupled to a field mode in a dissipative environment fed by an external source. The competition between the unitary atom-field (which leads to entanglement) and the dissipative field-environment couplings are investigated in detail. We find the time evolution of the global atom-field system for any initial state and we show that atom-field steady state is at most classically correlated. For an initial state chosen, we evaluate the purity loss of the global system and of atomic and field subsystems as a function of time. We find that the source will tend to compensate for the dissipation of the field intensity and to accelerate decoherence of the global and atomic states. Moreover, we show that the degree of entanglement of the atom-field state, for the particular initial state chosen, can be completely quantified by concurrence. Analytical expression for time evolution of the concurrence is given.
The full quantum theory is applied to the investigation of the entanglement between atom and field and the losses of coherence of the total system and its subsystems in the Jaynes-Cummings model with a Kerr medium.Linear entropies of the system,the atom and the field are calculated under the assumptions of dispersive atom-field interaction and initial coherent field states.The results show that the coherence loss of the atom is independent of the Kerr effect,the coherence loss of the system and that of the field are enhanced by the presence of the Kerr medium,and the entanglement between atom and field is suppressed by the medium.The time evolution of field entropy is affected by the cavity dissipation qualitatively as well as quantitatively.Only through cavity dissipation can the influence of Kerr effect on field entropy exhibit.
The quantum dynamics of two weakly coupled nonlinear oscillators is analytically and numerically investigated in the context of nonlinear dissipation. The latter facilitates the creation and preservation of nonclassical steady states. Starting from a microscopic description of two oscillators individually interacting with their dissipative environments, it is found that in addition to energy relaxation, dephasing arises due to the mutual coupling. Using the negativity as an entanglement measure, it is shown that the coupling entangles the oscillators in the long-time limit. For finite temperatures, entanglement sudden death and rebirth are observed.
The entanglement dynamics of system, where atoms A and B interact with single mode cavity fields a and b respectively, is studied. The interaction between atom A and cavity a may be described by using the typical Jaynes–Cummings model, while that between the atom B and cavity b filled with a Kerr medium is of a two-photon process. For a certain initial atom entanglement state, there is an entanglement sudden death effect between the two atoms. The Kerr medium in the cavity b can effectively prevent the undesirable entanglement sudden death from occurring. Also, from the viewpoint of the population dynamics, we discuss why the Kerr medium can do so.
An analytical solution is found for the master equation of a system described by a nonlinear Jaynes–Cummings model, in the presence of nonlinear quantum dissipation at zero temperature in the large detuning approximation. We study the influence of nonlinear quantum dissipation on the output entanglement dynamics of the atom–field system, considering the field to be initially in SU (1, 1) coherent states. It is found that in the presence of the nonlinear quantum dissipation, the amplitude of the output entanglement between the field and the atom decreases with time, however the entanglement between the field–atom system and the environment increases with time.