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Brazilian Journal of Physics

Effects of noise on entanglement dynamics in atom-field interactions

Hünkar Kayhan

Published Sep 1, 2008• 5 citations
Publisher

Abstract

The entanglement dynamics in a system of the interaction of an atom with a single-mode cavity field in the presence of noise is studied by the Jaynes-Cummings model. Random phase telegraph noise is considered as the noise in the interaction and an exact solution to the model under this noise is obtained. The obtained solution is used to investigate the entanglement dynamics of the atom-field interaction. The mutual entropy is adopted for the quantification of the entanglement in the interaction. It is found that the entanglement is a non monotonic function of the intensity of the noise. The degree of the entanglement decreases to a minimum value for an optimal intensity of the noise and then increases for a sufficiently large intensity.

DOI
10.1590/s0103-97332008000300004

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The entanglement dynamics in a system of the interaction of an atom with a single-mode cavity field in the presence of noise is studied by the Jaynes-Cummings model. Random phase telegraph noise is considered as the noise in the interaction and an exact solution to the model under this noise is obtained. The obtained solution is used to investigate the entanglement dynamics of the atom-field interaction. The mutual entropy is adopted for the quantification of the entanglement in the interaction. It is found that the entanglement is a non monotonic function of the intensity of the noise. The degree of the entanglement decreases to a minimum value for an optimal intensity of the noise and then increases for a sufficiently large intensity.
In this paper, a system consisting of one atom coupled to two identical optical cavities in a stochastic interaction is investigated for the entanglement properties between the constituents by the Jaynes–Cummings model. The noise is considered to be the random phase telegraph noise and an exact solution of the model under this noise is obtained. The effects of the noise on the entanglement of the system reveal that the genuine three-partite entanglement cannot appear in the evolution of the system even in the presence of the random phase telegraph noise. The fields and the atom do not entangle with each other. However, the noise is cooperative and constructive in building a strong steady state field–field entanglement. Therefore, the separable state of the atom plays the role of a catalyst in the entanglement between the states of the cavity fields.
We consider an application of the Burshtein equation to Jaynes–Cummings interactions possessing a field-noise modeled as the two-state random phase telegraph noise in the presence of two extra physical cases. These cases are the incorporation of respectively, (i) the atomic-noise regarded as phase damping and (ii) the Stark shift. We obtain the exact solutions to these systems to investigate the dynamical behavior of their entanglements. We observed those for the case (i), phase damping does not affect the field-noise-induced nonmonotonic behavior of the entanglement other than the amplitude of the entanglement and the optimal value of the mean dwell time at which the minimum entanglement occurs. Also, phase damping naturally accelerates the decoherence of the entanglement caused by the field-noise. For the case (ii), the Stark shift reduces the maximum value of the entanglement and induce more oscillations of the entanglement in time under the influence of the noise. This shift delays the time for the complete destruction of the entanglement and restrains the influence of the noise. We also consider the time-average of the entanglement as depending on the shift parameters. The average entanglement is a nonmonotonic function of these parameters.
The Jaynes-Cummings model of a two-level atom interacting with a single quantized mode of radiation field is generalized to include the effects of stochastic fluctuations in the atom-field coupling. The coupling coefficient is assumed to fluctuate either in phase or in frequency. The fluctuations are modeled by binary random telegraph processes. Invoking the Markovian property of the telegraph noise, we derive in these two cases an equation for the density operator averaged over the distribution of fluctuations. The solution of this equation is used to study the resulting decoherence effects in the dynamical behavior of the atom and the statistical properties of the field.
In this study, we continue to consider stochastic processes in the atom‐field interaction for two atoms‐two fields interaction subject to random phase telegraph noise. An exact solution to the system is obtained by Jaynes‐Cumming Model to study the entanglement properties of the three‐partite entanglement of two atoms‐field sub‐system. The fidelity is adopted to evaluate the entanglement properties. We observe that two atoms‐field subsystem interaction does not entangle under the noise.
The Jaynes-Cummings model of a two-level atom interacting with a single quantized mode of radiation field is generalized to include the effects of stochastic phase fluctuations in the atom-field coupling coefficient. The fluctuations are modelled by random telegraph process and an equation for the density operator averaged over the distribution of fluctuations has been obtained. The solution of this equation is used to study the resulting decoherence effects in the dynamical behaviour of the atom and the statistical properties of the field.
The effects of a chaotic field on the entanglement dynamics in a system of interaction of a two-level atom with a single-mode cavity field prepared in a Glauber–Lachs state were investigated in the framework of the Jaynes–Cummings model. We found that the entanglement is a non-monotonic function of the ratio of the mean numbers of thermal photons and coherent photons or, equivalently, the degree of initial mixedness of the system. There is an optimal value of this ratio up to which thermal photons contribute increasingly to the entanglement and after which they weaken the strength of the entanglement.