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Journal of Computational and Theoretical Nanoscience

Numerical Investigation of Phase Space Entropy for a Quantum System in Kerr Medium Under Cavity Damping Effects

Bothayna S. H. Kashkari, S. Abdel‐Khalek

Published Aug 1, 2017• 0 citations
Publisher
DOI
10.1166/jctn.2017.6700

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Analytical description for a Su(2)-quantum system interacting with a damped Su(1, 1)-cavity, which is filled with a non-linear Kerr medium, is presented. The dynamics of non-classicality of Su(1, 1)-state is investigated via the negative part of the Wigner function. We show that the negative part depends on the unitary interaction and the Kerr-like medium and it can be disappeared by increasing the dissipation rate and the detuning parameter. The phase space information of the Husimi function and its Wehrl density is very sensitive not only to the coupling to the environment and the unitary interaction but also to the detuning as well as to the Kerr-like medium. The phase space information may be completely erased by increasing the coupling to the environment. The coherence loss of the Su(2)-state is investigated via the Husimi Wehrl entropy. If the effects of the detuning parameter or/and of the Kerr-like medium are combined with the damping effect, the damping effect of the coupling to the environment may be weaken, and the Wehrl entropy is delayed to reach its steady-state value. At the steady-state value, the phase space information and the coherence are quickly lost.
We study the interaction of a three-level atom with a one-mode cavity field in the presence of a Kerr-like medium. The atom is initially prepared in a momentum eigenstate and the field in the squeezed state. We obtain the constants of motion and the wavefunction for the atomic system of Λ-configuration. Also, we calculate the momentum increment, the momentum diffusion and the field entropy. The analytic results are employed to perform some investigations of the temporal evolution of the momentum increment and the field entropy. The effect of the detuning and the Kerr-like medium is analysed. The results show that the effect of the detuning and/or the Kerr-like medium changes the quasi-period of both the momentum increment and the field entropy evolution and entanglement between the atom and the field. Conclusions and discussion are given and illustrated by numerical results.
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.