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Nonclassical Atomic System Dynamics Time-dependently Interacts With Finite Entangled Pair Coherent Parametric Converter Cavity Fields

Abdelrahman Mohamed, Eied Mahmoud Khalil, Mahmoud Youssef Abd‐Rabbou

Published Feb 19, 2021• 1 citation
Publisher

Abstract

Abstract We consider a time-dependent model that describes a qubit time-dependently interacts with a cavity containing finite entangled pair coherent parametric converter fields. The dynamics of some quantum phenomena, as: phase space information, quantum entanglement and squeezing, are explored by atomic Husimi function, atomic Wehrl entropy, variance, and entropy squeezing. The influences of the unitary qubit-cavity interaction, the difference between the two-mode photon numbers, the initial atomic coherence, and the time-dependent qubit location are investigated. It is found that the regularity, the amplitudes and the frequency of the quantum phenomena can be controlled by the physical parameters. For the initial atomic pure state, the qubit-cavity entanglement, the qubit phase space information, and atomic squeezing can be generated strongly compared to those of the initial atomic mixed state. The time-dependent location parameters enhance the generated quantum phenomena, and its effect can be enhanced by the parameters of the two-mode photon numbers and the initial atomic coherence.

DOI
10.21203/rs.3.rs-211029/v1

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In this manuscript, the phenomenon of time dependence is treated using the integral property of a model consisting of interaction of an atom with a cavity in which a bi-mode field of an amplifier type. The exact solution is obtained through the Schrodinger equation, followed by the wave function characteristic of the proposed system. The effect of both the deformed pair coherent states and the time dependence on some statistical quantities are studied. The phenomena of revival and collapse are studied by computing the atomic inversion. Moreover, the entanglement between the parts of the quantum system is studied, and the periods of squeezing are determined by entropy squeezing and variance squeezing. The results are also compared and statistical quantities linked together.
In this paper, we study the interaction between the time-dependent field and a two-level atom with one mode electromagnetic field. We consider that the field of photons is assumed to be coupled with modulated coupling parameter which depends explicitly on time. It is shown that the considered model can be reduced to a well-known form of the time-dependent generalized Jaynes–Cummings model. Under special initial conditions, in which the atom and the field are prepared in the excited and the coherent states, respectively, the explicit time evolution of the wave function of the entire system is analytically obtained. Our proposal has many advantages over the previous optical schemes and can be realized in several multiple experiments, such as trapped ions and quantum electrodynamics cavity. The influence of the time-dependent field parameter on the collapses-revivals, the normal squeezing of the radiation, the anti-bunching of photons and the entanglement phenomena for the considered atomic system is examined. The linear entropy, the von Neumann entropy are used to quantify entanglement in the quantum systems. We noticed that these phenomena are affected by the existence of both the time-dependent coupling field and detuning parameters.
The influence of chaotic behavior of coherent state (CS) parameters on entanglement dynamics in system of two level atoms and photons in cavity is investigated. The initial state of the system is chosen as factorized production of photon and atomic coherent states. To find a solution of the Schrödinger equation, we presented the time-dependent wave function in the form of a wave packet in CS representation. The phase portraits and Poincare sections for classical dynamics of CS were computed, and time dependence of the mean number of photons level populations and atomic entropy were calculated in quantum case. The analysis showed that the chaotic behavior in quantum-optical Dicke model increases the degree of entanglement in the atomic subsystem. At the same time greater entanglement is generated when selecting the initial atomic CS parameters near the center of the corresponding Poincare sections. It is considered dynamics of two identical two-level atoms in non-ideal cavity (nonideal Tavis-Cummings model). Accounting for decay showed that the generation of atomic entanglement is accompanied by the return of the initial separable state (”death” of entanglement), but this behavior with the increase of the initial parameter of the field CS is only at sufficiently small times. Influence of detuning and damping constants are considered.
A quantum optics model is considered where the cavity field interacts with two coupled atoms. The time-dependent wave function is obtained and used to derive the density matrix from which we discussed some statistical properties for the present system. The atom-atom entanglement, atoms-cavity entanglement, entropy and variance squeezing, the Pegg-Barrnet phase and the fidelity are discussed with the effects of the initial conditions, atom-atom coupling and the detuning parameter displayed. It is shown that an increase in the value of the atom-atom coupling parameter leads to an increase in the degree of entanglement. Numerical results show that under some conditions the phenomena of entanglement and the collapses and the revivals emerge. Nonclassical properties are demonstrated by means of the field quantum statistical characteristics, such as photon-number distribution, Husimi, Wigner and Glauber-Sudarshan quasidistributions and the corresponding variances.