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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Dynamics of two N-level atoms (N=2, 3) in nonideal cavities

Sergey N. Agapov, Alexander V. Gorokhov

Published Apr 14, 2017• 0 citations
Publisher

Abstract

We investigated numerically the time-dependent behavior of atoms populations and mean number of photons in cavities with losses. To derive the dynamic equations, we used the method of oscillator and atomic coherent states. We also took into account the various locations of the atoms in the cavity and their movement through the cavity. The losses of photons in the cavities were considered in the Wigner-Weisskopf approximation.

DOI
10.1117/12.2267954

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We investigated numerically the time-dependent behavior of atoms populations and mean number of photons in cavities with losses. To derive the dynamic equations, we used the method of oscillator and atomic coherent states. We also took into account the various locations of the atoms in the cavity and their movement through the cavity. The losses of photons in the cavities were considered in the Wigner-Weisskopf approximation.
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The Jaynes-Cummings model (JCM) of two-level atom interacting with the photon mode in ideal cavity plays an essential role in modern quantum optics. In previous papers 1,2 an exact form of density matrix of the JCM with fixed atom position and photons dissipation was found. Here, taking into account the classical motion of the atom through the cavity, it is considered a case of nonideal cavity with zero temperature. We have obtained an exact expression for density matrix and calculated photon spectra and spectra of the mean number of photons in a cavity and and time dependencies of some values relevant for the one-atom maser theory.
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.