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

Exact solution of damped Cummings-Tavis model and entanglement

Alexander V. Gorokhov, I. E. Sinaysky

Published Mar 3, 2008• 0 citations
Publisher

Abstract

The dynamics of two identical two-level atoms in non-ideal cavity it is considered. Using approach developed before by us for case of one two-level atom, the analytical expression for density matrix of the system is presented. Dynamics of level populations, mean number of photons and correlation function for photons are calculated. Using Peres - Horodecki criteria exact expression for entanglement dynamics of two identical two-level atoms in cavity is given. Influence of detuning and damping constants are investigated.

DOI
10.1117/12.801581

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The dynamics of two identical two-level atoms in non-ideal cavity it is considered. Using approach developed before by us for case of one two-level atom, the analytical expression for density matrix of the system is presented. Dynamics of level populations, mean number of photons and correlation function for photons are calculated. Using Peres - Horodecki criteria exact expression for entanglement dynamics of two identical two-level atoms in cavity is given. Influence of detuning and damping constants are investigated.
It is considered dynamics of two identical two-level atoms in non-ideal cavity. Using approach developed before by us for case of one two-level atom, analytical expression for density matrix of the system is presented. Dynamics of level populations, mean number of photons and correlation function for photons are considered. Using Peres-Horodecki criteria exact expression for entanglement dynamics of two identical two-level atoms in cavity is given. Influence of detuning and damping constants are considered.
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.
The entanglement between two two-level atoms (qubits) interacting not-resonantly with a one mode of thermal field in a lossless cavity via effective degenerate two-photon transitions is investigated. Based on the exact solution for the time-dependent density matrix of the system under consideration, negativity is calculated as a measure of the entanglement of atoms. The influence of a detuning on the dynamics of entanglement of atoms for separable and entangled initial atomic states and thermal cavity state is investigated.
Abstract Entanglement between two identical two-level atoms (qubits) that interact nonresonantly with the thermal field of a single-mode ideal resonator via effective degenerate two-photon transitions is studied. Based on an exact solution for the time-dependent density matrix, negativity is calculated as a measure of atom entanglement. The effect detuning between the atomic frequencies and the doubled frequency of the resonator field has on the dynamics of qubit entanglement in cases of separable and entangled initial atomic states is investigated.
A coherent dynamics of two-and three-level atoms in the ideal cavity were investigated. In particular, the investigation of the dynamics of three-level atoms (qutrits) interacting with photons in the cavity having two resonant frequencies close to the frequencies of the two allowed atomic transitions were performed. This model generalizes the well-known Tavis-Cummings model. Time dependencies of mean number of the cavity photons and level populations of atoms are computed and entanglement of atoms and photon fields states are discussed.