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Vestnik of Samara University Natural Science Series

Dynamics of atom-atom entanglement in two-atom model with degenerate two-photon raman transitions

A. Othman, Eugene K. Bashkirov

Published Apr 24, 2024• 0 citations
Publisher

Abstract

The exact dynamics of a model consisting of two two-level atoms interacting with the electromagnetic field mode of an ideal resonator through degenerate Raman transitions are found for coherent and thermal field states. The exact solution is used to calculate atom-atom negativity. It is shown that for separable initial states of atoms, their interaction with the resonator field does not lead to the occurrence of atom-atom entanglement. It was found that for the Bell initial states of atoms in the case of a coherent resonator field, the effect of sudden death of entanglement takes place for large average values of the number of photons in the resonator, while in case of thermal noise, this effect is absent for any intensities of the resonator field.

DOI
10.18287/2541-7525-2024-30-1-112-121

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The exact dynamics of a model consisting of two two-level atoms interacting with the electromagnetic field mode of an ideal resonator through degenerate Raman transitions are found for coherent and thermal field states. The exact solution is used to calculate atom-atom negativity. It is shown that for separable initial states of atoms, their interaction with the resonator field does not lead to the occurrence of atom-atom entanglement. It was found that for the Bell initial states of atoms in the case of a coherent resonator field, the effect of sudden death of entanglement takes place for large average values of the number of photons in the resonator, while in case of thermal noise, this effect is absent for any intensities of the resonator field.
An exact solution of the problem of two two-level atoms with degenerate Raman two-photon transitions interacting with one-mode coherent or thermal radiation field in cavity is presented. Asymptotic solution for system state vector is obtained in the approximation of large initial coherent fields. The atom-field is investigated on the basis of the reduced atomic entropy dynamics. The possibility of the system being initially in a pure disentangled state to revive into this state during the evolution process is shown. Conditions and times of disentanglement are derived. The atom-atom entanglement is investigated with using negativity. The possibility of sudden death and birth of atom-atom entanglement is predicted for a coherent field with large mean photon numbers.
In this paper, we investigate the entanglement between two two-level atoms non-resonantly in-teracting with a thermal field of a lossless one-mode resonator via degenerate two-photon transi-tions. On the basis of the exact solution of the time-dependent density matrix we calculate the negativity as a measure of atomic entanglement. We show that for separable initial atomic states a slight atom-field detuning may generate the high amount of atom-atom entanglement. The re-sults also show that for non-resonant atom-field interaction the entanglement induced by nonlin-ear two-photon interaction is smaller than that induced by one-photon interaction in contrast to the resonant interaction situation. For a Bell-type entangled initial atomic state we obtain that if the detuning increases, there is an appreciable decrease in the amplitudes of the negativity oscilla-tions. The results also show that elimination of the sudden death of entanglement for non-resonant two-photon atom-field interaction may take place.
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.
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.
The exact dynamics of a model consisting of two identical qubits interacting non-resonantly with the electromagnetic field mode of an ideal resonator via single-photon transitions is found in the presence of direct Ising interaction of qubits. The exact solution is used to calculate the two-qubit negativity of qubits in the case of a coherent initial state of qubits and a thermal state of the resonator field. It is shown that in the case of resonant interaction of qubits with the field, the initial atomic coherence leads to a significant increase in the maximum degree of entanglement. The inclusion of direct Ising interaction of qubits can significantly enhance the entanglement of qubits in both coherent and non-coherent initial states of qubits. In the case of non-resonant interaction of qubits and the resonator field, the detuning leads to a weakening of the effect of atomic coherence on the dynamics of qubit entanglement.
The entanglement between two qubits not-resonantly interacting with a single-mode field of an ideal resonator with Kerr media via degenerate two-photon transitions was studied. The exact solution for time-dependent density matrix and calculated on its basis the qubit-qubit entanglement parameter - negativity was derived. The results showed that Kerr media and detuning dramatically affected the entanglement behavior. More interestingly, that for initial entangled qubits states Kerr media and detuning avoids the entanglement sudden death effect.