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Bulletin of the Russian Academy of Sciences Physics

Atom–Atom Entanglement in a Nonresonant Two-Photon Tavis–Cummings Model

Maria O. Guslyannikova, Eugene K. Bashkirov

Published Mar 1, 2020• 4 citations
Publisher

Abstract

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.

DOI
10.3103/s1062873820030107

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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.
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 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.
In this article, author investigated the dynamics of entanglement of two dipole-coupled natural or artificial two-level atoms (qubits) interacting nonresonantly with the intensive one-mode cavity thermal field. Author found an exact solution of the quantum Liouville equation for the full density matrix of the system two atoms + field mode for a coherent initial state of atoms in the dressed states representation. The full system density matrix is used to calculate the two-atom reduced density matrix and to calculate the quantitative criterion for atom-atom entanglement ‒ negativity. The results of computer simulation of the time dependence of negativity showed that in the case of a model with nonresonant interaction, the presence of initial atomic coherence leads to a significant decrease in the maximum degree of atomic entanglement, in contrast to the model with resonant interaction of atoms and a field. For the resonance model, the initial atomic coherence greatly enhances the degree of atomic entanglement.