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Saratov Fall Meeting: Laser Physics, Photonic Technologies, and Molecular Modeling

Entanglement in Tavis-Cummings model with Kerr nonlinearity induced by a thermal noise

Eugene K. Bashkirov

Published May 4, 2021• 8 citations
Publisher

Abstract

In this paper, we investigated the entanglement dynamics between two superconducting qubits interacting with a thermal one-mode field of lossless cavity with the Kerr media. We obtained the exact solution for time- dependent density matrix and calculated on its basis the qubi-qubit entanglement parameter-negativity. The results show that Kerr nonlinearity greatly affected the entanglement behaviour. More interestingly, that initial qubits coherence greatly enhances the degree of entanglement in the presence of the Kerr medium.

DOI
10.1117/12.2588673

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In this paper, we investigated the entanglement dynamics between two dipole-coupled qubits not-resonantly interacting with a thermal one-mode field of lossless cavity with Kerr media. We obtained the exact solution for time-dependent density matrix and calculated on its basis the qubit-qubit entanglement parameter – negativity. The results show that Kerr nonlinearity greatly affected the entanglement behavior. More interestingly, that for initial entangled qubits states Kerr media avoids the entanglement sudden death effect.
We obtained a solution of the Liouville equation for a system of three identical qubits interacting without detuning with a thermal field of a cavity with a Kerr medium, for two type of initial pure genuine W-entangled qubits states. On its basis, three entanglement parameters: fidelity, tangle and pairwise negativities were calculated. We obtained that sudden death of entanglement takes place for large intensities of the cavity thermal noise for all considered W-states. We also showed that Kerr nonlinearity prevents the destruction of the initial qubits entanglement induced by the thermal noise of the cavity and eliminates the sudden death of 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.
The system consisting of two identical artificial atoms (qubits), resonantly interacting with the mode of quantum field of an ideal microwave cavity in the presence o Abstract The system consisting of two identical artificial atoms (qubits), resonantly interacting with the mode of quantum field of an ideal microwave cavity in the presence of Kerr nonlinearity, is considered. For the considered model, an exact solution of the quantum Liouville equation for the full density matrix of the system two qubits + resonator field mode is obtained. To solve the quantum equation of evolution, the representation of dressed states, that is, the eigenfunctions of the Hamiltonian, was used. A complete set of dressed states of the considered model is found. With its help, the solution of the evolution equation was initially found for coherent initial states of qubits and Fock states of the field, that is, states with a certain number of photons in the resonator mode. Then, the above solution was generalized to the case of the thermal state of the resonator field. A reduced density matrix of two qubits is found by averaging over the field variables. The two-qubit density matrix is used to calculate the parameter of qubit entanglement in the analytical form. Concurrence was chosen as a quantitative criterion for qubit entanglement. A numerical simulation of the time dependence of the consistency of qubits for various parameters of the model and the initial states of qubits was carried out. The most interesting result seems to be that taking into account the initial coherence of qubits in the model with Kerr nonlinearity leads to a significant increase in the maximum degree of entanglement of qubits induced by the thermal field, even in the case of high intensities of the resonator field. f Kerr nonlinearity, is considered. For the considered model, an exact solution of the quantum Liouville equation for the full density matrix of the system two qubits + resonator field mode is obtained. To solve the quantum equation of evolution, the representation of dressed states, that is, the eigenfunctions of the Hamiltonian, was used. A complete set of dressed states of the considered model is found. With its help, the solution of the evolution equation was initially found for coherent initial states of qubits and Fock states of the field, that is, states with a certain number of photons in the resonator mode. Then, the above solution was generalized to the case of the thermal state of the resonator field. A reduced density matrix of two qubits is found by averaging over the field variables. The two-qubit density matrix is used to calculate the parameter of qubit entanglement in the analytical form. Concurrence was chosen as a quantitative criterion for qubit entanglement. A numerical simulation of the time dependence of the consistency of qubits for various parameters of the model and the initial states of qubits was carried out. The most interesting result seems to be that taking into account the initial coherence of qubits in the model with Kerr nonlinearity leads to a significant increase in the maximum degree of entanglement of qubits induced by the thermal field, even in the case of high intensities of the resonator field.