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Computer Optics

Thermal entanglement in the three-qubit Tavis-Cummings model with Kerr nonlinearity

Alexander R. Bagrov, Eugene K. Bashkirov

Published Feb 1, 2025• 3 citations
Publisher

Abstract

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.

DOI
10.18287/2412-6179-co-1544

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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.
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.
In this paper, a three-qubit Tavis-Cummings model with two independent lossless single-mode resonators is considered. It is assumed that the initial states of the resonator fields are thermal fields and the qubits are in genuine entangled W- and GHZ-type states. For the model under study and the specified initial states of the resonator fields and qubits, we have exactly solved the quantum Liouville equation for the full density matrix. The full density matrix was used to calculate the entanglement parameters - negativity and fidelity. The computer simulation results showed that in the investigated model, the entanglement for all initial qubit states breaks down rapidly with increasing intensity of the thermal fields of the resonators compared to the previously investigated three-qubit models. Moreover, a sudden death of entanglement is observed even for vacuum resonator fields.
In this article, we consider the entanglement between three identical qubits resonantly interacting with a thermal field of an Q-infinite resonator. We derived the exact solution of the evolution equation for density matrix of the considered system. On it basis we calculate the negativity as a criteria of entanglement between pairs of qubits for biseparable and entangled W-type states of qubits. The results showed that for considered initial qubits states the effect of the entanglement sudden death occurs for all values of the average number of thermal photons.
Abstract An exact solution for the evolution operator of the multiphoton three-qubit Tavis–Cummings model was found. On this basis, the entanglement dynamics and the phenomenon of entanglement sudden death for entangled initial W-, GHZ-, and GHZ-like qubit states and the thermal state of the resonator were studied by means of pairwise negativity and fidelity. The results of entanglement parameters calculations showed that in the nonlinear multiphoton processes, the atomic entanglement is stronger than in the linear one-photon process. We also obtained that the so-called sudden death phenomenon occurs only for some kind of initial qubit states and some thermal noise intensities, i.e. the phenomenon is sensitive to the initial conditions. The length of the time interval for the zero entanglement is dependent on not only the initial qubit states but also the photon transition multiple. We also showed that for large values of the multiple, only one W-type initial state and one GHZ-like initial state are the long-lived and maximally persistent and robust states.
In this article, we have studied the entanglement dynamics of three identical qubits (natural or artificial two-level atoms) resonantly interacting with the one mode of the thermal field of a microwave lossless resonator via one-photon transitions. An exact solution of the quantum time Schrodinger equation is found for the total wave function of the system for the initial separable and entangled states of qubits and the Fock initial state of the resonator. On the basis of this solution, an exact solution of the quantum Liouville equation for the total time-dependent density matrix of the system in the case of a thermal field of the resonator is constructed. The exact solution for the full density matrix is used to calculate the criterion of entanglement of pairs of qubits negativity. The resultsof numerical simulation of the time dependence of the negativity of pairs of qubits showed that with an increase in the intensity of the thermal resonator field, the degree of entanglement of pairs of qubits decreases. It is also shown that In the model under consideration, for any initial states of qubits and intensities of the thermal field of the resonator, the effect of sudden death of entanglement takes place. This behavior of the entanglement parameter in the model under consideration differs from that in the two-qubit model. For two-qubit model, the effect of the sudden death of entanglement takes place only for the initial entangled states of qubits and intense thermal fields of the resonator.
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.