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International Journal of Quantum Information

PAIRWISE ENTANGLEMENT DYNAMICS OF A MULTIPARTITE SYSTEM IN THE TAVIS–CUMMINGS MODEL

Feng Han, Yun‐Jie Xia

Published Oct 1, 2009• 3 citations
Publisher

Abstract

The pairwise entanglement dynamics in a multipartite system consisting of three two-level atoms A, B, C and a single-mode cavity field a is studied via negativity. Three atoms are arranged in such a way that atoms BC are embedded in and locally interact with the cavity while atom A is located in a spatially separate place outside of the cavity. Initially, atom-pair AB is prepared in a Bell-like state while atom C in a superposition of ground and excited state, |gC〉 and |eC〉. It shall be shown that all the pairwise negativities of the total system including atoms and cavity undergo qualitatively different evolutions. The so-called entanglement sudden death is observed for atom-pair AB under certain conditions and the entanglement transfer among all the possible degrees of freedom of the whole system is also discussed.

DOI
10.1142/s0219749909005821

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The pairwise entanglement dynamics in a multipartite system consisting of three two-level atoms A, B, C and a single-mode cavity field a is studied via negativity. Three atoms are arranged in such a way that atoms BC are embedded in and locally interact with the cavity while atom A is located in a spatially separate place outside of the cavity. Initially, atom-pair AB is prepared in a Bell-like state while atom C in a superposition of ground and excited state, |gC〉 and |eC〉. It shall be shown that all the pairwise negativities of the total system including atoms and cavity undergo qualitatively different evolutions. The so-called entanglement sudden death is observed for atom-pair AB under certain conditions and the entanglement transfer among all the possible degrees of freedom of the whole system is also discussed.
We have studied entanglement evolution and transfer in a double Tavis-Cumming model where two pairs of entangled two-level atoms AB and CD interact with two single-mode cavity fields a and b. We show that the Bell-like initial state of atoms AB can exhibit entanglement sudden death which should be independent of the initial entanglement of atoms CD. Also, we show that the initial entanglement of one atomic pair can be transferred into another pair, as well as the possible subsystems, that become entangled during evolution.
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.
The article studies the dynamics of pairwise entanglement of three qubits, two of which are trapped in a resonator and interact with a single-mode ideal resonator through single-photon transitions, and the third qubit is outside the resonator. This takes into account the dipole-dipole coupling between the isolated qubit and the qubit in the resonator. We have found a solution to the quantum nonstationary Schrodinger equation for the total wave function of the system for the initial separable and biseparable states of qubits and the thermal initial state of the resonator field. Using these solutions, the criterion of entanglement of qubit pairs - negativity is calculated. The results of numerical simulation of the negativity criterion have shown that the including of a small dipole-dipole coupling between an isolated and one of the trapped qubits can lead to significant entanglement of qubit pairs for all initial states. There is a transition of entanglement from one pair of atoms to other pairs of atoms during the evolution of the system. It is also shown that for some separable and biseparable states, the dipole-dipole interaction can suppress the effect of sudden death of entanglement.
A double Tavis-Cummings model (DTCM) is developed to simulate the entanglement dynamics of realistic quantum information processing where two entangled atom-pairs AB and CD are distributed in such a way that atoms AC are embedded in a cavity a while BD are located in another remote cavity b .T he evolutions of different types of initially shared entanglement of atoms are studied under various initial states of cavity fields. The results obtained in the DTCM are compared with that obtained in the double Jaynes- Cummings model (DJCM) (M. Yonac, T. Yu, J.H. Eberly, J. Phys. B40, S45 (2007)) and an interaction strength theory is proposed to explain the parameter domain in which the so-called entanglement sudden death occurs for both the DTCM and DJCM.
In this work, we have studied the dynamics of entanglement of two identical superconducting qubits resonantly interacting with the one-mode field of a coplanar microwave cavity without loss through single-photon transitions in the presence of third- and fifth-order nonlinearities. Based on the solution of the equation of evolution of the system for the Fock initial states of the cavity field, the criterion of qubits entanglement negativity is calculated. The results of the negativity calculation show that for the initial separable states, the cavity nonlinearity can lead to a significant increase in the maximum degree of qubit entanglement. It is shown that for the initial entangledstates of qubits and intense cavity fields, taking into account nonlinearities leads to stabilization of the degree of entanglement of qubits in the cavity and contributes to the disappearance of the effect of the entanglement sudden death of qubits.