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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Sustainable entangled state of two qubits with time-dependent dipole-dipole interaction under coherent electromagnetic field influence

Alexander Alexandrovich Biryukov, Марк Александрович Шлеенков

Published Apr 14, 2017• 0 citations
Publisher

Abstract

In this paper we study the quantum entanglement of two identical qubits which interact with electromagnetic field and each other by time-dependent dipole-dipole interaction. We develop original method in path integral approach for numerical calculation of density matrix and Peres-Horodecki parameter (the measure of qubits entanglement). By the use of obtained equations we investigate the dependence of quantum entanglement on dipole-dipole interaction amplitude and frequency as well as qubits phase difference. The results indicate on possibility of high-entanglement states exiting and long-time non-destructive control of them.

DOI
10.1117/12.2267961

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In this paper we study the quantum entanglement of two identical qubits which interact with electromagnetic field and each other by time-dependent dipole-dipole interaction. We develop original method in path integral approach for numerical calculation of density matrix and Peres-Horodecki parameter (the measure of qubits entanglement). By the use of obtained equations we investigate the dependence of quantum entanglement on dipole-dipole interaction amplitude and frequency as well as qubits phase difference. The results indicate on possibility of high-entanglement states exiting and long-time non-destructive control of them.
We study the evolution of quantum entanglement in the model of two identical qubits interacting with a single-mode laser field. The density matrix and Peres-Horodecki parameter are calculated within the frameworks of path-integral formalism. The quantum entanglement measure is shown to be strongly dependent upon the phase difference between the laser radiation acting on each cubit. This observation may offer the possibility of quantum entanglement stationary control by varying the distance between the qubits.
Background. The study of entangled states in Jaynes–Cummings models and its multiqubit generalizations and extensions remains an important and relevant topic in modern quantum optics, quantum information science and solid state physics. This is due to the fact that such models naturally describe the dynamics of interaction of logical elements of quantum devices, such as quantum computers or quantum networks (qubits) with microwave fields of resonators used to control the states of qubits. In this regard, it is very important to search for the most efficient schemes of generation, control and monitoring of entangled qubit states within the framework of Jaynes–Cummings type models. Aim. To investigate the entanglement dynamics of a pair of qubits, each of which is locked in a single-mode resonator and interacts non-resonantly with the vacuum field mode, in the presence of detuning between frequencies of transitions in the qubits and frequencies of resonator modes and dipole-dipole interaction of the qubits. Methods. To analyze the dynamics of the considered system, the solution of the time-dependent quantum Schrödinger equation is investigated. The exact solution of the above equation in the case of entangled Bell-type initial qubits states is found. This is used to calculate the criterion of entanglement of a pair of qubits – negativity. Numerical modeling of the time dependence of negativity for different values of the parameters of the considered model has been carried out. Results. It is shown that the presence of detuning, the difference in the qubit-photon couplings and the intensity of the dipole-dipole interaction significantly affect the maximum degree of entanglement of the qubit subsystem during its evolution. It is found that for certain parameters of the model under consideration, the initial Bell entangled states of qubits can be considered as long-lived stable states. Conclusion. The possibility of realization of long-lived and robust two-qubit entangled states in the system under consideration has been established. The obtained results can be used for effective control and manipulation of the degree of entanglement of qubits interacting with microwave fields of resonators.
In this paper we have investigated the dynamics of entanglement of two identical qubits non-resonantly interacting with one mode of a vacuum or a thermal electromagnetic field in lossless cavity in the presence of a direct dipole-dipole interaction. Based on the exact solution to the equation used in this analysis, the Peres-Horodecki entanglement parameter (negativity) for qubits has been found. Numerical simulation of the negativity for various model parameters has been carried out. It has been shown that the interactions of qubits with a thermal field in a cavity can lead to their entanglement. It has been established that the detuning and dipole-dipole interaction of qubits can be used to manipulate and control the amount of atomic entanglement.
The paper studies entangled states of two qubits interacting with each other and with an electromagnetic field. The state of the qubits is determined by a statistical density matrix. The degree of entanglement of the state is characterized by the Peres-Gorodeckii (PG) parameter. The statistical density matrix and its evolution are determined in the energy representation within the framework of the path integral formalism. The obtained equations determine the dependence of the PG parameter on the parameters of qubit dipole-dipole interaction and the acting electromagnetic field. The results of numerical calculations are presented in graphs for the PG parameter. It is shown that it is possible to choose parameters corresponding to qubit states with a high degree of entanglement (0.99).
In this paper we have investigated the dynamics of entanglement of two identical qubits nonresonantly interacting with one mode of a thermal electromagnetic field in lossless resonator in the presence of a direct dipole-dipole interaction. On the basis of the exact solution of the considered model, the Peres-Horodetskii entanglement parameter (negativity) for qubits has been found. Numerical simulation of the negativity for various model parameters has been carried out. It has been shown that the interaction of qubits with the thermal field of the resonator can lead to their entanglement. It ha been established that the detuning and dipole-dipole interaction of qubits can be used to manipulate and control the degree of their entanglement.