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Iranian Journal of Physics Research

The effect of the classical driving field on the dynamics of entanglement of two qubits interacting with two dissipative cavities

Alireza Nourmandipour

Published Jun 1, 2023• 0 citations
Publisher

Abstract

In this article, we first introduce a system consisting of two dissipative cavities, in each of which there is a two-level atom. Each of the atoms is under the influence of a classical laser field, which causes the displacement of their energy levels. The correlation between two cavities is given by the field-field interaction term. We use the Gardiner-Collet model to describe the dissipation in this research. After introducing the Hamiltonian of the system, we simplify the Hamiltonian by using the Fano technique and introducing two sets of new operators. Also, with introducing the atomic bare bases, the Hamiltonian of the system will become a solvable form. Then, by using the technique of Laplace transforms, we solve the time-dependent Schrödinger equation and find the explicit form of the system's wave function at every moment of time. Having the wave function of the atom-atom system and using the concurrence criterion, we investigate the entanglement dynamics of the system in two strong and weak interaction regimes corresponding to the non-Markovian and Markovian regimes. The results show that there will be no stable state of entanglement in this system. We will also show that the classical laser field will play a constructive role in maintaining the initial entanglement as well as the generated entanglement.

DOI
10.47176/ijpr.23.1.21652

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In this article, we first introduce a system consisting of two dissipative cavities, in each of which there is a two-level atom. Each of the atoms is under the influence of a classical laser field, which causes the displacement of their energy levels. The correlation between two cavities is given by the field-field interaction term. We use the Gardiner-Collet model to describe the dissipation in this research. After introducing the Hamiltonian of the system, we simplify the Hamiltonian by using the Fano technique and introducing two sets of new operators. Also, with introducing the atomic bare bases, the Hamiltonian of the system will become a solvable form. Then, by using the technique of Laplace transforms, we solve the time-dependent Schrödinger equation and find the explicit form of the system's wave function at every moment of time. Having the wave function of the atom-atom system and using the concurrence criterion, we investigate the entanglement dynamics of the system in two strong and weak interaction regimes corresponding to the non-Markovian and Markovian regimes. The results show that there will be no stable state of entanglement in this system. We will also show that the classical laser field will play a constructive role in maintaining the initial entanglement as well as the generated entanglement.
Recently, strong coupling dominating dissipative and decoherence effects between the atom and a quantum cavity has been investigated experimentally. In this paper, we study the entanglement dynamics of two two-level atoms coupling to a quantum cavity where each mirror is formed by a chain of atoms trapped near a one-dimensional waveguide. We consider the effects of both Markovian dynamics and non-Markovian dynamics on the entanglement evolution of the two central atoms. Our results show that the steady entanglement can be generated between the two central atoms whether the system is under the Markov regime or non-Markov regime when the number of atoms of the atomic mirrors is finite. When the number of the atomic mirrors is large enough, the entanglement of two central atoms takes oscillating behavior without a stable value. The effect of detuning and dissipation on entanglement dynamics is also discussed and the results imply that the detuning plays an important role in improving the entanglement amplitude.
Abstract In this paper, we study the exact entanglement dynamics of two two-level atoms in a dissipative cavity. We use the Gardiner–Collett Hamiltonian to model the dissipative cavity, in which we assume that the two atoms resonantly interact with the cavity field and the cavity field itself interacts with the surrounding medium. Then, with the help of the Fano’s technique we show that this system can be regarded as two atoms interacting with a heat bath. In such a case, we find that there exists a decoherence-free state that does not evolve in time. At this time there exists a so-called super-radiant state which decays in time due to dissipation. At last, we use the quantum Zeno effect to preserve the entanglement which already has been stored in the system.
In this paper, the pairwise entanglement of two qubits in a system consists of a dissipative cavity with an arbitrary number of qubitsis investigated. To model the dissipation in this cavity, the Gardiner-Collett approach has been utilized.Theanalytical expression of the wave function of the system is obtainedby solving the time-dependent Schrodinger equation with the initial state as a superposition of single-excitation of two arbitrary qubits. Entanglement dynamics of any two qubitsfor different number of qubits and various coupling regimeshas been investigated.
Preventing quantum entanglement from decoherence effect is of theoretical and practical importance in the quantum information processing technologies. In this regard, we consider the entanglement dynamics of two identical qubits where the qubits which are coupled to two independent (Markovian and/or non-Markovian) as well as a common reservoir at zero temperature are further interacted with a classical driving laser field. Then, we study the preservation of generated two-qubit entanglement in various situations using the concurrence measure. It is shown that by applying the classical driving field and so the possibility of controlling the Rabi frequency, the amount of entanglement of the two-qubit system is improved in the off-resonance condition between the qubit and the central cavity frequencies (central detuning) in both non-Markovian and Markovian reservoirs. While the central detuning has a constructive role, the detuning between the qubit and the classical field (laser detuning) affects negatively on the entanglement protection. The obtained results show that long-living entanglement in the non-Markovian reservoir is more accessible than in the Markovian reservoir. We demonstrate that, in a common reservoir non-zero stationary entanglement is achievable whenever the two-qubit system is coupled to the reservoir with appropriate values of relative coupling strengths.
Abstract The dynamics of entanglement and quantum discord (QD) between two two-level atoms interacting with two dissipative coupled cavities in the presence of initial atom-cavity correlations is investigated. In comparison with the result of the initial factorized state, we show that the initial state contained quantum correlation of atom-cavity is most robust against the dissipative environment, and the initial atom-cavity correlations, especially the quantum correlation, play a constructive role in the generation of atomic entanglement and QD. Simultaneously, the comparison between Markovian and non-Markovian dynamics, and the influences of inter-cavity hopping rate are also taken into account and analyzed.
In this paper, we consider the entanglement dynamics of two identical qubits (two-level atoms) accompanied by dipole–dipole interaction within a common reservoir in the strong and weak coupling regimes. We suppose that the qubits move in the reservoir which is at zero temperature. Using the time-dependent Schrödinger equation, the state vector of the qubits-reservoir system is obtained by which we can evaluate the concurrence as a suitable measure of entanglement between the two qubits. The results show that by choosing special initial conditions for the qubits, a different dynamical behavior of entanglement is visible in such a way that entanglement protection occurs. Also, we find that the qubit motion in the absence of dipole–dipole interaction leads to preservation or at least more slowly decay of entanglement. However, in the presence of dipole–dipole interaction with the movement of qubits, different results can be observed which depend on the initial states of the qubits, i.e. entanglement may or may not be protected.