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arXiv:1607.00126 · Journal of Physics B Atomic Molecular and Optical Physics

Dynamics and protecting of entanglement in two-level systems interacting with a dissipative cavity: the Gardiner–Collett approach

Alireza Nourmandipour, M K Tavassoly

Published Jul 8, 2015• 30 citations
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Abstract

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.

DOI
10.1088/0953-4075/48/16/165502

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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.
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.
We present analytical results on entanglement and decoherence in a system of N strongly driven two-level atoms resonantly coupled to a dissipative cavity mode. In the specific cases of N = 3 and 4 qubits we show the existence of decoherence-free subspaces for the whole system and/or the atomic subsystem and we discuss examples where a multipartite qubit entanglement remains preserved. Also we illustrate the conditional preparation of cat-like states of the cavity field and the generation of atomic correlations.
The entanglement dynamics of two two-level atoms which are respectively trapped in two independent dissipative single-mode cavities and strongly driven by the classical fields is investigated analytically utilizing the super operator method.It is found that the entanglement is not related to the initial value of the cavity coherent states.The driving field enhances the entanglement sudden death for small dissipation of the cavity,while it protects the entanglement from sudden death for large dissipation in the presence of strong driving field.These results show that even in the bad cavity(with large decay rate),the entanglement can be free from sudden death with the assistance of classical driving field.
An open quantum bipartite system consisting of two independent two-level atoms interacting nonlinearly with a two-mode electromagnetic cavity field is investigated by proposing a suitable non-Hermitian generalization of the Hamiltonian. The mathematical procedure of obtaining the corresponding wave function of the system is clearly given. Pancharatnam phase is studied to give a precise information about the required initial system state, which is related to artificial phase jumps, to control the degree of entanglement (DEM) and get the highest concurrence. We discuss the effect of time-variation coupling, and dissipation of both atoms and cavity. The effect of the time-variation function appears as frequency modulation (FM) effect in the radio waves. Concurrence rapidly reaches the disentangled state (death of entanglement) by increasing the effect of field decay. On the contrary, the atomic decay has no effect.
The entanglement between two two-level atoms (qubits) interacting not-resonantly with a one mode of thermal field in a lossless cavity via effective degenerate two-photon transitions is investigated. Based on the exact solution for the time-dependent density matrix of the system under consideration, negativity is calculated as a measure of the entanglement of atoms. The influence of a detuning on the dynamics of entanglement of atoms for separable and entangled initial atomic states and thermal cavity state is investigated.