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Chinese Physics B

Exact solution of entanglement of the double Jaynes–Cummings model without rotating wave approximation

Xuezao Ren, Jiang Dao-Lai, Cong Hong-Lu, Lei Li

Published Sep 1, 2010• 2 citations
Publisher

Abstract

This paper investigates the influences of atom-field coupling and dipole–dipole coupling for atoms on the entanglement between two atoms by means of concurrence. The results show that the sudden death occurs when the atom-field coupling is strong enough, and the collapse and the revival appear when the dipole–dipole interaction is strong enough.

DOI
10.1088/1674-1056/19/9/090309

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This paper investigates the influences of atom-field coupling and dipole–dipole coupling for atoms on the entanglement between two atoms by means of concurrence. The results show that the sudden death occurs when the atom-field coupling is strong enough, and the collapse and the revival appear when the dipole–dipole interaction is strong enough.
Applying the method of coherent-state orthogonalization expansion, the influnences of dipole-dipole interaction and the coupling strength on the entanglement between two atoms of the Tavis-Cummings model without rotating wave approximation(without-RWA) are studied. Compared with the rotating wave approximation(RWA), it is found that the entanglement of the without-RWA agree with that of RWA when the coupling strength is weak. In the strong coupling regime, the sudden death phenomena occurs. The results also show that the stronger the atom-field coupling strength is, the longer the state stays in the disentangled separable state, which means that the length of the time interval for the distanglement depends on the atom-field coupling strength. When the dipole-dipole interacton is taken into account, the entanglement of the two atoms will be enhanced with the increace of dipole-dipole interaction.
The influences of dipole-dipole interaction and detuning on the entanglement between two atoms with different initial tripartite entangled W -like states in the Tavis–Cummings model have been investigated by means of Wootters' concurrence, respectively. The results show that the entanglement between the two atoms can be enhanced via appropriately tuning the strength of dipole-dipole interaction of two atoms or the detunings between atom and cavity, and the so-called sudden death effect can be weakened simultaneously.
The atomic entanglement dynamics is studied in the double Jaynes-Cummings model composed of two coupled cavities.Effect of the cavity-cavity coupling constant A and the atomic initial states on entanglement sudden death(ESD) and entanglement sudden birth(ESB) is analysed.By studying the atomic concurrence,it was shown that when the atomic initial states are the first kind Bell-like states,ESD and ESB doesn't appear,coupling of the cavities can increase the atomic entanglement and entanglement occurs even the initial states are disentangled.When the atomic initial states are the second kind Bell-like states,the time intervals between the ESD and ESB,and whether the ESD occurs or not are controlled by the coupling constant A.The atomic entanglement can't be produced by the coupling between the cavities when the atomic initial states are disentangled and in the second kind Bell-like states.
The entanglement dynamics involving the so-called entanglement sudden death of atoms in two-photon Tavis-Cummings model is investigated.Various initial conditions that may have influences on the entanglement evolution of atoms, especially on the appearance of atomic entanglement sudden death, are studied.The appearance of entanglement sudden death is sensitive to the initial conditions of the whole system, i.e., the concrete type of atomic initial state, the photon number in the cavity field, and the dipole-dipole interaction between atoms.It is shown that the strong dipole-dipole interaction between atoms can weaken the atomic entanglement sudden death.
Extending the double Jaynes–Cummings model to a more complicated case where the mode–mode competition is considered, we investigate the entanglement character of two isolated atoms by means of concurrence, and discuss the dependence of atom–atom entanglement on the different initial state and the relative coupling strength between the atom and the corresponding cavity field. The results show that the amplitude and the period of the atom–atom entanglement evolution can be controlled by the choice of initial state and relative coupling strength, respectively. We find that the phenomenon of entanglement sudden death (ESD) is sensitive to the initial conditions. The length of the time interval for zero entanglement depends not only on the initial degree of entanglement between two atoms but also on the relative coupling strength of atom–field interaction. The ESD effect can be weakened by enhancing the mode–mode competition between the three- and single-photon processes.
In this paper, we investigate the entanglement dynamics of two entangled two-level atoms with initial X state and dipole-dipole coupling intensity in Tavis-Cummings model. The interesting phenomena of entanglement sudden death as well as sudden birth appear during the evolution process. We analyze in detail the effect of purity of initially entangled state of two atoms, the dipole-dipole coupling intensity between two atoms, and the field in the Fock state on the apparition time of entanglement sudden death and entanglement sudden birth. Furthermore, the conditions for the conversion of entanglement sudden death and entanglement sudden birth can be generalized when the initial entangled state is not pure. The results show that the above system parameters affect the concurrence, entanglement sudden birth and sudden death remarkably, the dipole-dipole coupling intensity affects amplitudes of the concurrence oscillation and leads time interval of the ESD to decrease. With the increasing of the purity, the time of entanglement sudden death and entanglement sudden birth will decrease, it is also notable that invariant and stable entanglement, which can be controlled by different initial states of the atoms, occurs for particular initial X state.