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Acta Sinica Quantum Optica

The Entanglement Properties of Two Λ-type atoms in a Dissipative Cavity

Liu Bao-ping

Published Jan 1, 2008• 0 citations

Abstract

The entanglement between two Λ-type three-level atoms interacting with coherent field in a dissipative cavity is investigated by means of the entanglement degree of quantum conditional entropy.A solution of the master equation is obtained by super operator method.The authors discuss the entanglement between the two atoms based on two kinds of different initial states(|ψa(0),|Φa(0)) and analyze the influence of decay coefficient of the cavity and mean photon number of the field on entanglement degree.In conclusion,when the atoms are initially in entangled state |ψa(0),the evolution of the entanglement degree depends on decay coefficient of the cavity and intensity of the field.If there is absence of dissipation,the entanglement degree evolves periodically;otherwise,the entanglement degree decays sharply and approaches a stable value.The weaker the intensity of the field is,the greater the stable value becomes.The greater the decay coefficient is,the faster it reaches the stable value.But for the other initial entangled state |Φa(0),the entanglement between the two atoms doesn't evolve with the time.It implies that the entangled state |Φa(0) can be preserved in such a dissipative system.

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Applying the method of coherent-state orthogonalization expansion, the quantum entropy of the coherent state light field interacting with a Λ type three level atom is caculated accurately without rotating wave approximation. The influences of the couplings, mean photon number and the atom in different levels at the initial time on quantum entanglement are studied via quantum entropy theory. The results obtained from using the numerical method show that when atom is initially in the excited state, the entanglement reaches the maximum value in a short time, with the increase of the mean photon number, the period of entanglement evolution becomes clearly. The degrees of enganglement in a short time become lower due to the atom is initially in the superposition state of all three levels. Compared with the results of using the method of rotating wave approximation, the contribution of the without rotating wave approximation terms increase notably and the quantum entanglement curvies displays small zigzag-shaped oscillation, with the increasing of couplings and mean photon number.

We have investigated the entangleable properties of two two-level atoms inside the dissipative cavity coupled to a single-mode radiation field under the big detuning,and discussed the influence of the initial state of the two atoms,the cavitity decay constant and the mean photon number on the entanglement degree.It have shown that if the two atoms are initially in the exicited or the ground states,they will be separate always;if the two atoms are initially in the coherent superposition of the excited and the ground states,the influence of cavity dissipation on the entanglement degree will vanish gradually with the time evolution,but the dipole-dipole interaction can enhance the entanglement degree.

Some investigations have been made on the evolution of the linear entropies of atom-field system, in which two identical two-level atoms simultaneously interact with a single-mode dissipative cavity field under large detuning. The effects of the initial atom states and the dissipative factors of the cavity on all linear entropies are also discussed. The results show that the influence of the cavity decay constant on different kinds of Bell states is completely different, and the state |Ψ〉12 is a robust entangled state against the decoherence while the state |Φ〉12 is a fragile entangled state.

In this paper, we investigate the entanglement dynamics of two entangled two-level atoms interacting with a single-mode field in a dissipative cavity. The results show that the evolution properties of the entanglement degree of two entangled atoms depend on the initial atomic entanglement degree and form, the average photon number of the cavity field, and the cavity leakage rate. When the atoms are initially in a particular entangled state, the degree of entanglement can be amplified and not influenced by the dissipation of the cavity field.

We investigate the evolution of the atomic quantum entropy and the atom–field entanglement in a system of a Λ-configuration three-level atom interacting with a two-mode field with additional forms of nonlinearities of both the field and the intensity-dependent atom–field coupling. With the derivation of the unitary operator within the frame of the dressed state and the exact results for the state of the system we perform a careful investigation of the temporal evolution of the entropy. A factorization of the initial density operator is assumed, considering the field to be initially in a non-correlated two-mode squeezed coherent or binomial state. The effects of the mean photon number, detuning, Kerr-like medium and the intensity-dependent coupling functional on the entropy are analysed.

We investigate the Raman coupled model of two entangled Λ-type three-level atoms interacting with a two-mode quantized cavity field.With the negative eignevalues of the partial transposition matrix,we obtain the time evolution of entanglement between the two atoms.The results show that the entanglement of the two atoms displays periodicity;the evolution regular of entanglement is influenced by the initial state of two atoms and initial photon number of the cavity.For special initial state,the two-atom quantum state will stay in the maximum entangled state forever and have no relation with the initial photon number.Compared with Tavis-Commings model,the entanglement of the two atoms can live for much longer time in the proposed model.