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Journal of Modern Optics

Preparing entangled states of two atoms through the intensity-dependent interaction with the two-mode squeezed vacuum

Fuli Li, Peng Peng, Zhang‐qi Yin

Published Jun 30, 2006• 5 citations
Publisher

Abstract

Two four-level atoms resonantly interacting with a two-mode squeezed vacuum field through the intensity-dependent Jaynes–Cummings-like model are considered. It is shown that the atoms can evolve into pure entangled states at certain time. Moreover, the pure entangled states can probabilistically be projected onto extremely entangled states by quantum jump technique. It is shown that the success probability monotonously increases with increasing degree of squeezing without any decoherence processes. However, it is found that if decoherence processes such as atomic spontaneous emission and photon leakage out of the cavity take place, the total success probability first increases but then decreases with increasing degree of squeezing and finally approaches zero as the squeezing becomes stronger and stronger. Therefore, the high degree of squeezing in the initial state of the cavity field is not always helpful for a high probability of creating extremely entangled states when spontaneous emission and cavity decay exist. Given spontaneous emission and photon leakage rates, there is an optimal squeezing degree for which the total success probability becomes maximum.

DOI
10.1080/09500340600798900

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Two four-level atoms resonantly interacting with a two-mode squeezed vacuum field through the intensity-dependent Jaynes–Cummings-like model are considered. It is shown that the atoms can evolve into pure entangled states at certain time. Moreover, the pure entangled states can probabilistically be projected onto extremely entangled states by quantum jump technique. It is shown that the success probability monotonously increases with increasing degree of squeezing without any decoherence processes. However, it is found that if decoherence processes such as atomic spontaneous emission and photon leakage out of the cavity take place, the total success probability first increases but then decreases with increasing degree of squeezing and finally approaches zero as the squeezing becomes stronger and stronger. Therefore, the high degree of squeezing in the initial state of the cavity field is not always helpful for a high probability of creating extremely entangled states when spontaneous emission and cavity decay exist. Given spontaneous emission and photon leakage rates, there is an optimal squeezing degree for which the total success probability becomes maximum.
Under the condition of two-mode squeezed vacuum state field interacting with an atom via the intensity-dependent coupling,the degree of entanglement between the two mode fields is investigated by using quantum relative entropy.It is found that the evolution of degree of two-mode fields entanglement is periodic.When the initial field is strong,the degree of entanglement reach maximum at scaled time gt=kπ(k=0,1,2,…),and the different between the maximum and minimum of the entanglement measures is about 1.3 generally.When the initial field is very weak,the influence of atom initial state on the entanglement evolution is sensitive.And the maximum entanglement appears under the situation of atom in a superposition state of upper level and lower level with equal probability.The entanglement of the two mode fields can be adjusted by controlling the time of the atom passing the cavity and the initial state of the atom.
Abstract We investigate the entanglement between two atoms in an overdamped cavity injected with squeezed vacuum when these two atoms are initially prepared in coherent states. It is shown that the stationary entanglement exhibits a strong dependence on the initial state of the two atoms when the spontaneous emission rate of each atom is equal to the collective spontaneous emission rate, corresponding to the case where the two atoms are close together. It is found that the stationary entanglement of two atoms increases with decreasing effective atomic cooperativity parameter. The squeezed vacuum can enhance the entanglement of two atoms when the atoms are initially in coherent states. Valuably, this provides us with a feasible way to manipulate and control the entanglement, by changing the relative phases and the amplitudes of the polarized atoms and by varying the effective atomic cooperativity parameter of the system, even though the cavity is a bad one. When the spontaneous emission rate of each atom is not equal to the collective spontaneous emission rate, the steady-state entanglement of two atoms always maintains the same value, as the amplitudes of the polarized atoms varies. Moreover, the larger the degree of two-photon correlation, the stronger the steady-state entanglement between the atoms.
The evolution of the entanglement degree of two-mode fields and atom with the intensity-dependent coupling is investigated using von Neumann entropy. The results for the initial fields in both coherent states and two-mode squeezed vacuum state are calculated. The influence of the field intensity on the entropy is discussed. It is found that the field and atom are generally in maximum entanglement but subject to periodic pulsed disentanglement completely under the condition of strong initial field.
We study the entanglement properties of a pair of two-level Rydberg atoms passing one after another into a lossless cavity with two modes. The atoms interact with the cavity field via an intensity-dependent, non-degenerate two-photon transition. The initial joint state of two successive atoms that enter the cavity is unentangled. Interactions mediated by the two-mode cavity photon field result in the final two-atom mixed entangled type state. The entanglement of formation of the joint two-atom state as a function of the Rabi angle, gt, is calculated for the two-mode Fock state field, coherent field, and thermal field, respectively, inside the cavity. The change in the magnitude of atomic entanglement with cavity photon number in two modes has been studied.
The temporal evolution of entanglement for a single-mode field interacting with a two-level atom via intensity-dependent coupling in the off-resonant case has been studied, where the leakage of photon through the cavity is taken into account. The effects of cavity damping on the coherence properties of the atom and the field are studied. The amount of entanglement is compared with the total correlations. It is found that the atom–field system is inhibited from going into a pure state in the off-resonant case.