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Physical Review A

Entanglement between two atoms in an overdamped cavity injected with squeezed vacuum

Gao‐xiang Li, Klaas Allaart, Daan Lenstra

Published May 17, 2004• 34 citations
Publisher

Abstract

The generation of an entangled state for a pair of two-level atoms embedded in a bad cavity injected with a squeezed vacuum is investigated. The degree of entanglement between the two atoms strongly depends on the mean photon number and the strength of two-photon correlations of the squeezed vacuum, the cavity-induced decay rate of atoms, and the atomic separation.

DOI
10.1103/physreva.69.055802

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The generation of an entangled state for a pair of two-level atoms embedded in a bad cavity injected with a squeezed vacuum is investigated. The degree of entanglement between the two atoms strongly depends on the mean photon number and the strength of two-photon correlations of the squeezed vacuum, the cavity-induced decay rate of atoms, and the atomic separation.
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.
We propose a method to produce entangled spin squeezed states of a large number of atoms inside an optical cavity. By illuminating the atoms with bichromatic light, the coupling to the cavity induces pairwise exchange of excitations which entangles the atoms. Unlike most proposals for entangling atoms by cavity QED, our proposal does not require the strong coupling regime ${g}^{2}/\ensuremath{\kappa}\ensuremath{\Gamma}\ensuremath{\gg}1,$ where g is the atom cavity coupling strength, $\ensuremath{\kappa}$ is the cavity decay rate, and $\ensuremath{\Gamma}$ is the decay rate of the atoms. In this work the important parameter is ${\mathrm{Ng}}^{2}/\ensuremath{\kappa}\ensuremath{\Gamma},$ where N is the number of atoms, and our proposal permits the production of entanglement in bad cavities as long as they contain a large number of atoms.
A system of two two-level atoms interacting with a squeezed vacuum field can exhibit stationary entanglement associated with nonclassical two-photon correlations characteristic of the squeezed vacuum field. The amount of entanglement present in the system is quantified by the well known measure of entanglement called concurrence. We find analytical formulas describing the concurrence for two identical and nonidentical atoms and show that it is possible to obtain a large degree of steady-state entanglement in the system. Necessary conditions for the entanglement are nonclassical two-photon correlations and nonzero collective decay. It is shown that nonidentical atoms are a better source of stationary entanglement than identical atoms. We discuss the optimal physical conditions for creating entanglement in the system, in particular, it is shown that there is an optimal and rather small value of the mean photon number required for creating entanglement.
A scheme is presented for generation of entangled states for two atoms trapped in two distant bad cavities. The scheme can work with bad cavities with the coupling strength smaller than the cavity decay rate, which is important from the viewpoint of experiment. In the scheme the atoms have no probability of being populated in the excited state and thus the atomic spontaneous emission is suppressed, which increases the probability of success. The fidelity of the entangled state is not affected by the detection efficiency. Furthermore, the scheme does not require the detection of the left-polarized photon and right-polarized photon at the same time.