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arXiv:quant-ph/0309182 · Physical Review A

Generation of entangled states of two atoms inside a leaky cavity

T. W. Chen, C. K. Law, P. T. Leung

Published Nov 19, 2003• 11 citations
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Abstract

An in-depth theoretical study is carried out to examine the quasideterministic entanglement of two atoms inside a leaky cavity. Two $\ensuremath{\Lambda}$-type three-level atoms, initially in their ground states, may become maximally entangled through the interaction with a single photon. By working out an exact analytic solution, we show that the probability of success depends crucially on the spectral function of the injected photon. With a cavity photon, one can generate a maximally entangled state with a certain probability that is always less than $50%.$ However, for an injected photon with a narrower spectral width, this probability can be significantly increased. In particular, we discover situations in which entanglement can be achieved in a single trial with an almost unit probability.

DOI
10.1103/physreva.68.052312

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An in-depth theoretical study is carried out to examine the quasideterministic entanglement of two atoms inside a leaky cavity. Two \ensuremathΛ\ensuremath{\Lambda}\ensuremathΛ-type three-level atoms, initially in their ground states, may become maximally entangled through the interaction with a single photon. By working out an exact analytic solution, we show that the probability of success depends crucially on the spectral function of the injected photon. With a cavity photon, one can generate a maximally entangled state with a certain probability that is always less than 5050%.50 However, for an injected photon with a narrower spectral width, this probability can be significantly increased. In particular, we discover situations in which entanglement can be achieved in a single trial with an almost unit probability.
The generation of entanglement between three identical coupled cavities, each containing a single three-level atom, is studied when the cavities exchange two coherent photons and are in the N=2, 4, and 6 manifolds, where NNN represents the maximum number of photons possible in any one cavity. The combined states of the atom and the photon in a cavity is given by a qutrit for N=2, a five-dimensional qudit for N=4, and a seven-dimensional qudit for N=6. The conservation of the operator N^\hat{N}N^ for the interacting three-cavity system limits the total number of tripartite states to only 6, 18, and 38, rather than the usual 33=273^3=2733=27, 53=1255^3=12553=125, and 73=3437^3 =34373=343 states for N=2, 4, and 6, respectively. The deterministic generation of entanglement from general initially unentangled tripartite states is studied in the limit of large hopping strength, where all the solutions are analytic and given in terms of exponential functions. Several types of resulting tripartite entanglement are analyzed in order to obtain maximally entangled states.
We propose a potentially practical scheme to generate two-atom maximally entangled states by the large-detuning interaction between two three-level Λ-type atoms and coherent optical fields. Conditioned on the results of detecting cavity field, four pairs of atomic maximally entangled states with unity fidelity and high successful probability can be prepared. We also investigate the influence of the cavity dissipation on the generated entangled states and discuss the experimental feasibility of our scheme.
The generation of entanglement between two identical coupled cavities, each containing a single three-level atom, is studied when the cavities exchange two coherent photons and are in the N=2,4N=2,4N=2,4 manifolds, where NNN represents the maximum number of photons possible in either cavity. The atom-photon state of each cavity is described by a qutrit for N=2N=2N=2 and a five-dimensional qudit for N=4N=4N=4. However, the conservation of the total value of NNN for the interacting two-cavity system limits the total number of states to only 4 states for N=2N=2N=2 and 8 states for N=4N=4N=4, rather than the usual 9 for two qutrits and 25 for two five-dimensional qudits. In the N=2N=2N=2 manifold, two-qutrit states dynamically generate four maximally entangled Bell states from initially unentangled states. In the N=4N=4N=4 manifold, two-qudit states dynamically generate maximally entangled states involving three or four states. The generation of these maximally entangled states occurs rather rapidly for large hopping strengths. The cavities function as a storage of periodically generated maximally entangled states.
The generation of entanglement between three identical coupled cavities, eachcontaining a single three-level atom, is studied when the cavities exchange two coherent photonsand are in the N =2, 4, and 6 manifolds, where N represents the maximum number of photonspossible in any one cavity. The combined states of the atom and the photon in a cavity is given bya qutrit for N = 2, a five-dimensional qudit for N = 4, and a seven-dimensional qudit for N = 6. Theconservation of the operator Nˆ for the interacting three-cavity system limits the total number oftripartite states to only 6, 18, and 38, rather than the usual 33 = 27, 53 = 125, and 73 = 343 states for N =2, 4, and 6, respectively. The deterministic generation of entanglement from general initiallyunentangled tripartite states is studied in the limit of large hopping strength, where all the solutionsare analytic and given in terms of exponential functions. Several types of resulting tripartiteentanglement are analyzed in order to obtain maximally entangled states.