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arXiv:quant-ph/0508198 · Journal of the Optical Society of America B

Entanglement, teleportation, and single-photon storage with two-level atoms inside an optical parametric oscillator

Perry R. Rice

Published Jul 1, 2005• 6 citations
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Abstract

I consider several interesting aspects of a new light source, a two-level atom, or N two-level atoms inside an optical parametric oscillator. I find that in the weak driving limit, detection of a transmitted or fluorescent photon generates a highly entangled state of the atom and the cavity. This entanglement can be used with beam splitters to create more complex quantum states and implement teleportation protocols. Also, one can store a single photon in the atoms, along the lines of recent slow and stopped light proposals and experiments.

DOI
10.1364/josab.22.001561

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I consider several interesting aspects of a new light source, a two-level atom, or N two-level atoms inside an optical parametric oscillator. I find that in the weak driving limit, detection of a transmitted or fluorescent photon generates a highly entangled state of the atom and the cavity. This entanglement can be used with beam splitters to create more complex quantum states and implement teleportation protocols. Also, one can store a single photon in the atoms, along the lines of recent slow and stopped light proposals and experiments.
There is increasing interest in the photon statistics and spectroscopic properties of the radiation from atoms confined in an optical cavity. Effects such as the cavity enhancement and inhibition of spontaneous emission, which were first observed using microwave cavities, have recently been measured at optical frequencies.1 Recent measurements of squeezing and the dynamic effects of single-quantum-level splittings also demonstrate the possibilities for quantum-statistical studies of coupled atom-cavity systems at optical frequencies.2 We study a single two-level atom confined inside an optical cavity which is driven by coherent light in resonance with both cavity and atom. For weak driving field intensities we have calculated the spectrum of the light transmitted by the cavity and fluorescence out the sides of the cavity.
Mapping quantum states of light on atoms opens up the possibilities for quantum information storage,teleportation of atoms, and quantum computing. We describe a novel approach to such mapping based on creation of pairwise atomic entanglement in a large macroscopic atomic ensemble. As opposed to the previously demonstrated methods involving strong coupling of a single two-level atom to a cavity field, our strategy utilizes a large sample of three- and more level atoms weakly interacting with a free propagating qua ntum field. Besides practical advantages offered by the new method (no high-Q cavities involved), it also allows for production of a large number of correlated atoms which can be spatially separated and trapped in magnetic or magneto-optical traps.
An optical field with a definite number of photons is very important for quantum metrology and quantum information. Some theoretical protocols for creating such a Fock-state have been proposed, but it is still a big challenge to produce it with a large number photons experimentally. We revisit the system of atoms inside an optical parametric oscillator that was proposed in 1990s, and it is found that for the atom ensemble, the optical Fock-state with an arbitrary number of photons can be generated. Compared to the previous proposals, the scheme presented here is simple and seems physically realizable. The system also provides the possibility to demonstrate the strong interaction between nonclassical light and atoms in a confined space.
We consider intensity-field correlation functions for a two-level atom in a degenerate optical parametric oscillator (OPO), which would result from a conditioned homodyne measurement. Analytic results are obtained in the limit of weak driving fields using quantum trajectory methods for both the transmitted and fluorescent fields. This system is unique in that after detection of a photon, it is known that one excitation is in the system, in either the atom or cavity mode. We find large violations of inequalities satisfied by classical fields, for both transmitted and fluorescent fields. This is in contrast to the usual cavity QED system of an atom in a driven cavity where we do not find nonclassical behavior in the intensity-field correlation function in fluorescence. This is understood in terms of a relationship between the intensity-field correlation function and the second-order intensity correlation function, as well as the different amount of field-atom entanglement in the two systems. We show that for weak-field cavity QED one must have photon bunching to have nonclassical behavior in the intensity-field correlation function. We compare our results to those of an ordinary OPO. Finally, we also consider cross correlations, where we examine the transmitted (fluorescent) field conditioned by detection of a fluorescent (transmitted) photon.