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Physical Review A

Nonlocality of a single photon in cavity QED

Christopher C. Gerry

Published Jun 1, 1996• 50 citations
Publisher

Abstract

We study a model of single-photon nonlocality in which two separated cavities are prepared in an entangled state containing only one photon. The nonlocality is then transferred to two atoms probing each cavity. When the atoms are subsequently analyzed by classical microwave fields and selective ionization, Bell's inequalities are found to be violated for a wide range of atomic velocities. \textcopyright{} 1996 The American Physical Society.

DOI
10.1103/physreva.53.4583

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We study a model of single-photon nonlocality in which two separated cavities are prepared in an entangled state containing only one photon. The nonlocality is then transferred to two atoms probing each cavity. When the atoms are subsequently analyzed by classical microwave fields and selective ionization, Bell's inequalities are found to be violated for a wide range of atomic velocities. \textcopyright{} 1996 The American Physical Society.
There have been studies on the formation of quantum-nonlocal states in two spatially separate cavities. We suggest a nonlocal test for a field prepared in two cavities. We couple classical driving fields with cavities where a nonlocal state is prepared. Two independent two-level atoms are then sent through respective cavities to interact off-resonantly with the cavity fields. The atomic states are measured after the interaction. Bell's inequality can be tested by the joint probabilities of the two-level atoms being in their excited or ground states. We find that a violation of Bell's inequality can also be tested using a single atom sequentially interacting with the two cavities. Potential experimental errors are also considered. We show that with the present experimental condition of 5% error in the atomic velocity distribution, the violation of Bell's inequality can be measured.
No instrument is able to measure directly the quantum entanglement of a system. However, both theory and experiment, following the well-known Bell inequality, reveal the existence of the entanglement phenomenon in quantum mechanics. To examine the characterization of quantum entanglement, here we present a two-site cavity system, in which each cavity contains a Λ-type three-level atom and the two sites are identical and coupled with each other. We investigate and calculate the bipartite entanglement entropy of the system for the ground states. For photons of different types, corresponding to the two ground states of the atom, we investigate the correlations and violation of the Bell inequality.
We consider the entanglement of orthogonal generalized Bernoulli states in two separate single-mode high-QQQ cavities. The expectation values and the correlations of the electric field in the cavities are obtained. We then define, in each cavity, a dichotomic operator expressible in terms of the field states which can be, in principle, experimentally measured by a probe atom that ``reads'' the field. Using the quantum correlations of couples of these operators, we construct a Bell's inequality which is shown to be violated for a wide range of the degree of entanglement and which can be tested in a simple way. Thus the cavity fields directly show quantum nonlocal properties. A scheme is also sketched to generate entangled orthogonal generalized Bernoulli states in the two separate cavities.
Summary form only given. We have prepared a single-photon entangled state involving two field modes of a high finesse microwave superconducting cavity, and we have probed its coherence after storing it for a variable time in the cavity. We use the resonant interaction between circular Rydberg atoms and the field. This coupling is stronger than any dissipation rate so that the energy exchange between the atoms and the cavity is periodic (Rabi oscillation). A first atom prepares the entangled field state (writer atom) and a second one probes its coherence (reader atom).