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arXiv:quant-ph/0112029 · Physical Review A

Tripartite entanglement in a Bose-Einstein condensate by stimulated Bragg scattering

Bimalendu Deb, G. S. Agarwal

Published Jun 17, 2002• 19 citations
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Abstract

We show that it is possible to entangle three different many-particle states by Bragg spectroscopy with nonclassical light in a Bose condensate of weakly interacting atomic gases. Among these three states, two are of atoms corresponding to two opposite momentum side modes of the condensate; and the other is of single-mode photons of the output probe beam. We demonstrate strong dependence of the multiparticle entanglement on the quantum statistics of the probe light. We present detailed results on entanglement keeping in view the possible experimental situation.

DOI
10.1103/physreva.65.063618

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We show that it is possible to entangle three different many-particle states by Bragg spectroscopy with nonclassical light in a Bose condensate of weakly interacting atomic gases. Among these three states, two are of atoms corresponding to two opposite momentum side modes of the condensate; and the other is of single-mode photons of the output probe beam. We demonstrate strong dependence of the multiparticle entanglement on the quantum statistics of the probe light. We present detailed results on entanglement keeping in view the possible experimental situation.
We propose an experiment for entangling two spatially separated Bose-Einstein condensates by Bragg scattering of light. When Bragg scattering in two condensates is stimulated by a common probe, the resulting quasiparticles or particles in the two condensates get entangled due to quantum communication between the condensates via the probe beam. The entanglement is shown to be significant and occurs in both number and quadrature phase variables and depends strongly on the relative detuning of the two pumps and the relative atom-field coupling strengths of the two condensates. We present two methods of detecting the generated entanglement.
We consider the interaction between a Bose-Einstein condensate and a single-mode quantized light field in the presence of a strong far-off-resonant pump laser. The dynamics is characterized by an exponential instability, hence the system acts as an atom-photon parametric amplifier. Triggered by a small injected probe field, or simply by quantum noise, entangled atom-photon pairs are created which exhibit nonclassical correlations similar to those seen between photons in the optical parametric amplifier. In addition, the quantum statistics of the matter and light field depend strongly on the initial state which triggers the amplifier. Thus, by preparing different initial states of the light field, one can generate matter waves in a variety of quantum states, demonstrating optical control over the quantum statistics of matter waves.
We study a system represented by a Bose-Einstein condensate interacting with a cavity field in presence of a strong off-resonant pumping laser. This system can be described by a three-mode Gaussian state, where two are the atomic modes corresponding to atoms populating upper and lower momentum sidebands and the third mode describes the scattered cavity field light. We show that, as a consequence of the collective atomic recoil instability, these modes possess a genuine tripartite entanglement that increases unboundedly with the evolution time and is larger than the bipartite entanglement in any reduced two-mode bipartition. We further show that the state of the system exhibits genuine tripartite nonlocality, which can be revealed by a robust violation of the Svetlichny inequality when performing displaced parity measurements. Our exact results are obtained by exploiting the powerful machinery of phase-space informational measures for Gaussian states, which we briefly review in the opening sections of the paper.