Entanglement of Matter Waves by a Quantized Optical Field

M. G. Moore, O. Zobay, Pierre Meystre

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.

P. Tombesi

Keye Zhang, Pierre Meystre, Weiping Zhang

We analyze the optomechanicslike properties of a Bose-Einstein condensate (BEC) trapped inside an optical resonator and driven by both a classical and a quantized light field. We find that this system exhibits the nature of role reversal between the matter-wave field and the quantized light field. As a result, the matter-wave field now plays the role of the quantized light field, and the quantized light field behaves like a movable mirror, in contrast to the familiar situation in BEC-based cavity optomechanics [Brennecke et al., Science 322, 235 (2008); Murch et al., Nature Phys. 4, 561 (2008)]. We demonstrate that this system can lead to the creation of a variety of nonclassical matter-wave fields, in particular, cat states, and discuss several possible protocols to measure their Wigner function.

David S. Simon, Gregg S. Jaeger, Alexander V. Sergienko

Ying Wu, Xiaoxue Yang

We solve exactly a set of fully quantized coupled equations that describe the quantum dynamics, including the evolution of quantum fluctuations, entanglements, and correlations, of four-wave mixing (FWM) with matter waves. The analytical solution reveals Rabi oscillations, collapses and revivals, and agrees with FWM experiments. It also applies to optical FWM and the Rayleigh superradiance in Bose-Einstein condensates.

F. J. Duarte