Multimode mean-field model for the quantum phase transition of a Bose-Einstein condensate in an optical resonator
Research Institute for Solid State Physics and
Optics, P.O Box
2 ICFO-Institut de Ciències Fotòniques, Mediterranean Techonoly Park, 08860 Castelldefels (Barcelona), Spain
a e-mail: email@example.com
Published online: 15 April 2011
We develop a mean-field model describing the Hamiltonian interaction of ultracold atoms and the optical field in a cavity. The Bose-Einstein condensate is properly defined by means of a grand-canonical approach. The model is efficient because only the relevant excitation modes are taken into account. However, the model goes beyond the two-mode subspace necessary to describe the self-organization quantum phase transition observed recently. We calculate all the second-order correlations of the coupled atom field and radiation field hybrid bosonic system, including the entanglement between the two types of fields.
© EDP Sciences, Società Italiana di Fisica and Springer-Verlag 2011