Multimode mean-field model for the quantum phase transition of a Bose-Einstein condensate in an optical resonator

G. Kónya; G. Szirmai; P. Domokos

doi:10.1140/epjd/e2011-20050-3

EPJ

Multimode mean-field model for the quantum phase transition of a Bose-Einstein condensate in an optical resonator

G. Kónya¹, G. Szirmai¹^,2^a and P. Domokos¹

¹ Research Institute for Solid State Physics and Optics, P.O Box 49, 1525 Budapest, Hungary
² ICFO-Institut de Ciències Fotòniques, Mediterranean Techonoly Park, 08860 Castelldefels (Barcelona), Spain

Received: 19 January 2011
Published online: 15 April 2011

Abstract

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.