The Dicke Quantum Phase Transition in a Superfluid Gas Coupled to an Optical Cavity

A fundamental concept to describe the collective matter-light interaction is the Dicke model which has been predicted to how an intriguing quantum phase transition. We have realize d the Dicke quantum phase transition in an open system formed by a Bose-Einstein condensate coupled to an optical cavity, and observed the emergence of a self-organized supersolid phase. The phase transition is driven by infinitely long-ranged interactions between the condensed atoms. We show that the phase transition is described by the Dicke Hamiltonian, including counter-rotating coupling terms, and that the supersolid phase is associated with a spontaneously broken spatial symmetry. The boundary of the phase transition is mapped out in quantitative agreement with the Dicke model.