Abstract

The Dicke phase transition has recently come to prominence due to the experimental observation (at the ETH and elsewhere) of a self-organization transition in a BEC inside an optical cavity. In this talk I will discuss two other examples. When a BEC is placed in a double well potential each atom can in general be in a superposition of both wells. If a single impurity atom is now added we find that there is a critical interaction strength above which the system spontaneously breaks its symmetry so that the impurity atom becomes localized in one well and the majority of bosons in the other. I will explain how this system can be mapped onto the Dicke model and back this up with the results of a calculation of the critical exponents of the fidelity susceptibility which indicate that this transition falls into the same universality class as the Dicke model (and the Lipkin-Meshkov-Glick model). We take the view that this system is a toy model for quantum measurement with the BEC acting as a meter that measures the position of the impurity atom thereby describing wave function collapse as a phase transition. Time permitting, I will mention a second example which concerns the membrane-in-the-middle version of optomechanics realized in experiments at Yale. I point out that there is a symmetry breaking phase transition of the Dicke-type in this * driven * model where the membrane suddenly displaces to the left or the right.