Non-Equilibrium Dynamics of Ultra Cold Atoms and Effective Spin Models in Optical Cavities

There has been spectacular progress in exploring the properties of ultra cold atoms using light. Recent experiments [1] on Bose--Einstein condensates in optical cavities have reported a novel self-organization transition of the atom-light system. This coincides with the superradiance transition in an effective non-equilibrium Dicke model, describing two-level ``spins'' coupled to light. The light leaking out of the cavity provides valuable information on this hybrid matter-light system, and the time-dependent nature of the experiments demands consideration of the associated dynamics. We present a rich dynamical phase diagram [2,3], accessible by quench experiments, with distinct regimes of collective dynamics separated by non-equilibrium phase transitions. These findings open new directions to study the emergent dynamics and non-equilibrium phase transitions of quantum many body systems and effective spin models.\\[4pt] In collaboration with J. Keeling (University of St Andrews), J. Mayoh (University of Cambridge) and B. D. Simons (University of Cambridge).\\[4pt] [1] K. Baumann, C. Guerlin, F. Brennecke and T. Esslinger, ``Dicke Quantum Phase Transition with a Superfluid Gas in an Optical Cavity,'' Nature 464, 1301 (2010).\\[0pt] [2] J. Keeling, M. J. Bhaseen and B. D. Simons, ``Collective Dynamics of Bose--Einstein Condensates in Optical Cavities,'' Phys. Rev. Lett. 105, 043001 (2010).\\[0pt] [3] M. J. Bhaseen, J. Mayoh, B. D. Simons and J. Keeling, ``Dynamics of Nonequilibrium Dicke Models,'' Phys. Rev. A 85, 013817 (2012).