Mercredi 28 novembre 2012 à 10h15
Salle 234, Ecole de Physique

Dynamical phases in open quantum systems and in the 1d quantum Ising model

James M. Hickey, University of Nottingham

Recent investigations into the dynamics of quantum jump trajectories [1] revealed that the statistics of the trajectories admitted a thermodynamic formalism and that several systems possessed dynamical phase transitions. This formalism is a form of full counting statistics known as the s-ensemble, which allows for a thermodynamic interpretation of the temporal statistics, where instead of ensembles of configurations one considers ensembles of trajectories. We formulate this approach in terms of generalized master equations and apply it to the study of the temporal statistics of the quadratures of light emitted from an open quantum system, these define quadrature trajectories. We illustrate this approach using two simple examples: a "blinking" 3-level system and two weakly coupled driven 2-level systems. We find the statistics of the quadratures may capture not only equivalent dynamical information as the jump trajectories, they may also elucidate dynamical phases which are not readily visible from the jump trajectories [2]. We then extend this approach to the study of time-integrated observables in closed quantum systems. We discuss in detail the case of the quantum Ising chain in a transverse field . We show that this model displays a continuum of quantum dynamical transitions, of which the static transition is just an end point [3]. These singularities can be probed generically through the quantum jump statistics of an associated open problem, and for the case of the quantum Ising chain we outline a possible experimental realisation of this scheme by digital quantum simulation with cold ions. [1] J. P. Garrahan and I. Lesanovsky, "Thermodynamics of Quantum Jump Trajectories", Phys. Rev. Lett. 104, 160601 (2010) [2] J. M. Hickey et al., "Thermodynamics of quadrature trajectories in open quantum systems", arXiv:1206.5719 [3] J. M. Hickey et al., "Time-integrated observables as order parameters for dynamical phase transitions in closed quantum systems", arXiv:1211.4773