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Bulletin of the American Physical Society

Time-Translation Symmetry Breaking and Reentrant First Order Transition in Periodically Driven Quantum Oscillators

Jennifer Gosner, Yaxing Zhang, Björn Kubala, Joachim Ankerhold, M. I. Dykman

Published Mar 16, 2017• 0 citations
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We study the breaking of the discrete time-translation symmetry in small periodically driven quantum systems. These systems are intermediate between large closed systems and small dissipative systems, which both display such symmetry breaking but have qualitatively different dynamics. As a nontrivial example, strongly different from the familiar case of parametric resonance, we consider period tripling in a quantum nonlinear oscillator. We develop theoretical methods of the analysis of period tripling, including the theory of multiple-state resonant tunneling in phase space with the account taken of the involved geometric phase. For moderately strong driving, the period tripling persists for a time, which is exponentially long compared with all dynamical times. This time is further extended by an even weak decoherence.
Despite being forbidden in equilibrium, spontaneous breaking of time translation symmetry can occur in periodically driven, Floquet systems with discrete time-translation symmetry.The period of the resulting discrete time crystal is quantized to an integer multiple of the drive period, arising from a combination of collective synchronization and many body localization.Here, we consider a simple model for a onedimensional discrete time crystal which explicitly reveals the rigidity of the emergent oscillations as the drive is varied.We numerically map out its phase diagram and compute the properties of the dynamical phase transition where the time crystal melts into a trivial Floquet insulator.Moreover, we demonstrate that the model can be realized with current experimental technologies and propose a blueprint based upon a one dimensional chain of trapped ions.Using experimental parameters (featuring long-range interactions), we identify the phase boundaries of the ion-time-crystal and propose a measurable signature of the symmetry breaking phase transition.
Despite being forbidden in equilibrium, spontaneous breaking of time translation symmetry can occur in periodically driven, Floquet systems with discrete time-translation symmetry. The period of the resulting discrete time crystal is quantized to an integer multiple of the drive period, arising from a combination of collective synchronization and many body localization. Here, we consider a simple model for a one-dimensional discrete time crystal which explicitly reveals the rigidity of the emergent oscillations as the drive is varied. We numerically map out its phase diagram and compute the properties of the dynamical phase transition where the time crystal melts into a trivial Floquet insulator. Moreover, we demonstrate that the model can be realized with current experimental technologies and propose a blueprint based upon a one dimensional chain of trapped ions. Using experimental parameters (featuring long-range interactions), we identify the phase boundaries of the ion-time-crystal and propose a measurable signature of the symmetry breaking phase transition.