Abstract
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.
- Received 2 March 2017
DOI:https://doi.org/10.1103/PhysRevA.96.052124
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