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arXiv:1903.05874 · The European Physical Journal Plus

Quantum parametric resonance of a dissipative oscillator: fading and persistent memory in the long-time evolution

L. Ferrari

Published Apr 1, 2019• 1 citation
arXivHTMLPDF
DOI
10.1140/epjp/i2019-12625-y

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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.
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We study theoretically the driven-dissipative dynamics of an array of two-level emitters, coupled to a single photonic mode, in the presence of disorder in the resonant frequencies. We introduce the notion of subradiant correlations in the dynamics, corresponding to the eigenstates of the Liouvillian with a low decay rate, that can also oscillate in time. While the usual collective subradiant states do not survive the emitter resonant frequency fluctuations, these subradiant correlations are immune to such a type of disorder. These long-living correlations exist in finite-size systems, when their lifetime is parametrically longer than in the so-called Dicke time crystal phase.