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arXiv:cond-mat/0505671 · Chemical Physics

Dynamics of the quantum Duffing oscillator in the driving induced bistable regime

Vittorio Peano, Michael Thorwart

Published Sep 6, 2005• 40 citations
arXivHTMLPDF
DOI
10.1016/j.chemphys.2005.06.047

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Optical bistability in nonlinear media is potentially useful because of its fast transition speed for all-optical logic operation [1-3]. The dynamics of these mirrorless systems have been described by a anharmonic Duffing oscillator [1-4]. After normalization the equation of motion is described by x + k x + x - f(x) = F sinwt, where k is the damping factor, F is the driving amplitude, w is the driving frequency and f(x) is a nonlinear function of x. Such a model predicts the existence of bistability under appropriate conditions [3]. It would be particularly important for this system to be tuned to some situation in order to efficiently generate these nonlinear phenomena. In this summary we would provide a global picture of possible dynamic behaviours in Eq.(1), which can be used as a guide line in real experiment.

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A Josephson junction embedded in a dissipative circuit can be externally driven to induce nonlinear dynamics of its phase. Classically, under sufficiently strong driving and weak damping, dynamic multistability emerges, associated with dynamical bifurcations so that the often-used modeling as a Duffing oscillator, which can exhibit bistability at most, is insufficient. The present work analyzes in this regime corresponding quantum properties by mapping the problem onto a highly nonlinear quasienergy operator in a rotating frame. This allows us to identify in detail parameter regions where simplifications such as the Duffing approximation are valid, to explore classical-quantum correspondences, and to study how quantum fluctuations impact the effective junction parameters as well as the dynamics around higher-amplitude classical fixed points.
The quantum dynamics of a quartic double well, subjected to a harmonically oscillating field, is studied in the framework of the Floquet formalism. The modifications of the familiar tunneling process due to driving and dissipation are investigated numerically and explained in terms of the quasienergy spectrum. In absence of dissipation, there is a onedimensional manifold in the parameter space spanned by amplitude and frequency of the driving force, where tunneling is almost completely suppressed by the coherent driving. The influence of dissipation is described on basis of the reduced density matrix in the Floquet representation. In particular, we consider the effect of weak Ohmic damping. In the classical limit, this system corresponds to a damped bistable Duffing oscillator
Optical bistability in nonlinear media is potentially useful because of its fast transition speed for all-optical logic operation [1-3]. The dynamics of these mirrorless systems have been described by a anharmonic Duffing oscillator [1-4]. After normalization the equation of motion is described by x + k x + x - f(x) = F sinwt, where k is the damping factor, F is the driving amplitude, w is the driving frequency and f(x) is a nonlinear function of x. Such a model predicts the existence of bistability under appropriate conditions [3]. It would be particularly important for this system to be tuned to some situation in order to efficiently generate these nonlinear phenomena. In this summary we would provide a global picture of possible dynamic behaviours in Eq.(1), which can be used as a guide line in real experiment.