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arXiv:1201.6621 · Physical Review A

Oscillatory dynamics in nanocavities with noninstantaneous Kerr response

Andrea Armaroli, Stefania Malaguti, Gaetano Bellanca, S. Trillo, Alfredo De Rossi, Sylvain Combrié

Published Nov 9, 2011• 37 citations
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Abstract

We investigate the impact of a finite response time of Kerr nonlinearities over the onset of spontaneous oscillations (self-pulsing) occurring in a nanocavity. The complete characterization of the underlying Hopf bifurcation in the full parameter space allows us to show the existence of a critical value of the response time and to envisage different regimes of competition with bistability. The transition from a stable oscillatory state to chaos is found to occur only in cavities which are detuned far off-resonance, which turns out to be mutually exclusive with the region where the cavity can operate as a bistable switch.

DOI
10.1103/physreva.84.053816

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We investigate the impact of a finite response time of Kerr nonlinearities over the onset of spontaneous oscillations (self-pulsing) occurring in a nanocavity. The complete characterization of the underlying Hopf bifurcation in the full parameter space allows us to show the existence of a critical value of the response time and to envisage different regimes of competition with bistability. The transition from a stable oscillatory state to chaos is found to occur only in cavities which are detuned far off-resonance, which turns out to be mutually exclusive with the region where the cavity can operate as a bistable switch.
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We present a detailed analysis showing that positive-branch instabilities occur in nonlinear resonators in the Fabry-Pérot (folded) configuration. Responses in the unstable region can be unstable or chaotic, depending on parameter values. Values of the response/round-trip time ratio in excess of unity can still yield instabilities, albeit on progressively higher branches as the ratio increases. The analysis proceeds from the basic optical bistability equations through the Maxwell-Debye equations to an explicit expression for the nonlinear phase shift. Linearization leads to thresholds in good agreement with direct computation. A simple expression for the accessible domain of phase-space is derived. The fundamental oscillation is interpreted as a cavity-resonant sideband instability.
We analyze the Jaynes-Cummings model of quantum optics, in the strong-dispersive regime. In the bad-cavity limit and on time scales short compared to the atomic coherence time, the dynamics are those of a nonlinear oscillator. A steady-state nonperturbative semiclassical analysis exhibits a finite region of bistability delimited by a pair of critical points, unlike the usual dispersive bistability from a Kerr nonlinearity. This analysis explains our quantum trajectory simulations that show qualitative agreement with recent experiments from the field of circuit quantum electrodynamics.
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