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Physical Review A

Semiclassical quantization of an optical pulse confined in a Kerr-effect nonlinear ring cavity

J. C. Martinez, Muhammad Taufik, A. Toon

Published Dec 14, 2006• 1 citation
Publisher

Abstract

We obtain two stationary solutions for an intense optical pulse propagating in a Kerr-effect nonlinear ring cavity using elliptic functions associated with a parameter $m$. The solutions may be associated with distinct phases of the system, the transition from one to the other being dictated by an energy ratio. Semiclassical quantization reveals excitations that are quantized rotational states for the spatially constant solution and $N$-particle bound states for the soliton solution. On invoking periodic boundary conditions, a constraint relating the number of particles, wavelength, and $m$ emerges. This constraint fundamentally modifies the binding energy of the soliton for a large range of $m$. At the phase transition point, the energy undergoes a discontinuity in both value and derivative, a conclusion that differs markedly from results of a mean-field calculation.

DOI
10.1103/physreva.74.063813

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The interplay of quantum fluctuations with nonlinear dynamics is a central topic in the study of open quantum systems, connected to fundamental issues (such as decoherence and the quantum-classical transition) and practical applications (such as coherent information processing and the development of mesoscopic sensors and amplifiers). With this context in mind, we here present a computational study of some elementary bifurcations that occur in a driven and damped cavity quantum electrodynamics (cavity QED) model at low intracavity photon number. In particular, we utilize the single-atom cavity QED master equation and associated stochastic Schr\"odinger equations to characterize the equilibrium distribution and dynamical behavior of the quantized intracavity optical field in parameter regimes near points in the semiclassical (mean-field, Maxwell-Bloch) bifurcation set. Our numerical results show that the semiclassical limit sets are qualitatively preserved in the quantum stationary states, although quantum fluctuations apparently induce phase diffusion within periodic orbits and stochastic transitions between attractors. We restrict our attention to an experimentally realistic parameter regime.