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Annual Meeting Optical Society of America

Nonlinear system size quantum fluctuations in optics

Christopher J. Mertens, T. A. B. Kennedy, S. Swain

Published Jan 1, 1992• 0 citations
Publisher

Abstract

Quantum properties of intracavity nonlinear optical processes such as parametric oscillation and second harmonic generation are limited to a linearized analytical treatment except for certain special cases. Perfect squeezing in one quadrature and the divergence in fluctuations of the conjugate quadrature predicted at threshold in parametric oscillation are a consequence of the approximate linearized analysis. We investigate nonlinear quantum fluctuation corrections by using nonequilibrium Green’s function methods1,2 in concert with quantum master equations, to assess when these system-size effects may be observable in the laboratory.

DOI
10.1364/oam.1992.fnn7

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Quantum properties of intracavity nonlinear optical processes such as parametric oscillation and second harmonic generation are limited to a linearized analytical treatment except for certain special cases. Perfect squeezing in one quadrature and the divergence in fluctuations of the conjugate quadrature predicted at threshold in parametric oscillation are a consequence of the approximate linearized analysis. We investigate nonlinear quantum fluctuation corrections by using nonequilibrium Green’s function methods1,2 in concert with quantum master equations, to assess when these system-size effects may be observable in the laboratory.
We analyze the influence of system-size effects on the quantum properties of a degenerate parametric oscillator below, at, and above the classical threshold using a Green's-function approach. The many-body technique permits a systematic analysis of finite-size corrections to standard linearization results. In particular we study a ``semiquantum'' limit, where even above threshold only few photons are in the subharmonic mode while the pump mode is highly populated and behaves quasiclassically. Substantial deviations from classical and linearization predictions are found. We show that the depletion of the pump mode is rather strong and the threshold of parametric oscillation is shifted to higher pump strength, when the subharmonic system is small.
We present a method for the study of quantum fluctuations of dissipative structures forming in nonlinear optical cavities, which we illustrate in the case of a degenerate, type I optical parametric oscillator. The method consists in (i) taking into account explicitly, through a collective variable description, the drift of the dissipative structure caused by the quantum noise, and (ii) expanding the remaining---internal---fluctuations in the biorthonormal basis associated to the linear operator governing the evolution of fluctuations in the linearized Langevin equations. We obtain general expressions for the squeezing and intensity fluctuations spectra. Then we theoretically study the squeezing properties of a special dissipative structure, namely, the bright cavity soliton. After reviewing our previous result that in the linear approximation there is a perfectly squeezed mode irrespective of the values of the system parameters, we study which are the better squeezed modes at the different bifurcations that the cavity soliton can suffer, as well as the squeezing level attainable when the homodyne detection is made with a plane-wave local oscillator field. In this last case, the squeezing level is quite large in most of the existence domain of the cavity soliton. We then take into account the effect of the detector size and find that, in general, squeezing degrades as the detector is made smaller, except for detector sizes around the cavity soliton size, in which case there is an interesting deviation from the general trend.
An analytical solution of the Fokker–Planck equation for the nonlinear degenerate optical parametric amplifier (DOPA) is presented, taking into account the influence of pump depletion on the generation of squeezed light. Results conform to those obtained using perturbation series expansion theory near threshold, and also apply to the whole region far away from threshold. When the nonlinear term(η → 0) is neglected, the solution transitions naturally to the linear approximation solution; when the nonlinear term is retained (∞ η), in the case μ → 0, the quantum fluctuations are close to vacuum fluctuations; in the case μ ≫ 1, squeezing increases, and tends to the result obtained using linear theory, 1/(1 + μ).
A many-body theory of quantum fluctuations in the optical parametric oscillator is given. Dyson equations and diagrammatic representation of photon Green functions are derived from a combination of quantum Langevin and many-body techniques. Single-photon Green functions are used to compute dynamic spectra of the output using a self-consistent scheme which incorporates nonlinear, many-photon polarization effects. The latter scale with system size and their influence on the nonlinear quantum dynamics is addressed. We present results of dynamic output spectra and quantum-noise properties beyond the adiabatic approximation.