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Journal of Experimental and Theoretical Physics Letters

Entangled state generation and modulation of vacuum squeezing by classical optical fields in birefringent fiber

Sergey A. Podoshvedov

Published May 1, 2002• 1 citation
Publisher

Abstract

Evolution of the vacuum fluctuations in the two-wave mixing of the optical fields propagating in a birefringent fiber is studied. The two-wave mixing in the birefringent fiber was suggested as a possible scheme for the entangled-state generation. Our treatment in studying the entangled-state generation uses depleted pump approximation and enables one to trace the influence of the input conditions of classical optical fields on the evolution of vacuum squeezing. We report the periodical modulation of the vacuum squeezing when the input relative phase of coherent waves varies. The measure of nonclassical correlations imposed on the generated light is calculated.

DOI
10.1134/1.1497877

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We study scalar and vector modulation instabilities induced by the vacuum fluctuations in birefringent optical fibers. To this end, stochastic coupled nonlinear Schr\"odinger equations are derived. The stochastic model is equivalent to the quantum field operators equations and allows for dispersion, nonlinearity, and arbitrary level of birefringence. Numerical integration of the stochastic equations is compared to analytical formulas in the case of scalar modulation instability and nondepleted pump approximation. The effect of classical noise and its competition with vacuum fluctuations for inducing modulation instability is also addressed.
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Parametric interactions such as four wave mixing have been predicted to produce states of the radiation field where the quantum fluctuations in one phase quadrature are less than those of a coherent state.1 These “squeezed states” have proved remarkably difficult to generate and detect, not least because of the presence of additional classical noise in many laser sources and parametric devices. We have now demonstrated the reduction of classical fluctuations by means of four wave mixing in an optical fiber under conditions very similar to those needed to demonstrate squeezed state generation. This success reinforces the plausibility of related quantum noise experiments, and has implications for fiber optic communications.
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Squeezing is a fundamental quantum optical phenomenon - induced by various nonlinear optical processes - in which a special state of the electromagnetic field is generated, for which quantum noise fluctuations are reduced below the shot noise level for certain frequency ranges. Two qualitatively different kinds of squeezing are currently known to take place in optical fibers. The first is the four-wave mixing (FWM) induced quadrature squeezing, in which an intense continuous wave (CW) pump initiates a spontaneous emission of signal and idler waves from vacuum fluctuations at symmetric detunings from the pump. The noise components at the signal and idler frequencies become correlated via the fiber nonlinearity, leading to a reduction of the noise power spectrum below the shot noise level. All the waves participating to the FWM-induced squeezing are monochromatic waves. The second kind of squeezing is the so called self-phase modulation (SPM) induced squeezing, in which the spectral components of an intense short pulse in a coherent state become correlated via the SPM during propagation. We demonstrate theoretically that a third kind of squeezing is possible in optical fibers, in which the noise spectrum of the quasi-monochromatic resonant radiation (RR) emitted by optical solitons when subject to perturbations shows evidence of photon correlation and a reduction of noise below the shot-noise level.