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Parametric forward scattering and intensity fluctuations of light in squeezed states

Mikhail I. Kolobov, I. V. Sokolov

Published Apr 1, 1989• 0 citations
OpenAlex

Abstract

The intensity fluctuation spectrum of light in a squeezed state produced from three-wave parametric interaction of travelling waves is examined. The effect of dispersion of the medium (phase matching) on the possibility of reducing the photodetection noise below the Schottky level is investigated. The energy and spectral correlations of the parametric scattering and squeezing phenomena are discussed.

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Journal of the Optical Society of America B•Oct 1, 1995•0 citations
The intensity fluctuation spectrum of light in a squeezed state produced from three-wave parametric interaction of travelling waves is examined. The effect of dispersion of the medium (phase matching) on the possibility of reducing the photodetection noise below the Schottky level is investigated. The energy and spectral correlations of the parametric scattering and squeezing phenomena are discussed.
We have discussed the possibilities of correlation spectroscopy (light beating spectroscopy) technique if squeezed light is used as a probe radiation for medium monitoring. The dispersion of the fluctuation of photocurrent spectrum measured in this method is expressed in terms of fourth order photocurrent correlation function. This correlation function is considered and evaluated in assumptions of photodetection theory developed by Glauber in first nonvanishing orders in interaction of probe light with the atoms of a photodetector. We show that fourth order correlation function is determined by all field TN-ordered amplitude correlation functions up to the fourth order. In case of heterodyne detection, when the light incident on photodetector surface is the mix of strong coherent modes of local oscillator wave and weak non-coherent (squeezed) modes, the observable (photocurrent spectrum) as well as its fluctuation (noise of photocurrent spectrum) is expressed in terms of spectrum-dependent Mandel parameter. We have discussed possible improvement of sensitivity limit for correlation spectroscopy in this case.
This thesis is primarily a theoretical study of degenerate parametric amplification as a means of generating squeezed-state light. i) A wideband traveling-wave formalism is developed for analyzing quantum mechanically a degenerate parametric amplifier. The formalism is based on spatial differential equations — spatial Langevin equations — that propagate temporal Fourier components of the field through the nonlinear medium. In addition to the parametric nonlinearity, the Langevin equations include absorption and associated fluctuations, dispersion, and pump quantum fluctuations. The dominant effects of dispersion and pump quantum fluctuations on the squeezing produced by a degenerate parametric amplifier are analyzed. ii) The wideband formalism of i) is used to carry out a more detailed analysis of the effects of phase mismatching. With the assumption of a lossless medium and a classical pump, we find that parametric amplification is capable of generating squeezed-state light over a wide band if materials with large χ(2) nonlinearities can be found, and that the squeezing bandwidth can be enhanced by phase mismatching away from degeneracy. iii) We consider again the effect of pump quantum fluctuations on the squeezing produced by parametric amplification. We perform discrete-mode calculations for a parametric amplifier with a quantum pump, and discuss some of the limitations of calculations of this sort in quantum optics. We derive stochastic differential equations (SDEs) for one- and two-mode parametric amplifiers, and from them obtain an iterative solution showing that pump quantum fluctuations impose a limitation on the degree of squeezing obtainable from a parametric amplifier. iv) A possible application of squeezing is considered; in particular, we study the effects of squeezing the intracavity noise in a laser oscillator. We solve the classical noise problem of a realistic laser model by making a bold — and possibly unrealizable — assumption, that the in-phase and quadrature Langevin sources which are responsible for the "noisiness" of the laser can be squeezed. We show that the effect of squeezing the in-phase quadrature is to reduce the phase noise, including the linewidth, of the laser but, due to amplitude-phase coupling, not to eliminate them altogether.
Squeezed light, in which the quantum noise in one amplitude component is reduced below the vacuum level, has been generated using parametric processes. The starting point described here is the nonlinear Schrodinger equation which models light propagating through optical fibers. When such a dispersive nonlinear medium with a third-order susceptibility is pumped with an optical beam, squeezing can result. It is found that the degree of squeezing oscillates as a function of fiber length in the normal dispersion regime, whereas in the anomalous dispersion regime, it grows exponentially with fiber length. Examination of squeezing near the fiber’s zero dispersion wavelength shows that odd-order dispersive terms have no effect on squeezing. However, small values of higher-order even terms have significant effects on squeezing. In practice, high-frequency components of the squeezing spectrum are difficult to obtain. However, it is shown that a cross-correlation technique may be used to explore the frequency dependence of the squeezing spectrum.
Near-degenerate four-wave parametric mixing in an optical fiber couples fluctuations in signal and idler frequency bands in such a way that the noise at a particular optical phase is reduced while that in an orthogonal phase quadrature is amplified. We have performed experiments on this effect and explained our results in terms of a theory which incorporates a nonlinear dispersion effect. The nonlinear dispersion alters the mathematical character of the solutions and limits the effective interaction length. For relatively low frequency shifts (<100 GHz) and 100 m of fiber, the heterodyne detected optical noise can be reduced by 5 dB in the squeezed quadrature. Theory predicts that this parametric interaction should reduce the noise level below the standard quantum limit. In a realistic fiber, phase noise due to guided acoustic wave Brillouin scattering (GAWBS) dominates the quanturn noise and cannot be reduced by four-wave mixing. Narrow gaps in the GAWBS noise can be engineered into special fibers. At the frequencies of these gaps, the noise level indeed can be squeezed below the quantum limit.