Theory of multiwave mixing in a squeezed vacuum

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Abstract
We present a theory of nondegenerate multiwave mixing in a squeezed vacuum. The probe absorption and coupling coefficients are derived using a standard Fourier-series method. We average the coefficients over pump spatial holes and solve the coupled mode equations to find the four-wave-mixing reflection coefficient. Reflectivity peaks and dips are found to be narrower than in an unsqueezed vacuum. Both the absorption and the reflectivity provide sensitive ways to measure the amount of squeezing in the vacuum.