Gaussian functions are optimal for waveguided nonlinear-quantum-optical processes

Abstract

Many nonlinear optical technologies require the two-mode spectral amplitude function that describes them-the joint spectral amplitude (JSA)-to be separable. We prove that the JSA factorizes only when the incident pump field and phase-matching function are Gaussian functions. We show this by mapping our problem to a known result, in continuous variable quantum information, that only squeezed states remain unentangled when combined on a beam splitter. We then conjecture that only a squeezed state minimizes entanglement when sent through a beam splitter with another pre-specified ket. This implies that to maximize JSA separability when one of the (pump or nonlinear medium) functions is non-Gaussian, the other function must be Gaussian. This answers an outstanding question about optimal design of certain nonlinear processes, and is of practical interest to researchers using waveguide nonlinear optics to generate and manipulate quantum light.

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