Maximizing the Validity of the Gaussian Approximation for the biphoton State from Parametric Downconversion

• URL: http://arxiv.org/abs/2210.02340v2
• Date: Mon, 19 Dec 2022 14:48:25 GMT
• Title: Maximizing the Validity of the Gaussian Approximation for the biphoton State from Parametric Downconversion
• Authors: Baghdasar Baghdasaryan, Fabian Steinlechner, Stephan Fritzsche
• Abstract summary: We present a choice of $alpha$ which maximizes the validity of the Gaussian approximation. We also discuss the so-called textitsuper-Gaussian and textitcosine-Gaussian approximations as practical alternatives.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Spontaneous parametric down-conversion (SPDC) is widely used in quantum applications based on photonic entanglement. The efficiency of photon pair generation is often characterized by means of a $sinc(L\Delta k/2)$-function, where $L$ is the length of the nonlinear medium and $\Delta k$ the phase mismatch between the pump and down-converted fields. In theoretical investigations, the \textit{sinc} behavior of the phase mismatch has often been approximated by a Gaussian function $\exp{(-\alpha x^2)}$ in order to derive analytical expressions for the SPDC process. Different values have been chosen in the literature for the optimization factor $\alpha$, for instance by comparing the widths of \textit{sinc} and Gaussian functions or the momentum of down-converted photons. As a consequence, different values for $\alpha$ provide different theoretical predictions for the same setup. Therefore, an informed and unique choice of this parameter is necessary. In this work, we present a choice of $\alpha$ which maximizes the validity of the Gaussian approximation. Moreover, we also discuss the so-called \textit{super}-Gaussian and \textit{cosine}-Gaussian approximations as practical alternatives with improved predictive power for experiments.

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