Generalized Hermite-Gauss decomposition of the two-photon state produced by spontaneous parametric down-conversion

TL;DR

This paper introduces a comprehensive method to decompose two-photon states from spontaneous parametric down-conversion into Hermite-Gaussian modes, accounting for pump beam order and experimental parameters, aiding in the engineering of complex entangled states.

Contribution

It provides a generalized Hermite-Gauss decomposition framework for two-photon states with arbitrary pump beam modes, advancing the control of spatial entanglement in quantum optics.

Findings

Spatial correlations depend on pump beam order and experimental parameters.

Decomposition enables engineering of non-Gaussian two-photon states.

Results facilitate tailored quantum entanglement generation.

Abstract

We provide a general decomposition of the two-photon state produced by spontaneous parametric down-conversion in Hermite-Gaussian modes, in the case that the pump beam is described by a Hermite-Gaussian beam of any order. We show that the spatial correlations depend explicitly on the order of the pump beam, as well as other experimental parameters. We use the decomposition to demonstrate a few interesting cases. Our results are applicable to the engineering of two-photon spatial entanglement, in particular for non-Gaussian states.