Generalized description of the spatio-temporal biphoton State in spontaneous parametric down-conversion

TL;DR

This paper derives a comprehensive analytical expression for the spatio-temporal biphoton state in spontaneous parametric down-conversion, highlighting the role of Gouy phase and enabling better control of entangled photon states.

Contribution

It presents a universal formula for the biphoton state in SPDC that accounts for spatial-spectral non-separability and Gouy phase effects, advancing theoretical understanding.

Findings

Derived a general expression for the biphoton state

Formulated a criterion to reduce spatial-spectral coupling

Provided insights into Gouy phase effects in SPDC

Abstract

Spontaneous parametric down-conversion (SPDC) is a widely used source for photonic entanglement. Years of focused research have led to a solid understanding of the process, but a cohesive analytical description of the paraxial biphoton state has yet to be achieved. We derive a general expression for the spatio-temporal biphoton state that applies universally across common experimental settings and correctly describes the non-separability of spatial and spectral modes. We formulate a criterion on how to decrease the coupling of the spatial from the spectral degree of freedom by taking into account the Gouy phase of interacting beams. This work provides new insights into the role of the Gouy phase in SPDC, and also into the preparation of engineered entangled states for multidimensional quantum information processing.