Angular Schmidt Modes in Spontaneous Parametric Down-Conversion

TL;DR

This paper demonstrates that Hermite-Gaussian modes form a Schmidt basis for biphoton transverse momentum states in spontaneous parametric down-conversion, enabling mode-specific measurements and state reconstruction.

Contribution

It introduces a method to identify and utilize Hermite-Gaussian modes as a Schmidt basis for biphoton states, with experimental validation.

Findings

Successful realization of projective measurements in Schmidt basis

Observation of correlations between mode pairs

Reconstruction of single-photon density matrix eigenvalues

Abstract

We report a proof-of-principle experiment demonstrating that appropriately chosen set of Hermite-Gaussian modes constitutes a Schmidt decomposition for transverse momentum states of biphotons generated in the process of spontaneous parametric down conversion. We experimentally realize projective measurements in Schmidt basis and observe correlations between appropriate pairs of modes. We perform tomographical state reconstruction in the Schmidt basis, by direct measurement of single-photon density matrix eigenvalues.