Schmidt modes in the angular spectrum of bright squeezed vacuum

TL;DR

This paper analyzes the spatial properties of high-gain parametric down-conversion, identifying Schmidt modes and their eigenvalues, and confirms the theoretical approach through experimental comparisons.

Contribution

It provides an analytical framework for understanding Schmidt modes in high-gain PDC, extending low-gain results and linking them to measurable quantities.

Findings

Schmidt modes in high-gain PDC are similar to low-gain case

Schmidt eigenvalues depend strongly on parametric gain

Theoretical predictions agree with experimental data

Abstract

We study the spatial properties of high-gain parametric down-conversion (PDC). From the Hamiltonian we find the Schmidt modes, apply the Bloch-Messiah reduction, and calculate analytically the measurable quantities, such as the angular distributions of photon numbers and photon-number correlations. Our approach shows that the Schmidt modes of PDC radiation can be considered the same as for the low-gain (biphoton) case while the Schmidt eigenvalues strongly depend on the parametric gain. Its validity is confirmed by comparison with several experimental results, obtained by us and by other groups.