# Why a hole is like a beam splitter--a general diffraction theory for multimode quantum states of light

## TL;DR

This paper introduces a comprehensive diffraction theory for multimode quantum states of light, modeling the process as an effective interaction between spatial modes and validating it with numerical simulations and experiments.

## Contribution

It develops a formalism for describing how spatially multimode quantum states of light are affected by diffraction through a mask, linking diffraction to mode interactions.

## Key findings

- Qualitative agreement between theory and experimental data for squeezed-vacuum states
- Demonstration of diffraction producing two-mode squeezed vacuum and entanglement
- Prediction of Hong-Ou-Mandel-like effects in diffracted quantum states

## Abstract

Within the second-quantization framework, we develop a formalism for describing a spatially multimode optical field diffracted through a spatial mask and show that this process can be described as an effective interaction between various spatial modes. We demonstrate a method to calculate the quantum state in the diffracted optical field for any given quantum state in the incident field. Using numerical simulations, we also show that with single-mode squeezed-vacuum state input, the prediction of our theory is in qualitative agreement with our experimental data. We also give several additional examples of how the theory works, for various quantum input states, which may be easily tested in the lab; including two single-mode squeezed vacuums, single- and two-photon inputs, where we show the diffraction process produces two-mode squeezed vacuum, number-path entanglement and a Hong-Ou-Mandel-like effect--analogous to a beam splitter.