Multiphoton Quantum van Cittert-Zernike Theorem

TL;DR

This paper introduces a quantum version of the van Cittert-Zernike theorem to describe how multiphoton quantum systems evolve during propagation, revealing conditions for quantum-to-classical transitions and enabling new quantum state manipulations.

Contribution

It develops a fundamental formalism for multiphoton quantum interference and scattering, showing how quantum statistics can be modified without light-matter interactions and introducing a novel all-optical state preparation method.

Findings

Quantum statistical fluctuations can be altered during propagation without light-matter interactions.

Conditional measurements can produce multiphoton states with sub-shot-noise quantum statistics.

The formalism explains phenomena beyond classical optical coherence theory.

Abstract

Recent progress on quantum state engineering has enabled the preparation of quantum photonic systems comprising multiple interacting particles. Interestingly, multiphoton quantum systems can host many complex forms of interference and scattering processes that are essential to perform operations that are intractable on classical systems. Unfortunately, the quantum coherence properties of multiphoton systems degrade upon propagation leading to undesired quantum-to-classical transitions. Furthermore, the manipulation of multiphoton quantum systems requires of nonlinear interactions at the few-photon level. Here, we introduce the quantum van Cittert-Zernike theorem to describe the scattering and interference effects of propagating multiphoton systems. This fundamental theorem demonstrates that the quantum statistical fluctuations, which define the nature of diverse light sources, can be modified upon propagation in the absence of light-matter interactions. The generality of our formalism unveils the conditions under which the evolution of multiphoton systems can lead to surprising classical-to-quantum transitions. Specifically, we show that the implementation of conditional measurements may enable the all-optical preparation of multiphoton systems with attenuated quantum statistics below the shot-noise limit. Remarkably, this effect had not been discussed before and cannot be explained through the classical theory of optical coherence. As such, our work opens new paradigms within the established field of quantum coherence.