Principles of Optics in the Fock Space: Scalable Manipulation of Giant Quantum States

TL;DR

This paper introduces Fock-space optics, a framework that treats photon number as a synthetic dimension, enabling scalable manipulation of large quantum states with up to 180 photons using analogies to classical optical phenomena.

Contribution

It establishes a novel conceptual framework for wave propagation in quantum Fock space and demonstrates experimental analogues of optical effects with high photon numbers.

Findings

Demonstrated optical analogues in Fock space with up to 180 photons

Established a correspondence between Schrödinger evolution and classical wave propagation

Enabled scalable control of large quantum states for bosonic information processing

Abstract

The manipulation of distinct degrees of freedom of photons plays a critical role in both classical and quantum information processing. While the principles of wave optics provide elegant and scalable control over classical light in spatial and temporal domains, engineering quantum states in Fock space has been largely restricted to few-photon regimes, hindered by the computational and experimental challenges of large Hilbert spaces. Here, we introduce ``Fock-space optics", establishing a conceptual framework of wave propagation in the quantum domain by treating photon number as a synthetic dimension. Using a superconducting microwave resonator, we experimentally demonstrate Fock-space analogues of optical propagation, refraction, lensing, dispersion, and interference with up to 180 photons. These results establish a fundamental correspondence between Schr\"{o}dinger evolution in a single bosonic mode and classical paraxial wave propagation. By mapping intuitive optical concepts onto high-dimensional quantum state engineering, our work opens a path toward scalable control of large-scale quantum systems with thousands of photons and advanced bosonic information processing.