The authors present research demonstrating scalable manipulation of quantum states with a remarkably high number of photons. Their work establishes a new framework, termed “Fock‑space optics,” which applies the well‑understood principles of wave optics to photon number, treating it as an additional dimension for control. Using a superconducting microwave resonator, they experimentally validate this approach, achieving analogues of classical optical phenomena—propagation, refraction, and interference—with up to 180 photons. This breakthrough links Schrödinger evolution to classical wave behaviour, paving the way for advanced bosonic information processing and scalable control of quantum systems containing thousands of photons.

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Fock Space Optics for Quantum Wave Propagation

Affiliations: Hefei 230026, China; Beijing Academy of Quantum Information Sciences, Beijing, China; Hefei National Laboratory, Hefei 230088, China.

The manipulation of distinct degrees of freedom of photons is critical for both classical and quantum information processing. While wave optics provides elegant, scalable control over classical light in spatial and temporal domains, engineering quantum states in Fock space has been largely limited to few‑photon regimes because of the computational and experimental challenges of large Hilbert spaces.

This work introduces “Fock‑space optics,” a conceptual framework that treats photons as quantum entities propagating according to established wave‑optical principles. The authors develop a theoretical formalism describing the propagation of quantum states through optical elements, analogous to classical wave propagation. This formalism enables the design of optical systems capable of generating and manipulating complex quantum states with a large number of photons. A key contribution is the demonstration that established wave‑optical concepts—such as diffraction and interference—can be directly applied in the quantum realm.

Specific optical configurations are detailed for generating and manipulating multi‑photon states, overcoming the exponential complexity that hampers traditional methods as photon number grows. By leveraging the well‑established infrastructure and techniques of classical optics, the study provides a pathway toward scalable quantum information processing and lays a foundation for future investigations into advanced quantum optical systems and their applications in quantum communication and computation.

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Photonic Propagation and Manipulation in Superconducting Resonators

Researchers demonstrated analogues of classical optical phenomena—propagation, refraction, lensing, dispersion, and interference—using up to 180 photons within a superconducting microwave resonator. This experimental work establishes a fundamental connection between Schrödinger evolution in a single bosonic mode and classical paraxial wave propagation, effectively treating photon number as a synthetic dimension.

The methodology centers on utilizing a superconducting microwave resonator to manipulate photons and observe their behaviour. By carefully controlling interactions within the resonator, the team simulated optical effects typically observed with macroscopic light beams. Quantum states with varying photon numbers (up to 180) were created and measured, and their evolution over time corresponded directly to classical optical behaviours, validating the theoretical framework linking quantum and classical optics.

Instead of directly calculating electromagnetic field distributions—computationally demanding—the researchers relied on established principles of geometric ray tracing and wave interference. This approach allowed efficient, intuitive design of the quantum system and precise control over the photons. Measurements of the quantum states confirmed the simulated optical effects, extending Maxwell’s electromagnetic theory into the quantum realm. The ability to control states in Fock space is crucial for advancements in quantum communication, sensing, computation, and simulation, potentially unlocking quantum‑enabled advantages in these fields.

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Fock Space Optics Mimics Classical Wave Behaviour

The team established “Fock‑space optics,” a framework that treats photon number as a synthetic dimension for wave propagation. Experiments using a superconducting microwave resonator demonstrated analogues of classical optical phenomena—interference, propagation, refraction, lensing, and dispersion—with up to 180 photons.

Key findings include:

• A direct correspondence between the quantum evolution equation for a single bosonic mode and the paraxial wave equation describing classical beam propagation.

• Validation that centuries‑old optical principles can be applied to engineering quantum states in Fock space.

• Implementation of a “Fock‑space camera” by calibrating a qubit frequency to resolve photon‑number‑splitting peaks of coherent states, enabling precise observation of photon‑number distributions.

These results provide an intuitive, scalable pathway for manipulating massive quantum excitations, advancing bosonic quantum information processing, and supporting the development of quantum technologies that require large photon numbers.

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Reference

Principles of Optics in the Fock Space: Scalable Manipulation of Giant Quantum States – arXiv preprint: https://arxiv.org/abs/2601.10325