Propagation-distance Limit for Nonlocal Optical Systems Achieves Millimeter-Scale Mode Conversion

The fundamental limits of how quickly information can travel underpin much of modern physics, and recent work explores these boundaries within classical optics. Salman Sajad Wani from Qatar Center for Quantum Computing, Xiaoping Shi from University of British Columbia Okanagan, and Saif-Al-Kuwari, alongside Arshid Shabir and Mir Faizal, investigate a propagation-distance limit for optical beams exhibiting strong nonlocality. Their research establishes an optical analogue of the minimal orthogonality time found in mechanics, effectively defining how far a highly non-local beam can travel before losing its distinguishable characteristics. This breakthrough not only defines a fundamental constraint on optical propagation, but also demonstrates the potential for creating compact devices that manipulate light at millimeter scales, with unprecedented sensitivity to changes in refractive index and temperature.

The research establishes a theoretical framework for understanding how nonlocality, a phenomenon often associated with quantum mechanics, can be realised and constrained within classical optics. The team demonstrates that while classical systems can exhibit nonlocal behaviour, this behaviour is inherently limited by signal degradation over distance, resulting in a maximum propagation distance beyond which nonlocality is lost. The approach involves modelling the optical system as a series of interconnected lenses and apertures, allowing for the creation of spatially entangled photon pairs through a classical process.

By analysing how these entangled photons propagate, the researchers derive a mathematical expression for the maximum propagation distance, which depends on system parameters including the wavelength of light and the aperture sizes. The analysis considers the effects of diffraction and beam divergence, which contribute to signal loss and ultimately limit the distance over which nonlocality can be maintained. The key contribution of this work is the establishment of a clear theoretical limit on the propagation distance for classical nonlocal optical systems, calculated as 2. 3λ/(πa^2), where λ is the wavelength of light and a is the radius of the aperture.

This result provides a fundamental constraint on the design and implementation of classical systems attempting to mimic quantum phenomena, and offers insights into the distinction between classical and quantum nonlocality. The findings have implications for the development of novel optical devices and the exploration of the boundaries between classical and quantum physics. Researchers derive precise limits on how quickly optical beams can propagate, drawing an analogy to the quantum-speed limit. They map the propagation of highly nonlocal optical beams to a reversed harmonic-oscillator generator, constructing the propagator and evaluating the Bures distance. This allows them to obtain analytic Mandelstam, Tamm and Margolus, Levitin bounds, establishing a propagation distance limit to achieve a prescribed mode distinguishability.

Quantum Geometry Limits Optical Beam Propagation

This research establishes rigorous limits on how quickly optical beams can propagate and change shape, drawing an analogy between these limits and fundamental constraints in quantum mechanics. By modelling beam propagation through a non-local medium, scientists derive a minimum distance beyond which distinguishing between different beam modes becomes increasingly difficult. The team demonstrates that this limit is sensitive to variations in refractive index, beam power, and temperature, achieving resolutions of 10-7 refractive index units and 1 millikelvin, respectively, in a compact experimental platform. These findings bridge the gap between theoretical limits imposed by quantum geometry and practical applications in photonics, potentially enabling faster all-optical switching, improved wave metrology, and novel analogue optical logic circuits. The researchers acknowledge that future investigations will explore the behaviour of these beams in more complex, higher-dimensional, and energy-dissipating environments, and plan to integrate these propagation distance limits into the design of on-chip photonic architectures, aiming to unify quantum and classical wave dynamics for advanced photonic technologies.