Quantum Origin of Diffraction from Bright and Dark States

TL;DR

This work develops a continuous-mode bright- and dark-state framework to provide a particle-based quantum origin of diffraction, unifying it with classical wave optics. By constructing a detector-oriented basis $|\psi_n(\theta)\rangle$ and identifying a bright mode $|\text{Bright}_\theta\rangle$ and an infinite-dimensional dark subspace $|\text{Dark}_{n,\theta}\rangle$, diffraction is shown to arise from projection onto the bright mode, while dark states remain undetectable. For multi-photon states, the theory yields antibunching for Fock states via $G^{(2)}_{\text{Fock}}(\theta) = 1 - 1/N$ and reproduces classical diffraction with coherent states, where $G^{(1)}_{\text{Coh.}}(\theta) = g^2 |\alpha|^2 b (\sin\beta/\beta)^2$ and $G^{(2)}_{\text{Coh.}}(\theta)=1$, illustrating how quantum statistics shape higher-order correlations despite identical intensity patterns. The framework links quantum optics with classical diffraction, suggests experimental realizations in engineered multimode systems, and points to dark-space photonics as a potential decoherence-free quantum memory.

Abstract

Building upon the recently introduced particle interpretation of the double-slit experiment [Phys. Rev. Lett. 134, 133603 (2025)] which attributes interference phenomena to detector-coupled (bright) and detector-uncoupled (dark) states of light, we develop a continuous-mode extension of the bright- and dark-state framework. This extension addresses a conceptual distinction between interference and diffraction, that is, the transition from a finite set of discrete paths to a continuum of modes. Through the construction of a complete detector-oriented basis for single-slit diffraction, we demonstrate that the observed diffraction pattern arises from projection of the photon state onto a single bright mode by identifying the detectable and undetectable modes, with photons detected at intensity minima having zero probability, as they reside in modes spanning an infinite-dimensional dark subspace. Our approach thus provides a unified particle-based explanation of diffraction that connects quantum and classical wave optics, and reveals distinctive quantum signatures in higher-order correlations.

Figures (1)

• Figure 1: Fraunhofer single-slit diffraction intensity distribution, where the red envelope represents the diffraction pattern predicted by classical wave optics. The quantum interpretation is visualized as follows: the red dots on the screen represent photons in bright states, which can excite the sensor atoms and thereby cause a detectable response from the detector. In contrast, the gray dots correspond to photons in dark states which fail to excite the sensor atoms; hence although physically present, these photons remain undetectable.