Quantum super-oscillation of a single photon

Abstract

Super-oscillation is a counter-intuitive phenomenon describing localized fast variations of functions and fields that happen at frequencies higher than the highest Fourier component of their spectra. The physical implications of the effect have been studied in information theory and optics of classical fields, and have been used in super-resolution imaging. As a general phenomenon of wave dynamics, super-oscillations have also been predicted to exist in quantum wavefunctions. Here we report the first experimental demonstration of super-oscillatory behavior of a single quantum object, a photon. The super-oscillatory behavior is demonstrated by tight localization of the photon wavefunction after focusing with a dedicated slit mask designed to create an interference pattern with a sub-wavelength hotspot. The observed hotspot of the single-photon wavefunction is demonstrably smaller than the smallest hotspots that could have been created by the highest-frequency free-space wavevectors available as the result of scattering from the mask.