Quantum super-oscillation of a single photon

Abstract : Super-oscillation is a counterintuitive 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 this 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 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 an appropriately designed slit mask to create an interference pattern with a sub-diffraction hotspot (~0.45 λ). Such quantum super-oscillation can be used for low-intensity far-field super-resolution imaging techniques even down to single-photon counting regime, which would be of interest to quantum physics and non-invasive and label-free biological studies.