  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.
