Spatially structured photons that travel in free space slower than the speed of light

TLDR

The constancy of light speed in free space is a cornerstone of physics, yet finite transverse beam size modifies wavevectors, altering phase and group velocities. We study the group velocity of single photons by measuring a change in their arrival time that results from changing the beam's transverse spatial structure. Using time‑correlated photon pairs, we show a reduction of the group velocity of photons in both a Bessel beam and a focused Gaussian beam. The experiments reveal that photons in Bessel and focused Gaussian beams experience several‑micron delays over a meter, demonstrating that spatial structure reduces group velocity and that the speed‑of‑light invariance holds only for plane waves.

Abstract

That the speed of light in free space is constant is a cornerstone of modern physics. However, light beams have finite transverse size, which leads to a modification of their wavevectors resulting in a change to their phase and group velocities. We study the group velocity of single photons by measuring a change in their arrival time that results from changing the beam's transverse spatial structure. Using time-correlated photon pairs we show a reduction of the group velocity of photons in both a Bessel beam and photons in a focused Gaussian beam. In both cases, the delay is several microns over a propagation distance of the order of 1 m. Our work highlights that, even in free space, the invariance of the speed of light only applies to plane waves. Introducing spatial structure to an optical beam, even for a single photon, reduces the group velocity of the light by a readily measurable amount.