Photon motion in classically forbidden regions

Quantum mechanics suggests a variety of velocity definitions, and some of them are not fully consistent with each other. For instance, in the issue of including density gradients of the wave function. Here we intend to reveal the significance of density gradients in determining photon velocity. We consider photon motion in a system of waveguide potentials described in our recent theoretical proposal [1]. In such a system, density transfer between two coupled waveguides acts as a clock and allows photon velocities to be determined. We implement a system of waveguides, confining 2D gas of massive photons, on one of the microcavity mirrors using a novel direct laser writing technique for mirror nanostructuring [2]. Such a microcavity platform has full experimental access to the wave function, and allows us to measure the period of density transfer, which is related to photon in-plane velocity. Application of this scheme to tunneling phenomena at a reflective step potential also makes it possible to measure the velocity in the classically forbidden regime and reveals the existence of a classically forbidden long-range photon transport as predicted.