Probing Classically Forbidden Motion: Energy-Speed Relationship and Test to Bohmian Mechanics

In quantum mechanics, regions of negative local kinetic energy can manifest. This occurs when the wave function's amplitude undergoes significant decay, typically associated with quantum tunneling. Here, we investigate the particles motion in a system of two coupled waveguide potentials, where the population transfer between the waveguides effectively acts as a clock, allowing particle speeds along the waveguide axis to be determined [1]. We implement this idea for photons in optical microcavity, using a novel nanostructuring method [2] to create waveguides. By applying this scheme to evanescent phenomena at a reflective potential step, we determine an energy-speed relationship for classically forbidden motion, which shows speed increase as energy decreases. Our findings contribute to the ongoing tunneling time debate, and separately, can be viewed as a test of Bohmian trajectories in quantum mechanics.
[1] Klaers, J., Sharoglazova, V., & Toebes, C. (2023). Physical Review A, 107(5), 052201.
[2] Vretenar, M., Puplauskis, M., Klaers, J.. Adv. Optical Mater. 2023, 2202820.