Analogies between electron and photon tunneling: A proposed experiment to measure photon tunneling times

Abstract

The phenomenon of tunneling is a well-known fundamental consequence of quantum mechanics. All particles can in principle tunnel. In particular, both electrons and photons can tunnel through classically forbidden regions of space known as “barriers”. However, there have been numerous controversies over how long it takes a particle to cross a barrier. Exploiting an analogy between electrons and photons, we suggest an experiment to infer the characteristics of an electron's barrier-traversal time by measuring the time it takes a photon to traverse a similar barrier. Electron tunneling experiments are in general much more difficult to perform than analogous optical ones. With an optical technique one can construct optical barriers on the scale of microns, in contrast to theångstrom-scale barriers required for electron tunneling. Our experiment may help settle the controversies over tunneling times. By means of a newly developed quantum optical technique, we should be able to measure the tunneling times of individual photons with sub-picosecond resolution. In our experiments we are using a two-photon light source, in which a pair of tightly correlated photons is generated by the process of spontaneous parametric down-conversion. Hong, Ou and Mandel have already achieved a sub-picosecond comparison between the arrival times of two such photons at a beam splitter placed at the intersection of their paths. In our geometry, one member of the photon pair tunnels through a barrier, while the other does not. Then coincidence detection of this photon pair constitutes the detection of an individual tunneling event. The particle aspect of photon tunneling can thus be clearly observed. We propose to use the Hong-Ou-Mandel technique to measure the tunneling time. We have chosen for our tunneling barrier two glass prisms placed in close proximity, utilizing the phenomenon of frustrated total internal reflection.