When can Light GO Faster than Light? the Tunneling Time and its Sub-Femtosecond Measurement via Quantum Interference.

The quantum properties of light are reviewed, in particular as they are illuminated in two-photon interference effects. Special attention is paid to Einstein-Podolsky -Rosen-like correlations and to the effects of "which-path" (welcher Weg) information on interference. Theoretical and experimental results are presented demonstrating that these effects are useful for high-precision measurements of single-photon propagation times, and make these measurements largely insensitive to group-velocity dispersion. We confirm that single photons in glass travel at the group velocity, an example of 'wave-particle unity.' The longstanding controversy over the duration of quantum-mechanical tunneling is briefly described, and an analogy is drawn with evanescent wave phenomena in optics. The relationship between one- and two-dimensional tunneling times is discussed at some length, and certain general results relating transmission and reflection delays are derived. An experiment is presented in which a multilayer dielectric mirror, described as a "photonic bandgap" medium, serves as a tunnel barrier. The peaks of those single-photon wave packets which tunnel through this mirror are observed to arrive sooner than those which travel instead through an equivalent length of air. It is explained that this does not violate relativistic causality. Interpretational issues are analyzed to some extent. Another proposed experiment is described, in which similar effects could be observed with 100% transmission; such a scheme might be useful for compensating propagation delays in optical transmissions, and should be faithful even at the single-photon level. Finally, it is argued that there is a sensible way to define conditional probabilities in quantum theory, and that these probabilities describe physically measurable effects. They are related to Aharonov et al.'s concept of "weak measurements" and the Feynman-averaging procedure pioneered by Sokolovski et al. They allow one to discuss the history of a particle which has tunnelled, as distinct from that of those members of the initial ensemble which were reflected. I attempt to show that this approach unifies many of the previous discussions of tunneling times, in particular elucidating the meaning of imaginary momenta and complex times.