Abstract
The question of how long it takes a particle to traverse a tunneling barrier is an old and controversial one, which, because of its relevance to the design of nanostructures, has recently become of increasing practical importance. There have been many conflicting theoretical and experimental answers to this question. By means of a quantum- optical technique that allows the measurement of the time of flight of individual photons with high precision, viz. the Hong-Ou-Mandel interferometer, we have measured the time delay for a photon to appear on the far side of a tunneling barrier. This barrier consists of an 11-layer periodic dielectric coating whose overall thickness is d ≈ 1.1 µm. This periodic structure possesses a photonic band gap from λ = 600 to 800 nm. Photons of wavelength 702 nm, which we used, must tunnel through such a structure in order to be transmitted, since the effective wave vector at midgap is purely imaginary. The surprising result of our measurements is that this time delay of 1.47 ± 0.21 fs is significantly less than d/c, where c is the speed of light in vacuum. Hence the tunneling process is apparently superluminal [the apparent tunneling velocity is (1.7 ± 0.2)c]; however, genuine signals cannot be sent in this way, and therefore Einstein causality is not violated. The measured times are in agreement with the Wigner time (the phase time, or group delay) but disagree with the semiclassical time and Buetikker’s Larmor time; however, all of these theories agree that the tunneling time should be superluminal. Recent data are presented, as weil as a recent theoretical calculation of tunneling through a periodic dielectric medium with gain, which indicate that the interaction time, defined in terms of the effective time over which the tunneling light is amplified, also agrees with the Wigner time.
© 1994 Optical Society of America
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