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Applied Physics Letters

Delay-time measurements in narrowed waveguides as a test of tunneling

Anedio Ranfagni, Daniela Mugnai, Pasquale Fabeni, Gian Paolo Pazzi

Published Feb 18, 1991• 148 citations
Publisher

Abstract

Delay-time measurements with a microwave setup, where a step narrowing in the waveguide simulates a quantum mechanical potential barrier, have been performed even beyond the cutoff. This allows experimental measurements in a very accessible temporal range of the order of nanoseconds. The results, interpreted as tunneling times, are compared with the existing quantum mechanical models, translated into the electromagnetic framework.

DOI
10.1063/1.104544

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Delay-time measurements with a microwave setup, where a step narrowing in the waveguide simulates a quantum mechanical potential barrier, have been performed even beyond the cutoff. This allows experimental measurements in a very accessible temporal range of the order of nanoseconds. The results, interpreted as tunneling times, are compared with the existing quantum mechanical models, translated into the electromagnetic framework.
The analogy between quantum tunneling of particles and evanescent electromagnetic waves can be used to study particle tunneling. Possibilities for the measurement of the time delay resulting from the transmission of waves through an evanescent region, say with lower dielectric constant, are discussed. In contrast to particle tunneling, an electromagnetic pulse can consist of many photons and can be probed in a noninvasive way. We emphasize the delay of the centroid of an electromagnetic pulse transmitted below cutoff through a portion of a waveguide with the same cross section as the adjacent propagating guides. The boundary conditions at the interface between the propagating and the evanescent region lead to the same transmission and reflection coefficients as for a square-barrier tunneling problem. For a pulse restricted to a narrow frequency range, the time delay depends only on the frequency derivative of the phase shift associated with transmission. The delay of a centroid is just that; there is no deeper physical sense which links the incoming centroid to the outgoing centroid. For sufficiently long evanescent regions, the delay is independent of thickness.
Delay time results obtained in microwave experiments at frequencies above and below the cutoff frequency of different waveguide sections are interpreted on the basis of wave propagation in the presence of dissipative effects. Kac's original suggestion was the starting point for the formulation of a stochastic model, which has now been substantially improved, also in relation to the transition-elements theory of Feynman-Hibbs. In this way, an approach to the problem is provided, which is completely distinct from the ones formulated elsewhere.
How much time does a wave packet spent in tunneling a barrier? Quantum mechanical calculations result in zero time inside a barrier. In the nineties analogous tunneling experiments with microwaves were carried out confirming quantum mechanics. Electron tunneling time is hard to measure being extremely short. However, quite recently the atomic ionization tunneling time has been measured. Experimental data of photonic, phononic, and electronic tunneling time is available now. It appears that the tunneling time is a universal property in the investigated time range of twelve orders of magnitude.