More about Tunneling Time

Kaushik Maji, C. K. Mondal, S. P. Bhattacharyya

The concept of ‘tunnelling time’ in the context of quantum particle tunnelling is reviewed. Various suggestions of linking the tunnelling dynamics with a characteristic time (real or complex) like the phase time, barrier interaction time (bounce time), presence time, etc. are analysed. A simple but fully quantal method of defining and estimating a real tunnelling time is examined in a variety of situations. The recently proposed idea of interpreting ‘tunnelling time’ as the cavity lifetime of a particle is also explored. We emphasize that proton or H-atom transfer reactions in double or triple wells offer systems in which the signature of the tunnelling time should be recognizable not just indirectly through the tunnelling splitting of spectral lines, but by following the relaxation dynamics of the subsystem that the proton or H atom leaves by tunnelling.

H. M. Nussenzveig

Nicolas Teeny, Christoph H. Keitel, Heiko Bauke

The Salecker-Wigner-Peres quantum-clock approach is applied in order to determine the tunneling time of an electron in strong-field tunnel ionization via a time-dependent electric field. Our results show that the ionization of the electron takes a nonvanishing period of time. This tunneling time is of the order of the Keldysh time but strictly larger than the Keldysh time. Comparing the quantum-clock tunneling time to the mean tunneling time as obtained by the virtual-detector approach, one finds that these two complementary methods give very similar results. Due to the asymmetric distribution of the tunneling time, there is a nonnegligible discrepancy between the mean tunneling time and the most probable tunneling time.

Philip Caesar Flores, Dean Alvin L. Pablico, Eric A. Galapon

Abstract We introduce the concept of partial-tunneling and full-tunneling processes to explain the seemingly contradictory non-zero and vanishing tunneling times often reported in the literature. Our analysis starts by considering the traversal time of a quantum particle through a potential barrier, including both above- and below-barrier traversals, using the theory of time-of-arrival operators. We then show that there are three traversal processes corresponding to non-tunneling, full tunneling, and partial tunneling. The distinction among the three depends on the support of the incident wave packet's energy distribution in relation to the shape of the barrier. Non-tunneling happens when the energy distribution of the quantum particle lies above the maximum of the potential barrier. Otherwise, full-tunneling process occurs when the energy distribution of the particle is below the minimum of the potential barrier. For this process, the obtained traversal time is interpreted as the tunneling time. Finally, the partial-tunneling process occurs when the energy distribution lies between the minimum and maximum of the potential barrier. This signifies that the quantum particle tunneled only through some portions of the potential barrier. We argue that the duration for a partial-tunneling process should not be interpreted as the tunneling time but instead as a partial traversal time to differentiate it from the full-tunneling process. We then show that a full-tunneling process is always instantaneous, while a partial-tunneling process takes a non-zero amount of time. We are then led to the hypothesis that experimentally measured non-zero and vanishing tunneling times correspond to partial- and full-tunneling processes, respectively.

Μ. Büttiker, Rolf W. Landauer