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Applied Physics Letters

Measurement of tunneling time via electron interferometry

Jose C. Martinez, E. Polatdemir

Published Feb 12, 2004• 10 citations
Publisher

Abstract

After many decades, our understanding of the tunneling time across a barrier at the theoretical and experimental levels remains unsatisfactory and subject to debate. We describe an electron interference experiment by which the tunneling time across a symmetric potential barrier can be obtained from the phase shift introduced by the barrier to the interference pattern. We compare these phase shifts as predicted by three competing views of the tunneling time.

DOI
10.1063/1.1650553

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After many decades, our understanding of the tunneling time across a barrier at the theoretical and experimental levels remains unsatisfactory and subject to debate. We describe an electron interference experiment by which the tunneling time across a symmetric potential barrier can be obtained from the phase shift introduced by the barrier to the interference pattern. We compare these phase shifts as predicted by three competing views of the tunneling time.
Tunneling is one of the most bizarre phenomena in quantum mechanics. An attempt to understand it led to the next natural question of how long does a particle need to tunnel a barrier. The latter gave rise to several definitions such as the phase, dwell, Larmor and traversal times among others. A short review of the evolution of these time concepts, followed by an account of experiments involving field-induced tunnel ionization and electron tunneling in a solid state junction is presented here. Whereas the former experiments use sophisticated techniques involving femtosecond laser pulses and determine the tunneling time by mapping the angle of rotation of the field vector to time, like the hands of a watch, the latter provides a simpler method through the measurement of current-voltage characteristics of the junction.
Laser-induced electron tunneling ionization from atoms and molecules plays as the trigger for a broad class of interesting strong-field phenomena in attosecond community. Understanding the time of electron tunneling ionization is vital to achieving the ultimate accuracy in attosecond metrology. We propose a novel attosecond photoelectron interferometer, which is based on the interference of the direct and near-forward rescattering electron wave packets, to determine the time information characterizing the tunneling process. Adding a weak perturbation in orthogonal to the strong fundamental field, the phases of the direct and the near-forward rescattering electron wave packets are modified, leading to the shift of the interferogram in the photoelectron momentum distributions. By analyzing the response of the interferogram to the perturbation, the real part of the ionization time, which denotes the instant when the electron exits the potential barrier, and the associated rescattering time are precisely retrieved. Moreover, the imaginary part of the ionization time, which has been interpreted as a quantity related to electron motion under the potential barrier, is also unambiguously determined.
Quantum particles interacting with potential barriers are ubiquitous in physics, and the question of how much time they spend inside classically forbidden regions has attracted interest for many decades. Recent developments of new experimental techniques revived the issue and ignited a debate with often contradictory results. This motivates the present study of an exactly solvable model for quantum tunneling induced by a strong field. We show that the tunneling dynamics can depart significantly from the scenario in which the barrier-traversal time is zero or very small. However, our findings do not support the idea of a well-defined tunneling time either. Our numerically exact results should help in finding a consensus about this fundamental problem.
Quantum tunneling, a quintessential quantum phenomenon, challenges classical intuitions by allowing particles to pass through seemingly insurmountable barriers. This study delves into the intricate dynamics of electron tunneling, focusing on the critical role of sub-barrier interactions and complex time processes. Through a combination of experimental measurements and simulations based on Feynman’s path integral of complex time trajectories, we reveal that the sub-barrier potential interaction introduces an asymmetric electron wave packet probability distribution along the real time axis and a marked delay at the tunneling exit. The energy-dependent behavior of this delay in electronic tunneling agrees with that observed in the previous atomic tunneling studies, suggesting a universal mechanism underlying quantum tunneling across different scales. Our findings underscore the necessity of incorporating both the wave and particle aspects of quantum entities to fully comprehend tunneling dynamics, which holds promise for an intuitive interpretation of complex-number quantum processes.
In the so-called electric Aharonov-Bohm effect, a quantum interference pattern shift is produced when electrons move in an electric field-free region but, at the same time, under the presence of a time-dependent electric potential. Analogous fringe shifts are observed in interference experiments where electrons, travelling through an electrostatic field, suffer a classical lag effect produced by electric forces. Since these experiments are reported mainly in specialized journals, it could be rather difficult and time consuming for a student to attain a comprehensive overview of the subject. Therefore, particular attention has been addressed to reviewing the theory, to describing a couple of experiments and to the interpretation of the results. We believe that students can be suitably introduced to exploring the “paradoxical” aspects of the interaction of electrons with electric potentials and fields.