Particle Aspects in Tunneling Dynamics

Ciann‐Dong Yang

M. Kira, Ilkka Juhani Tittonen, Stig Stenholm

The dynamics of particle tunneling is characterized by the concept of a tunneling time. The various times suggested in the literature are considered in order to characterize the complementary features of the tunneling process. Explicit calculations show how to find the particle and the wave aspects of different tunneling times. We also expose the physics behind the various definitions and their interrelations. We show that in the classical limit the particle properties dominate and in the opaque limit the wave aspects do. The complementary analysis helps in the interpretation of the tunneling process and eliminates some of the controversies found in the literature. All tunneling times are found to be special cases of a universal tunneling time definition relating to parameter derivatives of the phases of the wave functions. We propose that these relations can be used to extract the tunneling times for any general potential by integrating the wave packet through the tunneling process and extracting the derivatives numerically from these results. Furthermore, we investigate the particle properties of resonant tunneling. They are shown to dominate the dynamics inside the well regions.

Xiwang Liu, Xiaokai Li, Yichong Lin +7 more

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.

Kaoru Awaka, Gen Tatara, Hidetoshi Fukuyama

M. Kira, Ilkka Juhani Tittonen, Stig Stenholm

The time evolution of a quantum-mechanical tunnelling process is discussed. The use of a quantum generalization of particle paths facilitates the separation of particle and wave aspects of tunnelling. We present a novel complex time object which enters invariantly several tunnelling times derived for barriers of arbitrary shape. Its asymptotic behaviour is shown to agree with an intuitive understanding of particle tunnelling. As a result, the complementary features of several tunnelling times are identified exactly for the first time.

G. Dekel, O. V. Farberovich, Avy Soffer +1 more