Different Approaches to the Tunneling

Arthur Cohn, Mario Rabinowitz

Jan von Delft, Christopher L. Henley

In some spin tunneling problems there are several different but symmetry-related tunneling paths that connect the same initial and final configurations. The topological phase factors of the corresponding tunneling amplitudes can lead to destructive interference between the different paths, so that the total tunneling amplitude is zero. In the study of tunneling between different ground-state configurations of the Kagom\'e-lattice quantum Heisenberg antiferromagnet, this occurs when the spin s is half odd integer.

Saleem I. Qashou

The nonlinear Landau-Zener tunneling of a Bose-Einstein condensate (BEC) of two different of particles in an accelerating optical lattice is investigated. The analytical eigenstates and the tunneling probability are obtained. It is shown that the eigenstates and the tunneling probability are modified dramatically by the interaction of the two different particles.

Aloïs Würger

Peter Hänggi A

Sheng-Chang Li

Abstract We theoretically study the tunneling time by investigating a wave packet of Bose-condensed atoms passing through a square barrier. We find that the tunneling time exhibits different scaling laws in different energy regimes. For negative incident energy of the wave packet, counterintuitively, the tunneling time decreases very rapidly with decreasing incident velocity. In contrast, for positive incident energy smaller than the barrier height, the tunneling time increases slowly and then reaches a maximum, which is in agreement with the Larmor clock experiments. The effect of the barrier width related to the uncertainty principle on the maximum tunneling time is also addressed. Our work provides a general scenario of tunneling time that can be used to understand and explain the controversy over tunneling time.