A General Scenario of Tunneling Time in Different Energy Regimes

TL;DR

This paper provides a comprehensive theoretical analysis of tunneling time for Bose-condensed atoms across different energy regimes, revealing distinct scaling laws and addressing longstanding controversies.

Contribution

It introduces a unified framework for understanding tunneling time behavior across energy regimes, including effects of barrier width and quantum uncertainty.

Findings

Tunneling time decreases rapidly for negative incident energy.

Tunneling time reaches a maximum for positive energies below the barrier height.

The results align with Larmor clock experimental observations.

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.