QI In the literature: open

Does the Larmor tunneling time saturate for thick barriers?

In plain words

The Hartman effect predicts that the tunneling delay stops growing as the barrier gets thicker, which would imply speeds above that of light. Cold-atom experiments that use an atom's spin as a built-in clock can now test this.

Precise statement

For cold atoms (e.g. 87Rb) tunneling through an optical barrier with an internal-state Larmor clock, measure the transmitted-atom Larmor times $\tau_y$ and $\tau_z$ versus barrier width $L$ in the opaque regime $\kappa L >> 1$, $\kappa = \sqrt{2 m (V_0 - E)} / \hbar$, and determine whether they saturate with $L$ as the Hartman effect predicts for the phase delay.

What would settle it

A Larmor-clock measurement over a range of $L$ reaching $\kappa L$ of several, with transmission high enough to resolve the precession.

Status in the literature

Larmor times of about 0.6 ms were measured for rubidium atoms in 2020, and their decrease at lower incident energy was reported in 2021 (arXiv:2101.12309).