From 2019... They used the spin precession of the Rb atoms as a clock to measure the time it takes them to cross the classically forbidden region; traversal time was 0.61(7) ms

Measurement of the time spent by a tunnelling atom within the barrier region. Ramón Ramos, David Spierings, Isabelle Racicot & Aephraim M. Steinberg. Nature volume 583, pages529–532(2020). Jul 22, 2020. https://www.nature.com/articles/s41586-020-2490-7

Abstract: Tunnelling is one of the most characteristic phenomena of quantum physics, underlying processes such as photosynthesis and nuclear fusion, as well as devices ranging from superconducting quantum interference device (SQUID) magnetometers to superconducting qubits for quantum computers. The question of how long a particle takes to tunnel through a barrier, however, has remained contentious since the first attempts to calculate it1. It is now well understood that the group delay2—the arrival time of the peak of the transmitted wavepacket at the far side of the barrier—can be smaller than the barrier thickness divided by the speed of light, without violating causality. This has been confirmed by many experiments3,4,5,6, and a recent work even claims that tunnelling may take no time at all7. There have also been efforts to identify a different timescale that would better describe how long a given particle spends in the barrier region8,9,10. Here we directly measure such a time by studying Bose-condensed 87Rb atoms tunnelling through a 1.3-micrometre-thick optical barrier. By localizing a pseudo-magnetic field inside the barrier, we use the spin precession of the atoms as a clock to measure the time that they require to cross the classically forbidden region. We study the dependence of the traversal time on the incident energy, finding a value of 0.61(7) milliseconds at the lowest energy for which tunnelling is observable. This experiment lays the groundwork for addressing fundamental questions about history in quantum mechanics: for instance, what we can learn about where a particle was at earlier times by observing where it is now11,12,13.

Free version from 2019... Measuring the time a tunnelling atom spends in the barrier. Ramón Ramos, David Spierings, Isabelle Racicot, Aephraim M. Steinberg. arXiv:1907.13523. Jul 31 2019. https://arxiv.org/abs/1907.13523

Abstract: Tunnelling is one of the most paradigmatic and evocative phenomena of quantum physics, underlying processes such as photosynthesis and nuclear fusion, as well as devices ranging from SQUID magnetometers to superconducting qubits for quantum computers. The question of how long a particle takes to tunnel, however, has remained controversial since the first attempts to calculate it, which relied on the group delay. It is now well understood that this delay (the arrival time of the transmitted wave packet peak at the far side of the barrier) can be smaller than the barrier thickness divided by the speed of light, without violating causality. There have been a number of experiments confirming this, and even a recent one claiming that tunnelling may take no time at all. There have also been efforts to identify another timescale, which would better describe how long a given particle spends in the barrier region. Here we present a direct measurement of such a time, studying Bose-condensed 87Rb atoms tunnelling through a 1.3-μm thick optical barrier. By localizing a pseudo-magnetic field inside the barrier, we use the spin precession of the atoms as a clock to measure the time it takes them to cross the classically forbidden region. We find a traversal time of 0.62(7) ms and study its dependence on incident energy. In addition to finally shedding light on the fundamental question of the tunnelling time, this experiment lays the groundwork for addressing deep foundational questions about history in quantum mechanics: for instance, what can we learn about where a particle was at earlier times by observing where it is now?