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# Measurement of the time spent by a tunnelling atom within the barrier region

## 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.

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• ### On the status of quantum tunnelling time

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## Data availability

The data presented in the figures and that support the other findings of this study are available from the corresponding author on reasonable request. Source data are provided with this paper.

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## Acknowledgements

We acknowledge years of hard work by the people who created the Bose–Einstein condensation apparatus and helped make the present experiment possible: A. Jofre, M. Siercke, C. Ellenor, M. Martinelli, R. Chang, S. Potnis and A. Stummer. We thank J. Thywissen, A. Vutha, J. McGowan, K. Bonsma-Fisher and A. Brodutch for discussions. This work was supported by NSERC and the Fetzer Franklin Fund of the John E. Fetzer Memorial Trust. A.M.S. is a fellow of CIFAR. R.R. acknowledges support from CONACYT.

## Author information

Authors

### Contributions

R.R., D.S. and I.R. performed the experiments. A.M.S. supervised the work. All authors made contributions to the work, discussed the results and contributed to the writing of the manuscript.

### Corresponding author

Correspondence to Ramón Ramos.

## Ethics declarations

### Competing interests

The authors declare no competing interests.

Peer review information Nature thanks Adolfo Del Campo, Olga Smirnova and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

## Extended data figures and tables

### Extended Data Fig. 1 Calculated time density of the Larmor components τy and τz using the transfer-matrix method for a 135-nK Gaussian barrier.

The black dashed lines indicate the 1/e2 radius of the Gaussian barrier and the grey lines show the classical turning points. The Larmor time τy (or τz) is obtained by integrating over space, taking into account the position-dependent coupling of the Raman beams.

### Extended Data Fig. 2 Simulations of the Larmor clock.

The simulations correspond to one-dimensional two-component time-dependent Schrödinger and Gross–Pitaevskii simulations. The parameters are as in Fig. 4.

## Rights and permissions

Reprints and Permissions

Ramos, R., Spierings, D., Racicot, I. et al. Measurement of the time spent by a tunnelling atom within the barrier region. Nature 583, 529–532 (2020). https://doi.org/10.1038/s41586-020-2490-7

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• DOI: https://doi.org/10.1038/s41586-020-2490-7

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