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


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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Fig. 1: Larmor clock.
Fig. 2: Experimental setup and sequence.
Fig. 3: Implementation of the Larmor clock.
Fig. 4: Traversal time of an atomic wavepacket through an optical potential.

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.


  1. 1.

    MacColl, L. A. Note on the transmission and reflection of wave packets by potential barriers. Phys. Rev. 40, 621–626 (1932).

    ADS  MATH  Google Scholar 

  2. 2.

    Wigner, E. P. Lower limit for the energy derivative of the scattering phase shift. Phys. Rev. 98, 145–147 (1955).

    ADS  MathSciNet  CAS  MATH  Google Scholar 

  3. 3.

    Ranfagni, A., Mugnai, D., Fabeni, P. & Pazzi, G. P. Delay-time measurements in narrowed waveguides as a test of tunneling. Appl. Phys. Lett. 58, 774–776 (1991).

    ADS  CAS  Google Scholar 

  4. 4.

    Enders, A. & Nimtz, G. On superluminal barrier traversal. J. Phys. I 2, 1693–1698 (1992).

    Google Scholar 

  5. 5.

    Steinberg, A. M., Kwiat, P. G. & Chiao, R. Y. Measurement of the single-photon tunneling time. Phys. Rev. Lett. 71, 708–711 (1993).

    ADS  CAS  PubMed  PubMed Central  Google Scholar 

  6. 6.

    Spielmann, C., Szipöcs, R., Stingl, A. & Krausz, F. Tunneling of optical pulses through photonic band gaps. Phys. Rev. Lett. 73, 2308–2311 (1994).

    ADS  CAS  PubMed  PubMed Central  Google Scholar 

  7. 7.

    Sainadh, U. S. et al. Attosecond angular streaking and tunnelling time in atomic hydrogen. Nature 568, 75–77 (2019).

    ADS  CAS  PubMed  PubMed Central  Google Scholar 

  8. 8.

    Hauge, E. H. & Støvneng, J. A. Tunneling times: a critical review. Rev. Mod. Phys. 61, 917–936 (1989).

    ADS  Google Scholar 

  9. 9.

    Landauer, R. & Martin, T. Barrier interaction time in tunneling. Rev. Mod. Phys. 66, 217–228 (1994).

    ADS  Google Scholar 

  10. 10.

    Chiao, R. Y. & Steinberg, A. M. in Progress in Optics Vol. 37 (ed. Wolf, E.) 345–405 (Elsevier, 1997).

  11. 11.

    Steinberg, A. M. How much time does a tunneling particle spend in the barrier region? Phys. Rev. Lett. 74, 2405–2409 (1995).

    ADS  CAS  Google Scholar 

  12. 12.

    Steinberg, A. M. Conditional probabilities in quantum theory and the tunneling-time controversy. Phys. Rev. A 52, 32–42 (1995).

    ADS  MathSciNet  CAS  Google Scholar 

  13. 13.

    Aharonov, Y. & Vaidman, L. How the result of a measurement of a component of the spin of a spin-½ particle can turn out to be 100. Phys. Rev. Lett. 60, 1351–1354 (1988).

    ADS  CAS  Google Scholar 

  14. 14.

    Büttiker, M. & Landauer, R. Traversal time for tunneling. Phys. Rev. Lett. 49, 1739–1742 (1982).

    ADS  Google Scholar 

  15. 15.

    Büttiker, M. Larmor precession and the traversal time for tunneling. Phys. Rev. B 27, 6178–6188 (1983).

    ADS  Google Scholar 

  16. 16.

    Hartman, T. E. Tunneling of a wave packet. J. Appl. Phys. 33, 3427–3433 (1962).

    ADS  Google Scholar 

  17. 17.

    Deutsch, M. & Golub, J. Optical Larmor clock: measurement of the photonic tunneling time. Phys. Rev. A 53, 434–439 (1996).

    ADS  CAS  Google Scholar 

  18. 18.

    Balcou, P. & Dutriaux, L. Dual optical tunneling times in frustrated total internal reflection. Phys. Rev. Lett. 78, 851–854 (1997).

    ADS  CAS  Google Scholar 

  19. 19.

    Hino, M. et al. Measurement of Larmor precession angles of tunneling neutrons. Phys. Rev. A 59, 2261–2268 (1999).

    ADS  CAS  Google Scholar 

  20. 20.

    Esteve, D. et al. Observation of the temporal decoupling effect on the macroscopic quantum tunneling of a Josephson junction. In Proc. 9th Gen. Conf. Condensed Matter Division of the European Physical Society (eds Friedel, J. et al.) 121–124 (1989).

  21. 21.

    Eckle, P. et al. Attosecond angular streaking. Nat. Phys. 4, 565–570 (2008).

    CAS  Google Scholar 

  22. 22.

    Eckle, P. et al. Attosecond ionization and tunneling delay time measurements in helium. Science 322, 1525–1529 (2008).

    ADS  CAS  PubMed  PubMed Central  Google Scholar 

  23. 23.

    Pfeiffer, A. N., Cirelli, C., Smolarski, M. & Keller, U. Recent attoclock measurements of strong field ionization. Chem. Phys. 414, 84–91 (2013).

    CAS  Google Scholar 

  24. 24.

    Landsman, A. S. et al. Ultrafast resolution of tunneling delay time. Optica 1, 343–349 (2014).

    ADS  CAS  Google Scholar 

  25. 25.

    Camus, N. et al. Experimental evidence for quantum tunneling time. Phys. Rev. Lett. 119, 023201 (2017).

    ADS  PubMed  PubMed Central  Google Scholar 

  26. 26.

    Zimmermann, T., Mishra, S., Doran, B. R., Gordon, D. F. & Landsman, A. S. Tunneling time and weak measurement in strong field ionization. Phys. Rev. Lett. 116, 233603 (2016).

    ADS  PubMed  PubMed Central  Google Scholar 

  27. 27.

    Klaiber, M., Hatsagortsyan, K. Z. & Keitel, C. H. Under-the-tunneling-barrier recollisions in strong-field Ionization. Phys. Rev. Lett. 120, 013201 (2018).

    ADS  CAS  PubMed  PubMed Central  Google Scholar 

  28. 28.

    Torlina, L. et al. Interpreting attoclock measurements of tunnelling times. Nat. Phys. 11, 503–508 (2015).

    CAS  Google Scholar 

  29. 29.

    Landauer, R. Barrier traversal time. Nature 341, 567–568 (1989).

    ADS  Google Scholar 

  30. 30.

    Fortun, A. et al. Direct tunneling delay time measurement in an optical lattice. Phys. Rev. Lett. 117, 010401 (2016).

    ADS  CAS  Google Scholar 

  31. 31.

    Baz’, A. I. Lifetime of intermediate states. Sov. J. Nucl. Phys. 4, 182–188 (1966).

    Google Scholar 

  32. 32.

    Rybachenko, V. F. Time of penetration of a particle through a potential barrier. Sov. J. Nucl. Phys. 5, 635–639 (1967).

    Google Scholar 

  33. 33.

    Pollak, E. & Miller, W. H. New physical interpretation for time in scattering theory. Phys. Rev. Lett. 53, 115–118 (1984).

    ADS  CAS  Google Scholar 

  34. 34.

    Sokolovski, D. & Baskin, L. M. Traversal time in quantum scattering. Phys. Rev. A 36, 4604–4611 (1987).

    ADS  CAS  Google Scholar 

  35. 35.

    Potnis, S., Ramos, R., Maeda, K., Carr, L. D. & Steinberg, A. M. Interaction-assisted quantum tunneling of a Bose–Einstein condensate out of a single trapping well. Phys. Rev. Lett. 118, 060402 (2017).

    ADS  Google Scholar 

  36. 36.

    Zhao, X. et al. Macroscopic quantum tunneling escape of Bose–Einstein condensates. Phys. Rev. A 96, 063601 (2017).

    ADS  Google Scholar 

  37. 37.

    Ramos, R., Spierings, D., Potnis, S. & Steinberg, A. M. Atom-optics knife edge: measuring narrow momentum distributions. Phys. Rev. A 98, 023611 (2018).

    ADS  CAS  Google Scholar 

  38. 38.

    Chu, S., Bjorkholm, J. E., Ashkin, A., Gordon, J. P. & Hollberg, L. W. Proposal for optically cooling atoms to temperatures of the order of 10−6 K. Opt. Lett. 11, 73–75 (1986).

    ADS  CAS  Google Scholar 

  39. 39.

    Ammann, H. & Christensen, N. Delta-kick cooling: a new method for cooling atoms. Phys. Rev. Lett. 78, 2088–2091 (1997).

    ADS  CAS  Google Scholar 

  40. 40.

    Morinaga, M., Bouchoule, I., Karam, J.-C. & Salomon, C. Manipulation of motional quantum states of neutral atoms. Phys. Rev. Lett. 83, 4037–4040 (1999).

    ADS  CAS  Google Scholar 

  41. 41.

    Maréchal, E. et al. Longitudinal focusing of an atomic cloud using pulsed magnetic forces. Phys. Rev. A 59, 4636–4640 (1999).

    ADS  Google Scholar 

  42. 42.

    Myrskog, S. H., Fox, J. K., Moon, H. S., Kim, J. B. & Steinberg, A. M. Modified “delta -kick cooling” using magnetic field gradients. Phys. Rev. A 61, 053412 (2000).

    ADS  Google Scholar 

  43. 43.

    Le Kien, F., Schneeweiss, P. & Rauschenbeutel, A. Dynamical polarizability of atoms in arbitrary light fields: general theory and application to cesium. Eur. Phys. J. D 67, 92 (2013).

    ADS  Google Scholar 

  44. 44.

    Leavens, C. R. & Aers, G. C. Extension to arbitrary barrier of the Büttiker–Landauer characteristic barrier interaction times. Solid State Commun. 63, 1101–1105 (1987).

    ADS  Google Scholar 

  45. 45.

    Cohen-Tannoudji, C., Diu, B. & Laloë, F. Quantum Mechanics (Wiley, 1977).

  46. 46.

    Sánchez-Soto, L. L., Monzón, J. J., Barriuso, A. G. & Cariñena, J. F. The transfer matrix: a geometrical perspective. Phys. Rep. 513, 191–227 (2013).

    ADS  MathSciNet  Google Scholar 

  47. 47.

    Bao, W. & Cai, Y. Mathematical theory and numerical methods for Bose–Einstein condensation. Kinetic Relat. Models 6, 1–135 (2012).

    MathSciNet  MATH  Google Scholar 

  48. 48.

    Wang, H. A time-splitting spectral method for computing dynamics of spinor F = 1 Bose–Einstein condensates. Int. J. Comput. Math. 84, 925–944 (2007).

    MathSciNet  MATH  Google Scholar 

  49. 49.

    Bao, W. Ground states and dynamics of multicomponent Bose–Einstein condensates. Multiscale Model. Sim. 2, 210–236 (2004).

    MATH  Google Scholar 

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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




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.

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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.

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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.

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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).

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