Interferometry has been at the heart of wave optics since its early stages, resolving the coherence of the light field and enabling the complete reconstruction of the optical information it encodes. Transferring this concept to the attosecond time domain shed new light on fundamental ultrafast electron phenomena. Here we introduce attosecond-gated interferometry and probe one of the most fundamental quantum mechanical phenomena, field-induced tunnelling. Our experiment probes the evolution of an electronic wavefunction under the tunnelling barrier and records the phase acquired by an electron as it propagates in a classically forbidden region. We identify the quantum nature of the electronic wavepacket and capture its evolution within the optical cycle. Attosecond-gated interferometry has the potential to reveal the underlying quantum dynamics of strong-field-driven atomic, molecular and solid-state systems.
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The main data supporting the findings of this study are available within the article and its Supplementary Information. Extra data are available from the corresponding author upon reasonable request.
The codes that support the findings of this study are available from the corresponding author upon reasonable request.
Corkum, P. B. & Krausz, F. Attosecond science. Nat. Phys. 3, 381–387 (2007).
Keldysh, L. V. Ionization in the field of a strong electromagnetic wave. Sov. Phys. JETP 20, 1307–1314 (1965).
Corkum, P. B. Plasma perspective on strong field multiphoton ionization. Phys. Rev. Lett. 71, 1994–1997 (1993).
Uiberacker, M. et al. Attosecond real-time observation of electron tunnelling in atoms. Nature 446, 627–632 (2007).
Klaiber, M., Hatsagortsyan, K. Z. & Keitel, C. H. Tunneling dynamics in multiphoton ionization and attoclock calibration. Phys. Rev. Lett. 114, 083001 (2015).
Ivanov, M. Y., Spanner, M. & Smirnova, O. Anatomy of strong field ionization. J. Mod. Opt. 52, 165–184 (2005).
Kheifets, A. S. The attoclock and the tunneling time debate. J. Phys. B 53, 072001 (2020).
Ni, H., Saalmann, U. & Rost, J.-M. Tunneling ionization time resolved by backpropagation. Phys. Rev. Lett. 117, 023002 (2016).
Wörner, H. J. et al. Conical intersection dynamics in NO2 probed by homodyne high-harmonic spectroscopy. Science 334, 208–212 (2011).
Schiffrin, A. et al. Optical-field-induced current in dielectrics. Nature 493, 70–74 (2013).
Yudin, G. L. & Ivanov, M. Y. Nonadiabatic tunnel ionization: looking inside a laser cycle. Phys. Rev. A 64, 013409 (2001).
Rost, J. M. & Saalmann, U. Attoclock and tunnelling time. Nat. Photon. 13, 439–440 (2019).
Eckle, P. et al. Attosecond ionization and tunneling delay time measurements in helium. Science 322, 1525–1529 (2008).
Sainadh, U. S. et al. Attosecond angular streaking and tunnelling time in atomic hydrogen. Nature 568, 75–77 (2019).
Shafir, D. et al. Resolving the time when an electron exits a tunnelling barrier. Nature 485, 343–346 (2012).
Landsman, A. S. et al. Ultrafast resolution of tunneling delay time. Optica 1, 343–349 (2014).
Arissian, L. et al. Direct test of laser tunneling with electron momentum imaging. Phys. Rev. Lett. 105, 133002 (2010).
Pfeiffer, A. N. et al. Probing the longitudinal momentum spread of the electron wave packet at the tunnel exit. Phys. Rev. Lett. 109, 083002 (2012).
Boge, R. et al. Probing nonadiabatic effects in strong-field tunnel ionization. Phys. Rev. Lett. 111, 103003 (2013).
Han, M., Ge, P., Shao, Y., Gong, Q. & Liu, Y. Attoclock photoelectron interferometry with two-color corotating circular fields to probe the phase and the amplitude of emitting wave packets. Phys. Rev. Lett. 120, 073202 (2018).
Eckart, S. et al. Direct experimental access to the nonadiabatic initial momentum offset upon tunnel ionization. Phys. Rev. Lett. 121, 163202 (2018).
Liu, K. et al. Detecting and characterizing the nonadiabaticity of laser-induced quantum tunneling. Phys. Rev. Lett. 122, 053202 (2019).
Li, M. et al. Photoelectron holographic interferometry to probe the longitudinal momentum offset at the tunnel exit. Phys. Rev. Lett. 122, 183202 (2019).
Pedatzur, O. et al. Attosecond tunnelling interferometry. Nat. Phys. 11, 815–819 (2015).
Eckart, S. et al. Ultrafast preparation and detection of ring currents in single atoms. Nat. Phys. 14, 701–704 (2018).
Hickstein, D. D. et al. Direct visualization of laser-driven electron multiple scattering and tunneling distance in strong-field ionization. Phys. Rev. Lett. 109, 073004 (2012).
Ni, H., Saalmann, U. & Rost, J.-M. Tunneling exit characteristics from classical backpropagation of an ionized electron wave packet. Phys. Rev. A 97, 013426 (2018).
Han, M. et al. Revealing the sub-barrier phase using a spatiotemporal interferometer with orthogonal two-color laser fields of comparable intensity. Phys. Rev. Lett. 119, 073201 (2017).
Han, M. et al. Complete characterization of sub-Coulomb-barrier tunnelling with phase-of-phase attoclock. Nat. Photon. 15, 765–771 (2021).
Dahlström, J. M., L’Huillier, A. & Mauritsson, J. Quantum mechanical approach to probing the birth of attosecond pulses using a two-colour field. J. Phys. B 44, 095602 (2011).
Zhao, J. & Lein, M. Determination of ionization and tunneling times in high-order harmonic generation. Phys. Rev. Lett. 111, 043901 (2013).
Azoury, D. et al. Electronic wavefunctions probed by all-optical attosecond interferometry. Nat. Photon. 13, 54–59 (2019).
Lewenstein, M., Balcou, P., Ivanov, M. Y., L’Huillier, A. & Corkum, P. B. Theory of high-harmonic generation by low-frequency laser fields. Phys. Rev. A 49, 2117–2132 (1994).
Freeman, R. et al. Above-threshold ionization with subpicosecond laser pulses. Phys. Rev. Lett. 59, 1092–1095 (1987).
De Boer, M. & Muller, H. Observation of large populations in excited states after short-pulse multiphoton ionization. Phys. Rev. Lett. 68, 2747–2750 (1992).
Gaarde, M. B., Tate, J. L. & Schafer, K. J. Macroscopic aspects of attosecond pulse generation. J. Phys. B 41, 132001 (2008).
Salières, P. et al. Feynman’s path-integral approach for intense-laser-atom interactions. Science 292, 902–905 (2001).
Torlina, L. & Smirnova, O. Coulomb time delays in high harmonic generation. New J. Phys. 19, 023012 (2017).
Azoury, D., Krüger, M., Bruner, B. D., Smirnova, O. & Dudovich, N. Direct measurement of coulomb-laser coupling. Sci. Rep. 11, 495 (2021).
Smirnova, O. & Ivanov, M. Y. in Attosecond and XUV Physics: Ultrafast Dynamics and Spectroscopy (eds Vrakking, M. & Schulz, T.) 201–256 (Wiley, 2013).
Zernike, F. Phase contrast, a new method for the microscopic observation of transparent objects. Physica 9, 686–698 (1942).
Smirnova, O. et al. High harmonic interferometry of multi-electron dynamics in molecules. Nature 460, 972–977 (2009).
Sansone, G. et al. Electron localization following attosecond molecular photoionization. Nature 465, 763–766 (2010).
Calegari, F. et al. Ultrafast electron dynamics in phenylalanine initiated by attosecond pulses. Science 346, 336–339 (2014).
Silva, R., Blinov, I. V., Rubtsov, A. N., Smirnova, O. & Ivanov, M. High-harmonic spectroscopy of ultrafast many-body dynamics in strongly correlated systems. Nat. Photon. 12, 266–270 (2018).
Jager, M. F. et al. Tracking the insulator-to-metal phase transition in VO2 with few-femtosecond extreme UV transient absorption spectroscopy. Proc. Natl Acad. Sci. USA 114, 9558–9563 (2017).
We thank D. Tannor, Y. Mairesse and B. Pons for helpful discussions. N.D. is the incumbent of the Robin Chemers Neustein Professorial Chair. N.D. acknowledges the Minerva Foundation, the Israeli Science Foundation, the Crown Center of Photonics and the European Research Council for financial support. M.I. and O.S. acknowledge support from the DFG SPP 1840 ‘Quantum Dynamics in Tailored Intense Fields’, DFG grants SM 292/5-2 and IV 152/6-2. This project has received funding from the European Union’s Horizon 2020 research and innovation programme under grant agreement no. 899794. O.K. acknowledges the Azrieli Foundation for the award of an Azrieli Fellowship. M.K. acknowledges financial support by the Minerva Foundation and the Koshland Foundation. D.A. acknowledges financial support by the Zuckerman STEM Leadership Program.
The authors declare no competing interests.
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Kneller, O., Azoury, D., Federman, Y. et al. A look under the tunnelling barrier via attosecond-gated interferometry. Nat. Photon. 16, 304–310 (2022). https://doi.org/10.1038/s41566-022-00955-7