(Published in Nature Photonics)
Laser-induced electron tunnelling—which triggers a broad range of ultrafast phenomena such as the generation of attosecond light pulses, photoelectron diffraction and holography—has laid the foundation for strong-field physics and attosecond science. Using the attoclock constructed by single-colour elliptically polarized laser fields, previous experiments have measured the tunnelling rates, exit positions, exit velocities and delay times for some specific electron trajectories, which are mostly created at the field peak instant, that is, when the laser electric field and the formed potential barrier are stationary in terms of the derivative versus time. From the view of wave-particle dualism, the electron phase under a classically forbidden, tunnelling barrier has not been measured, which is at the heart of quantum tunnelling physics.
The authors present a robust measurement of tunnelling dynamics including the electron sub-barrier phase and amplitude. They combine the attoclock technique with two-colour phase-of-phase (POP) spectroscopy to accurately calibrate the angular streaking relation and to probe the non-stationary tunnelling dynamics by manipulating a rapidly changing potential barrier. This POP attoclock directly links the measured phase of the two-colour relative phase with the ionization instant for the photoelectron with any final momentum on the detector, allowing the researchers to reconstruct the imaginary tunnelling time and the accumulated phase under the barrier. The POP attoclock provides a general time-resolved approach to accessing the underlying quantum dynamics in intense light–matter interactions.


Fig. 2: Experimental results of the POP attoclock. a,b, Measured POP (a) and contrast (b) spectra for krypton atoms in the POP attoclock configuration. c, The cuts of Φ_POP along energies of 4 eV (left), 8 eV (middle) and 16 eV (right). On the right vertical coordinate the phase of the phase is transformed to the ionization instant using Φ_POP = ωt.