The tunnelling of a particle through a barrier is one of the most fundamental and ubiquitous quantum processes. When induced by an intense laser field, electron tunnelling from atoms and molecules initiates a broad range of phenomena such as the generation of attosecond pulses1, laser-induced electron diffraction2, 3 and holography2, 4. These processes evolve on the attosecond timescale (1 attosecond ≡ 1 as = 10−18 seconds) and are well suited to the investigation of a general issue much debated since the early days of quantum mechanics5, 6, 7—the link between the tunnelling of an electron through a barrier and its dynamics outside the barrier. Previous experiments have measured tunnelling rates with attosecond time resolution8 and tunnelling delay times9. Here we study laser-induced tunnelling by using a weak probe field to steer the tunnelled electron in the lateral direction and then monitor the effect on the attosecond light bursts emitted when the liberated electron re-encounters the parent ion10. We show that this approach allows us to measure the time at which the electron exits from the tunnelling barrier. We demonstrate the high sensitivity of the measurement by detecting subtle delays in ionization times from two orbitals of a carbon dioxide molecule. Measurement of the tunnelling process is essential for all attosecond experiments where strong-field ionization initiates ultrafast dynamics10. Our approach provides a general tool for time-resolving multi-electron rearrangements in atoms and molecules11, 12, 13—one of the key challenges in ultrafast science.
Figures at a glance
Figure 1: Electron trajectories contributing to the recollision process. 
The coloured lines represent the spatio-temporal description of various trajectories; each colour encodes a recolliding energy, increasing from red to blue. The black dashed line shows the electric field along the cycle. arb. u., arbitrary units.
Figure 2: Schematic description of the two-colour gates. 
a, b, Displacement gate. Different electron trajectories are separated along the ionization time axis (a). The displacement gate induces a lateral shift that suppresses the return probability. Only a narrow region in time is selected by the gate (shaded red). As the two-colour delay is changed, the gate is shifted within the optical cycle; a delayed ionization window is selected (b). c, d, Velocity gate. The different trajectories are separated in recombination time (c). The velocity gate controls the lateral velocity and, hence, the angle at recombination. A narrow region in time corresponds to the maximal recombination angle, selected by the gate (shaded red). Modifying the two-colour delay shifts the velocity gate within the optical cycle, thereby choosing a delayed recombination window (d).
Figure 3: Reconstruction of the ionization and recollision times. 
a, Displacement gate: normalized harmonic signal (colour scale) as a function of harmonic order and two-colour delay (φ) for helium. (For each harmonic order the signal is divided by the maximal signal for that harmonic. Colour scale shows the relative strength of the normalized signal.) b, Velocity gate: normalized recollision angle (colour scale) as a function of harmonic order and φ . (For each harmonic order the angle is divided by the maximal angle for that harmonic. Colour scale shows the relative strength of the normalized signal.) c, Reconstructed ionization and recollision times extracted from a and b (red dots). The pink shaded areas represent the uncertainty in the reconstruction procedure. The extracted times are compared to the calculated times according to the semiclassical model (grey curves) and the quantum stationary solution (black curves). The reconstructed ionization times using the combined ionization–displacement gate (green curve) are also shown (Supplementary Information).
Figure 4: Gating two-channel tunnel ionization in aligned carbon dioxide molecules. 
a, Two stationary solutions associated with the HOMO (red curve) and HOMO−2 (grey curve) orbitals, calculated for I = 1.3 × 1014 W cm−2. b, Calculation of |G(1)|2 and |G(2)|2 as functions of the two-colour delay (φ). The black dashed lines indicate
for each channel. c, Calculation of GN for constructive (black curve) and destructive (blue curve) interference. d, Theoretical calculation of the normalized harmonic signal for a carbon dioxide molecule aligned at an angle of ±35° to the 40-fs, 800-nm, I = 1.3 × 1014 W cm−2 fundamental field, using the second-harmonic field at a 2% intensity level. e, f, Normalized measured harmonic spectra (colour scale) as functions of harmonic order and φ for carbon dioxide molecules aligned at 90° (e) and 0° (f). The white curves follow the phases ( 
) that maximize the harmonic signal. The two colour phase was shifted by 0.3 rad in panels d–f to show the full extent of the phase shift.
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