How long does an electron take to tunnel?

The combination of ab-initio numerical experiments and theory shows that the optical tunneling of an electron from an atom can take place instantaneously.

How much time does an atom take to absorb a photon and release an electron? And what if not one, but many photons are needed for the ionization? How much time would the absorption take by many photons? These questions lie at the core of attosecond spectroscopy, which aims to resolve electron motion on its natural time scale.

Ionization in strong infrared fields is often considered to be the tunneling of electrons through a potential barrier. The barrier is formed by the combination of the atomic potential, which binds the electron, and the electric field of the laser pulse, which pulls the electron away. Therefore, attosecond spectroscopy unexpectedly faces a nearly age-old and controversial question: how long does it take an electron to tunnel through a barrier?

In the publication by Torlina et al. this question is pursued on the basis of the so-called Attouhr structure. Attohr uses the rotating electric field of a circularly polarized laser pulse as a pointer of the clock. One full turn of this hand lasts one laser period, approximately 2.6 fs for experiments with 800 nm pulses of a titanium: sapphire laser. The tunneling barrier also rotates with the rotating electric field. Therefore, electrons tunneling at different times tunnels in different directions. It is this connection between time and direction of the electron movement that enables Attouhr to measure times.

Fig. Ionization times (left axis) reconstructed using the ARM theory from the offset angles (right axis) numerically obtained with TDSE calculations. Red circles indicate the numerically calculated offset angles divided by the laser frequency, θ / ω. Blue diamonds show the offset angles with the correction obtained by subtracting the effect of the pulse envelope, \(t_i^0 = θ / ω- | Δt_i^{env} (θ, p_{peak}) |\) , Green inverted triangles show the Coulomb correction to the ionization time, evaluated at the maximum of the photoelectron distribution, \(| Δt_i^C (θ, p_{peak}) |\). Orange triangles show the ionization times we obtained by applying the reconstruction procedure defined in Equation (4) in the publication on the picture they are the result of the subtraction of the green curve from the blue curve.

In each clock, the time zero must be set. At Attohr, this is done by using a very short laser pulse, which lasts only one to two cycles. The tunneling process takes place in a small time window when the rotating electric field passes through its maximum.

Furthermore, like any other watch, the Attouhr must also be calibrated. One must know how the time of electron emission - the electron's exit from the tunnel barrier - is mapped to the angle at which the electron is detected. This calibration of Attouhr has now been described by Torlina et al. achieved without making ad hoc assumptions about the nature of the ionization process or the underlying physical image. Finally, with the combination of analytical theory and accurate numerical experiments, and after Attouhr was calibrated, the authors were able to take a close look at electron tunneling delays. You get to the surprising answer: This time delay can be zero. At least in the field of non-relativistic quantum mechanics, the electron tunneling from the ground state of the hydrogen atom spends no time in the tunnel barrier. However, the situation may change if the electron strikes other electrons on its way, which may be important in other atoms or molecules. The interaction between the electrons can lead to delays.

Thus Attouhr presents a unique window, not only to the tunnel dynamics, but also to the interplay of the different electrons participating in the ionization process, and how the remaining electrons re-adapt to the loss of their comrades

Original publication

Interpreting attoclock measurements of tunnelling times

L. Torlina, F. Morales, J. Kaushal, I. Ivanov, A. Kheifets, A. Zielinski, A. Scrinzi, H. G. Muller, S. Sukiasyan, M. Ivanov, O. Smirnova

Nature Physics 11 (2015) 503-508