Time Delay in Tunnelling Ionization

A promising new method of attosecond spectroscopy, the attoclock, offers attosecond resolution without requiring attosecond laser pulses. However, it requires knowledge of the ionization time, opening up a long standing conceptual problem in physics (“how much time does tunnelling take?”). In this work, the time delay in the tunnel ionization process is considered. It is shown that a delay of the peak of the tunnelling wavefunction exists as a matter of principle, and is caused by the interference of transmitted and reflected components of the wavefunction. If sub-barrier reflections are neglected from the wavefunction, the delay in the peak vanishes and tunnelling is seen to be instantaneous. This is shown by considering a series of models of increasing complexity: the square barrier, an adiabatically tunnelling electron, and a wavefunction based on the Strong Field Approximation. This work has implications on the interpretation of attoclock experiments: treatments based on instantaneous tunnelling should be adjusted in order to achieve appropriate calibration of the attoclock

Role of reflections in the generation of a time delay in strong-field ionization

The problem of time delay in tunneling ionization is revisited. The origin of time delay at the tunnel exit is analysed, underlining the two faces of the concept of the tunnelling time delay: the time delay around the tunnel exit and the asymptotic time delay at a detector. We show that the former time delay, in the sense of a delay in the peak of the wavefunction, exists as a matter of principle and arises due to the sub-barrier interference of the reflected and transmitted components of the tunneling electronic wavepacket. We exemplify this by describing the tunnelling ionization of an electron bound by a short-range potential within the strong field approximation in a "deep tunnelling" regime. If sub-barrier reflections are extracted from this wavefunction, then the time delay of the peak is shown to vanish. Thus, we assert that the disturbance of the tunnelling wavepacket by the reflection from the surface of the barrier causes a time delay in the neighbourhood of the tunnel exit

Reconciling Conflicting Approaches for the Tunneling Time Delay in Strong Field Ionization

Several recent attoclock experiments have investigated the fundamentalquestion of a quantum mechanically induced time delay in tunneling ionizationvia extremely precise photoelectron momentum spectroscopy. The interpretationsof those attoclock experimental results were controversially discussed, becausethe entanglement of the laser and Coulomb field did not allow for theoreticaltreatments without undisputed approximations. The method of semiclassicalpropagation matched with the tunneled wavefunction, the quasistatic Wignertheory, the analytical R-matrix theory, the backpropagation method, and theunder-the-barrier recollision theory are the leading conceptual approaches putforward to treat this problem, however, with seemingly conflicting conclusionson the existence of a tunneling time delay. To resolve the contradictingconclusions of the different approaches, we consider a very simple tunnelingscenario which is not plagued with complications stemming from the Coulombpotential of the atomic core, avoids consequent controversial approximationsand, therefore, allows us to unequivocally identify the origin of the tunnelingtime delay.<br