Abstract
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.
Highlights
In both classical and quantum mechanics, the passage of time is always defined with respect to some dynamical variable
To reveal the contribution of the reflection to the tunneling time delay, we investigate the complex continuation of the integrand function of the strong-field approximation (SFA) wave function, Eq (17)
The wave function was calculated to first order in the SFA for any intermediate time, enabling a quantum treatment of dynamics in the region where quasiclassical descriptions break down, viz., around the classical tunnel exit
Summary
In both classical and quantum mechanics, the passage of time is always defined with respect to some dynamical variable (for instance, the hands of a clock). In this respect we emphasize the distinction between two concepts of the tunneling time in strong-field ionization, namely, the time delay near the tunnel exit (the classically expected coordinate for the tunneled electron to emerge) and the asymptotic time delay [37] While the latter is relevant to attoclock experiments, the former, known as the Wigner time delay, can be calculated theoretically and measured in a Gedanken experiment with a so-called virtual detector [68,69]. We concern ourselves with understanding the principles of the tunneling delay, and to this end we consider a simple, time-dependent model of a one-dimensional (1D) atom, with an electron bound by a short-range potential, which is ionized by a half-cycle laser pulse. Atomic units (a.u.) are used exclusively throughout this paper
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