Tunneling phase time in photoionization: in search of a clock

Abstract

The electron phase time in laser-induced ionization is shown to permit an intuitive physical interpretation with a clear, transparent relation to the parameters of the potential barrier modulated by the laser field. We demonstrate that the phase time delay induced by the tunneling process can be isolated from the overall phase time of a tunneling electron by clocking the quantum electron wave-packet dynamics, as described by the time-dependent Schrodinger equation, against the classical Newtonian electron dynamics driven by the laser field. The electron phase delay time retrieved with the use of this clockwork is directly related to the width of the laser-field-controlled potential barrier. With this delay added, the quasiclassical model of laser-induced ionization and subsequent free-electron wave-packet dynamics is shown to accurately reproduce the results of the full quantum analysis. As physically discernable manifestations, the tunneling-induced phase delay time shows up in the energy distribution of photoelectrons and shifts the cutoff in the spectra of high-order harmonics emitted by recolliding electron wave packets.