Wigner time delay in photoionization: a 1D model study

Abstract

In scattering theory, the Wigner-Smith time delay, calculated through a phaseshift derivative or its multichannel generalization, has been demonstrated to measure the amount of delay or advance experienced by colliding particles during their interaction with the scattering potential. Fetic, Becker, and Milosevic argue that this concept cannot be extended to include photoionization, viewed as a half-scattering experiment. Their argument is based on the lack of information about scattering phaseshifts in the part of the wavefunction (satisfying the ingoing-wave boundary condition) going to the detector. This article aims to test this claim by examining a photodetachment process in a simple 1D model with a short-range symmetrical potential. Using time-dependent perturbation theory with a dipole interaction, the relevant wavepacket of the outgoing particle is analyzed and compared to the free wavepacket as a reference. Our findings confirm that, indeed, a time delay arises in the liberated fragmentation wavepacket, which is expressed as an energy derivative of the scattering phaseshift. Our study highlights that the source of the phaseshift content in the wavepacket arriving at the detector is the dipole matrix element, which is a direct consequence of imposing the ingoing-wave boundary condition. We illustrate our results through numerical simulations of both the non-free and free wavepackets. The amount of the observed time delay is found to be half of that appearing in a typical scattering experiment.

Understanding attosecond streaking

“…Despite those problems, we can find several studies that use a 1D model to describe delays in a 3D Coulomb potential [13,32,36,[45][46][47][48]51]. In some cases this may be appropriate, such as when demonstrating the connection between the original definition of the Wigner delay as due to scattering and the photoionization delay [41]. However, one has to keep in mind that the specific delays differ from the ones we get in a full 3D system.…”

“…it is measurement-dependent. One usually tries to correct for this measurement-dependent effect by splitting the measured streaking delay t s into a Coulomb-laser-coupling term, t CLC , that depends on the probing IR field, and a so-called Eisenbud-Wigner-Smith (EWS) term that is independent of the IR field and that is considered as the 'actual' ionization delay [8,10,25,27,[35][36][37][38][39][40][41][42]:…”