Control of photoemission delay in resonant two-photon transitions

Abstract

The photoelectron emission time delay $\ensuremath{\tau}$ associated with one-photon absorption, which coincides with half the Wigner delay ${\ensuremath{\tau}}_{\mathrm{W}}$ experienced by an electron scattered off the ionic potential, is a fundamental descriptor of the photoelectric effect. Although it is hard to access directly from experiment, it is possible to infer it from the time delay of two-photon transitions, ${\ensuremath{\tau}}^{(2)}$, measured with attosecond pump-probe schemes, provided that the contribution of the probe stage can be factored out. In the absence of resonances, $\ensuremath{\tau}$ can be expressed as the energy derivative of the one-photon ionization amplitude phase, $\ensuremath{\tau}={\ensuremath{\partial}}_{E}arg{D}_{Eg}$, and, to a good approximation, $\ensuremath{\tau}={\ensuremath{\tau}}^{(2)}\ensuremath{-}{\ensuremath{\tau}}_{\mathrm{cc}}$, where ${\ensuremath{\tau}}_{\mathrm{cc}}$ is associated with the dipole transition between Coulomb functions. Here we show that, in the presence of a resonance, the correspondence between $\ensuremath{\tau}$ and ${\ensuremath{\partial}}_{E}arg{D}_{Eg}$ is lost. Furthermore, while ${\ensuremath{\tau}}^{(2)}$ can still be written as the energy derivative of the two-photon ionization amplitude phase, ${\ensuremath{\partial}}_{E}arg{D}_{Eg}^{(2)}$, it does not have any scattering counterpart. Indeed, ${\ensuremath{\tau}}^{(2)}$ can be much larger than the lifetime of an intermediate resonance in the two-photon process or more negative than the lower bound imposed on scattering delays by causality. Finally, we show that ${\ensuremath{\tau}}^{(2)}$ is controlled by the frequency of the probe pulse, ${\ensuremath{\omega}}_{\mathrm{IR}}$, so that by varying ${\ensuremath{\omega}}_{\mathrm{IR}}$, it is possible to radically alter the photoelectron group delay.