Control of photoemission delay in resonant two-photon transitions

The emission time delay $\tau$ in one-photon absorption, which coincides with half the Wigner scattering delay $\tau_W$, is a fundamental descriptor of the photoelectric effect. While it is hard to access $\tau$ in a direct way, it is possible to extrapolate it from the delay in two-photon transitions, $\tau^{(2)}$, measured with attosecond pump-probe schemes, provided that the contribution of the probe stage can be factored out. In absence of resonances, $\tau$ can be expressed as the energy derivative of the dipole ionization amplitude, $\tau= \partial_E \arg D_{Eg}$, and $\tau \simeq \tau^{(2)} - \tau_{cc}$ where $\tau_{cc}$ is associated to the dipole transition in the continuum. Here we show that in the presence of a resonance the correspondence between $\tau$ and $\partial_E \arg D_{Eg}$ is lost. Furthermore, while $\tau^{(2)}$ still coincides with $\partial_E \arg D^{(2)}_{Eg}$, it does not have any scattering counterpart. Indeed, $\tau^{(2)}$ 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, $\tau^{(2)}$ is controlled by the probe frequency. By varying $\omega_{IR}$, therefore, it is possible to radically alter a photoelectron group delay.