Control of photoemission delay in resonant two-photon transitions

The photoelectron emission time delay tau associated with one-photon absorption, which coincides with half the Wigner delay tau(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, 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, tau can be expressed as the energy derivative of the one-photon ionization amplitude phase, tau = partial derivative(E) arg D-Eg, and, to a good approximation, tau = tau((2)) - tau(cc), where tau(cc) is associated with the dipole transition between Coulomb functions. Here we show that, in the presence of a resonance, the correspondence between tau and partial derivative(E) arg D-Eg is lost. Furthermore, while tau((2)) can still be written as the energy derivative of the two-photon ionization amplitude phase, partial derivative(E) arg D-Eg((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, we show that tau((2)) is controlled by the frequency of the probe pulse, omega(IR,) so that by varying omega(IR), it is possible to radically alter the photoelectron group delay.