Many-body calculations of two-photon, two-color matrix elements for attosecond delays

Abstract

We present calculations for attosecond atomic delays in photoionization of noble gas atoms based on full two-color two-photon Random-Phase Approximation with Exchange in both length and velocity gauge. Gauge invariant atomic delays are demonstrated for the complete set of diagrams. The results are used to investigate the validity of the common assumption that the measured atomic delays can be interpreted as a one-photon Wigner delay and a universal continuum-continuum contribution that depends only on the kinetic energy of the photoelectron, the laser frequency and the charge of the remaining ion, but not on the specific atom or the orbital from which the electron is ionized. Here we find that although effects beyond the universal IR-photoelectron continuumcontinuum transitions are rare, they do occur in special cases such as around the 3s Cooper minimum in argon. We conclude also that in general the convergence in terms of many-body diagrams is considerably faster in length gauge than in velocity gauge.

Time delays from one-photon transitions in the continuum

“…We observe a remarkable quantitative agreement between the experiment and theoretical values for the phase difference ϕ cc± Although the observed phase difference has not been experimentally identified in the past, the above observations were already visible in earlier numerical simulations [23], and they had been predicted by Dahlström and co-workers [21,25,27,45] (see also supplemental material in [17]).…”

“…4 and 5, the theoretically calculated cc phase difference in hydrogen follows the same trend as in helium. This finding further supports the notion that, in systems with small polarizability such as helium, the relative phase between wave-packet components with different angular momenta is a universal feature of laser-assisted Coulomb scattering when the Coulomb and the centrifugal potential dominate any short-range admixtures [25,45]. For larger atoms or molecules, where electron correlation effects are more prominent, however, deviations from the observed trend cannot be excluded.…”

Complete characterization of multi-channel single photon ionization

“…We then determine the channel-resolved one-photon amplitudes from measurements with only the XUV field. The retrieved values for the scattering phases and channel amplitudes are in excellent agreement with calculations using angular-channel-resolved many-body perturbation theory [20,21,22].…”

“…The complex-valued two-photon matrix elements, expressed in Eq. ( 2), are then calculated as the transition from the perturbed wave function to the final continuum state in each angular momentum channel, following the procedure described in [20,21,22] for the non-relativistic case. The integration is performed numerically out to a distance far outside the atomic core, but within the unscaled region, while the last part of the integral is carried out using analytical Coulomb waves along the imaginary radial axis.…”

Attosecond electron–spin dynamics in Xe 4d photoionization

“…Exterior complex scaling is used in order to be able to use a finite numerical box. The two-photon matrix element is dominated by a one-photon dipole matrix element between the intermediate perturbed wave function and the final continuum state 48 . The integration is performed numerically out to a distance far outside the atomic core, but within the unscaled region, while the last part of the integral is carried out using analytical Coulomb waves along the imaginary radial axis.…”