Time-dependent Feshbach method to study resonant photoionization of He with ultrashort laser pulses

A time-dependent Feshbach formalism is proposed to study the resonant photoionization of the helium atom using ultrashort laser pulses. This spectral method consist in solving the time-dependent Schrodinger equation by expanding the time-dependent wavepacket in terms of eigenfunctions defined in two orthogonal halfspaces: a bound-like resonant Q and a non-resonant scattering-like P. The latter eigenfunctions for the projected Hamiltonians QHP and QHQ are not indeed eigenfunctions of the total Hamiltonian, so that the electrostatic coupling PHQ acts as a leaking operator Q→P responsible for the temporal decay of resonances into the underlying continuum, keeping the physical insight of the Fano-Feshbach time independent formalisms. This method allows not only for accurate descriptions of the resonance parameters (energies, widths and Fano shape parameters) but also for the temporal evolution of the photodynamics involved in the resonant photoionization when using short laser pulses. We illustrate the performance of the method by analyzing the temporal formation of i) the one-photon ionization cross section below the second ionization threshold and the buildup of Fano profiles and ii) the up-down asymmetry of photoelectron angular distributions resulting from interferences of S-, P- and D-waves after simultaneous photoexcitation and decay of the lowest ¹S^e, ¹P° and ¹D^e resonant states, by using two sequential laser pulses with XUV harmonic frequencies separated by a time delay.