Ultrafast time delay as a control parameter in resonant ionization by two XUV ultrashort pulses

We predict quantitatively that it is possible to use few-femtosecond positive or negative time delays, Delta t, between two XUV Gaussian few-femtosecond pulses of moderate intensities and central frequencies w1 and w2, in order to control the probability of ionization at clearly defined exit energies corresponding to the sums of photon frequencies (w1 + w1), (w2 + w2), and (w1 + w2, or w2 + w1). The phenomenon is demonstrated quantitatively by obtaining and using nonperturbative solutions of the time-dependent Schrodinger equation for a time-dependent scheme involving the process of two-photon resonant ionization of Helium via the 1s2p 1Po (58.4 nm) and 1s4p 1Po ( 52.22 nm) excited states. The calculations used wavefunctions which are state-specific for the discrete spectrum, (up to the 1s7g 1G Rydberg state), as well as for the energy-normalized continuous spectrum, (up to 2.0 a.u. above threshold with angular momenta l = 0, 1, 2, 3, 4). For this system, using Dt as a control knob, the effects on the photoelectron spectrum of the combination of the transition amplitudes via the two paths and their interference are determined clearly for pulses with field-cycles ranging from about 15 to about 80 cycles. The analysis has included the comparison of the nonperturbative results, obtained by implementing the state-specific expansion approach, with those obtained from the application of second order time-dependent perturbation theory with two Gaussian pulses of finite duration.