Sideband oscillations in four-photon RABBIFT scans.

Extracting sideband phase information from standard \hbox{RABBITT} (reconstruction of attosecond beating by interference of {\bf two}-photon transitions) scans is a common technique to measure atto\-second time delays in photoionization [1]. Here we further investigate the {\bf four}-photon setup (RABBIFT), suggested in~[2], where the intensity of the sidebands generated by a probe frequency $\omega_p$ oscillates according to $I(\tau) \propto$ cos$(-4\,\omega_p\tau+\Delta \phi_{\epsilon})$, where $\tau$ is the delay between the XUV and IR pulses and $\Delta \phi_{\epsilon}$ is an energy-dependent phase. Here we examine the intensity and pulse-length dependence of $\Delta\phi_{\epsilon}$ for realistic experimental setups ($I_{\rm XUV} = 10^9\,$W/cm$^2$, $I_{\rm IR} = 10^{11}-10^{12}$\,W/cm$^2$, pulse lengths $20-100\,$fs) by comparing RABBIFT scans from {\it ab initio} TDSE calculations~[3] for atomic hydrogen produced by different probe pulse durations and intensities. Preliminary results suggest a non-negligible dependence of $\Delta\phi_{\epsilon}$ on the latter parameters. [1]~P.~Paul et al., Science {\bf 292} (2001) 1689. [2]~A.~Harth et al., Phys. Rev. A~{\bf 99} (2019) 023410. [3]~N.~Douguet et al., Phys. Rev. A~{\bf 93} (2016) 033402.