A time-dependent generalized Floquet calculation of the laser-induced lineshape in attosecond transient absorption spectra

We introduce a time-dependent generalized Floquet (TDGF) approach to calculate attosecond transient absorption spectra of helium atoms subjected to the combination of an attosecond extreme ultraviolet (XUV) pulse and a delayed few-cycle infrared (IR) laser pulse. This TDGF approach provides a Floquet understanding of the laser-induced change of resonant absorption lineshape. It is analytically demonstrated that the phase shift of the time-dependent dipole moment that results in the lineshape changes consists of two components, the adiabatic laser-induced phase (LIP) due to the IR-induced Stark shifts of adiabatic Floquet states and the non-adiabatic phase correction due to the non-adiabatic IR-induced coupling between adiabatic Floquet states. Comparisons of the spectral lineshape calculated based on the TDGF approach with the results obtained with the LIP model Phys. Rev. A88 033409 (2013) and the rotating-wave approximation (RWA) are presented for several typical cases, demonstrating that TDGF universally and accurately captures IR-induced lineshape changes. It is suggested that the LIP model works as long as the generalized adiabatic theorem PRX Quantum2 030302 (2021) holds, and the RWA works when the higher-order IR-coupling effect in the formation of adiabatic Floquet states is neglectable.