Hydrogen quasienergies from spectral analysis of wavepackets

Quasienergies (qe) are calculated traditionally by solving the time-independent Floquet system of differential equations. A number of such calculations have been carried out successfully in the past for atomic hydrogen, albeit not at the frequencies of operation of current super intense lasers. We now present a method for calculating qe based on the evolution of a wave packet of the Schroedinger equation with a time-periodic Hamiltonian, that is an extension of the well known 'spectral method' for obtaining (real) eigenenergies of a time-independent Hamiltonian. The present method is based on propagating a wave packet Ψ(t) with an appropriately chosen initial condition Ψ(0) in a periodic field of constant amplitude, and then Fourier analyzing the autocorrelation function A(t) = <Ψ(0) | Ψ(t)>. The Fourier transform of the autocorrelation function displays a set of lines, whose location and widths are related to the complex qe of the Floquet states present in the expansion of the wave packet. When these lines are non-overlapping, standard fitting techniques allow the extraction of the real and imaginary parts of the qe. For the case of overlapping lines, we apply the more elaborate technique of 'filter diagonalization'. Our method was tested by comparison with qe obtained from other sources, e.g., the solution of the system of differential equations. We apply the method to 3D hydrogen in a laser field of linear polarization, at the frequently used photon energy ω = 1.55 eV (wavelength 800 nm). We consider Floquet states belonging to several symmetry manifolds m. The field amplitude is varied from zero to several a.u. We thus obtain a 'Floquet map' for the real part of the qe of the lower states, and separately, the imaginary parts (widths) of the qe. The Floquet map displays interesting pseudo-crossings. We interpret the results in terms of avoided crossings of trajectories of the qe in the complex energy plane, and discuss their physical significance. (authors)