We present ionization probability and lineshape calculations for the two-step three-photon ionization process, , of the ground state of hydrogenic atoms in a non-monochromatic laser field with a time-dependent amplitude. Within the framework of a three-level model, the AC Stark shifts and non-zero ionization rates of all states involved were taken into account, together with spatial and temporal inhomogeneities of the laser signal. In contrast with the usual perturbative technique, the time evolution of the atomic states was simulated by directly solving the system of coupled time-dependent inhomogeneous differential equations numerically, the equations being equivalent to the appropriate non-stationary Schrödinger equation. Particular numerical results were obtained for typical parameters of the pulsed laser field that are employed in a new experiment to measure the 1S-2S energy separation with muonium at the Rutherford Appleton Laboratory. The shifts and asymmetries of the photoionization lineshapes revealed may be of relevance for ultra-high-precision experiments in hydrogen in CW laser fields.
The Stark spectroscopy of the hydrogen atom has been investigated near the ionization threshold in static homogeneous external electric fields from \ensuremath{\sim}1000 to \ensuremath{\sim}8000 V/cm with use of a two-step excitation H(n=1)+\ensuremath{\Elzxh}${\ensuremath{\omega}}_{\mathrm{vuv}\ensuremath{\rightarrow}}$H(n=2)+\ensuremath{\Elzxh}\ensuremath{\omega} $_{\mathrm{uv}\ensuremath{\rightarrow}}$
H∗ with vuv and uv laser radiation, independently tunable and linearly polarized either parallel (\ensuremath{\pi}) or perpendicular (\ensuremath{\sigma}) with respect to the external field. Different from other, nonhydrogenic atoms, the hydrogen atom is a peculiar case insofar as the initial states of H(n=2), from which excitation takes place, are essentially of parabolic character at the field strengths employed in this study.Individual sublevels (
n1,
n2,\ensuremath{\Vert}
ml\ensuremath{\Vert}) have been prepared in the n=2 state with sub-Doppler resolution. Photoionization spectra have been obtained with \ensuremath{\pi}- and \ensuremath{\sigma}-polarized uv radiation from the four possible sublevels of the n=2 Stark manifold: \ensuremath{\Vert}1,0,0〉 \ensuremath{\Vert}\ifmmode\pm\else\textpm\fi{}1/2〉, \ensuremath{\Vert}0,1,0〉 \ensuremath{\Vert}\ifmmode\pm\else\textpm\fi{}1/2〉, \ensuremath{\Vert}0,0,\ifmmode\pm\else\textpm\fi{}1〉 \ensuremath{\Vert}\ifmmode\pm\else\textpm\fi{}1/2〉, and \ensuremath{\Vert}0,0,\ensuremath{\mp}1〉 \ensuremath{\Vert}\ifmmode\pm\else\textpm\fi{}1/2〉. All spectra show sharp line structures of quasistable field-ionizing states superimposed on continua in the energy region between the classical saddle point, ${E}_{\mathrm{SP}=\mathrm{\ensuremath{-}}2\phantom{\rule{0ex}{0ex}}\mathrm{\ensuremath{\surd}}\mathrm{F}}$ a.u., and the zero-field ionization threshold E=0 a.u. Employing existing theoretical treatments, the quasistable spectral structures are quantitatively completely analyzed and accounted for, as long as their field ionization rate is less than \ensuremath{\sim}5\ifmmode\times\else\texttimes\fi{}
1011 ${\mathrm{sec}}^{\mathrm{\ensuremath{-}}1}$. Field-ionization rates of quasistable states have been measured and are compared with theory. Oscillatory resonance structures of the ionization cross section near the zero-field threshold are observed with pronounced modulation degree only in the spectrum from the \ensuremath{\Vert}1,0,0〉 \ensuremath{\Vert}\ifmmode\pm\else\textpm\fi{}1/2〉 sublevel excited with the uv \ensuremath{\pi}-polarized. The energy spacing of the oscillations has been measured as a function of the electric field strength F and found to be nearly proportional to
F3/4, with slight but definite deviations. Theoretical analysis of the oscillations yields quantitative agreement with the experiment.
The authors describe a method for producing a fast atomic hydrogen beam with a large amount of population selected in 3l j, mod mj mod levels. This is realized by a one-step tunable laser excitation of the metastable component of the atomic beam inside a nonhomogeneous static electric field. The linear laser polarization is taken either parallel or perpendicular with respect to the external field. It allows the selective excitation of all the states of the n=3 Stark manifold (with the exception of the mod mj mod =5/2 state). The electric field strength vanishes immediately after the laser excitation. At this point the population of the excited states are better referred to the atomic basis. The shapes of the resonant lines show that two transient effects are leading the excitation process. The first is of an optical kind (i.e. Rabi oscillation and rapid adiabatic passage) and the second is the intra Stark manifold state mixing due to the nonadiabatic time evolution of the external field strength. The internal state of the atoms crossing these fields is completely described by the density matrix evolution calculated independently on two bases (the atomic basis and the Stark instantaneous basis).
Ionization characteristics of two-step excitation by two intense nonmonochromatic (finite bandwidth) lasers are investigated. By approximating the laser fields by a stochastic model of a chaotic field, the stochastic atomic-density-matrix equations for three-level atoms are first obtained. Comparing with the analytical solution, the accuracy of our model is confirmed. By using this model, the ionization characteristics are studied in detail as a function of laser bandwidth. The dependence of laser bandwidth on the Doppler averaged ionization probability is also investigated.
We have measured the resonance-enhanced four-photon ionization of atomic hydrogen. The degenerate four-photon process occurs via a three-photon resonance between the 1s and the 2p levels, with subsequent one-photon ionization near threshold. We have studied the highly asymmetric resonance-enhanced profile, i.e., the photoion yield as a function of laser detuning from three-photon resonance between the 1s and 2p levels. In particular, we have determined the width, shift, peak, and asymmetry of the profile as a function of laser intensity. The experimental results are compared to theoretical models. These models involve both the properties of the atom in an intense near-resonant radiative field, and a detailed model for the multimode laser field, particularly the field fluctuations due to mode beating. The asymmetric resonance-enhanced photoionization profile is well reproduced by both a random-phase and a chaotic-light model.
Analyses of the resonant multiphoton ionization of atoms require knowledge of ac Stark energy shifts and of multiphoton, bound-to-bound state, transition amplitudes. In this paper, we consider the three-photon photoionization of hydrogen atoms at frequencies that are at and surrounding the two-photon 1s to 2s resonance. AC energy shift sums of both the 1s and 2s states are calculated as a function of the laser frequency along with two-photon 1s ? 2s resonant transition amplitude sums. These quantities are calculated using an extended version of a method, which has often been employed in a variety of ways, of calculating these sums by expressing them in terms of solutions to a variety of differential equations that are derived from the different sums being evaluated. We demonstrate how exact solutions are obtained to these differential equations, which lead to exact evaluations of the corresponding sums. A variety of different cases are analysed, some involving analytic continuation, some involving real number analysis and some involving complex number analysis. A dc Stark sum calculation of the 2s state is carried out to illustrate the case where analytic continuation, pole isolation and pole subtraction are required and where the calculation can be carried out analytically; the 2s state, ac Stark shift sum calculations involve a case where no analytic continuation is required, but where the solution to the differential equation produces complex numbers owing to the finite photoionization lifetime of the 2s state. Results from these calculations are then used to calculate three-photon ionization probabilities of relevance to an analysis of the multiphoton ionization data published by Kyrala and Nichols (1991 Phys. Rev. A 44, R1450).