To describe the microscopic properties of matter, quantum mechanics uses wave functions, whose structure and time dependence is governed by the Schrödinger equation. In atoms the charge distributions described by the wave function are rarely observed. The hydrogen atom is unique, since it only has one electron and, in a dc electric field, the Stark Hamiltonian is exactly separable in terms of parabolic coordinates (η, ξ, φ). As a result, the microscopic wave function along the ξ coordinate that exists in the vicinity of the atom, and the projection of the continuum wave function measured at a macroscopic distance, share the same nodal structure. In this Letter, we report photoionization microscopy experiments where this nodal structure is directly observed. The experiments provide a validation of theoretical predictions that have been made over the last three decades.
Photoionization of an atom in the presence of a uniform static electric field provides the unique opportunity to expand and visualize the atomic wave function at a macroscopic scale. In a number of seminal publications dating back to the 1980s, Fabrikant, Demkov, Kondratovich, and Ostrovsky showed that this goal could be achieved by projecting slow (meV) photoionized electrons onto a position-sensitive detector and underlined the distinction between continuum and resonant contributions. The uncovering of resonant signatures was achieved fairly recently in experiments on the nonhydrogenic lithium atoms [Cohen et al., Phys. Rev. Lett. 110, 183001 (2013)]. The purpose of the present article is the general description of these findings, with emphasis on the various manifestations of resonant character. From this point of view, lithium has been chosen as an illustrative example between the two limiting cases of hydrogen, where resonance effects are more easily identified, and heavy atoms like xenon, where resonant effects were not observed.
Atomic photoionization provides an experimental situation where the outer electron is ejected to large distance without confinement condition. The application of an electric field during photoionization allows confining the electron flux along one coordinate. Therefore, photoionization in an electric field provides a unique opportunity where quantum properties of the wavefunction are projected into the macroscopic world, permitting a direct view of the square modulus of the electronic wavefunction. We present here the experimental observations of this effect, denominated photoionization microscopy. The analysis is carried out in the framework of the semiclassical model that allows a qualitative interpretation of the experimental results in terms of interferences among various classical trajectories.
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.
We present calculations of the photoionization spectrum of excited hydrogen using \ensuremath{\pi} polarization in the presence of a strong electric field as a function of the spherical (applicable to complex atoms) and parabolic quantum numbers of the excited state. We also present corresponding measurements of the photoionization yield from the individual parabolic states of n=2. Both the calculations and the measurements show an enhancement of the depth of the so-called ``Stark-induced modulation'' in the region E\ensuremath{\ge}0 when the initial excited state is a pure
ml=0 blue state, and disappear almost completely when the initial state is a pure
ml=0 red state. These results are understood using arguments based on the fact that the charge distribution of the Stark-induced states is tremendously extended up field. Because of the excellent signal to noise ratio of the enhanced modulations, we were able to measure the field dependence of the spacings with sufficient accuracy to confirm the (3/4) power law and rule out the recently suggested (2/3) power law.
Wave-function microscopy images for Stark resonance states of H atoms are simulated using the quantum-mechanical formalism developed previously. Spatial distributions of ejected electron current densities are compared with experiment, and a good agreement is shown. The nonzero values of minima in the experimentally observed electron current distributions are reproduced by convoluting the theoretical current distribution with an instrumental function representing uncertainties in the position. Our relative strengths of the ejected electron current densities differ from those calculated with the wave packet propagation technique. We show that for the full convergence of the calculation, the distance between the ionized atom and the detector should exceed $10\phantom{\rule{0.28em}{0ex}}\ensuremath{\mu}\mathrm{m}$.