We experimentally demonstrate one- and two-photon phase sensitive coherent control over the excitation and ionization of Rydberg states of Sr atom in the presence of a static homogeneous electric field. Without the field this excitation scheme can only be employed for the manipulation of angular distributions of photoelectrons and molecular photofragmentation products. Total atomic excitation-ionization yields cannot be modulated because the final states excited by each pathway are orthogonal to each other. When, however, a static electric field is applied,
s,
p and
d character is admixed into the final Rydberg state, which has no definite parity anymore. Hence, the excitation of the target Stark state from the ground state is possible with either two (fundamental laser frequency) photons or one (second harmonic frequency) photon and its population and further ionization can be controlled by varying the relative phase between the two radiation fields. The concept is successfully tested below as well as above the classical saddle point and with either mutually crossed or parallel linear laser beam polarizations (while the second harmonic beam polarization vector is always parallel to the static field direction). We examine the behavior of the obtained photoionization signal modulation depth
V as a function of the static field strength
F for otherwise identical experimental conditions. The
V(F) curve exhibits a maximum (typically $\ensuremath{\sim}65%--85%$) at a field strength value that is dictated by the interplay between the employed laser power densities, one- and two-photon transition dipole moments, and relative amounts of field-dependent
s,
p and
d character. It is therefore shown that the static field strength may serve as an additional, experimentally adjustable, control parameter in a fashion complementary to both the intensities and relative phase of the two light beams.
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.
Stark spectra of barium Rydberg states above the classical field-ionization limit have been recorded at high density of states employing high-resolution laser spectroscopy. The spectra, taken at a binding energy of about \ensuremath{\varepsilon}\ensuremath{\approxeq}-55 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$ with respect to zero-field threshold and at electric-field strengths F\ensuremath{\approxeq}100 V/cm exhibit dramatic variations in line profiles with increasing external field strength. The WKB quantum-defect theory of the Stark effect of nonhydrogenic atoms was used to analyze the recorded spectra, and excellent agreement between measured and calculated line profiles was achieved. Core-induced coupling of closed and open hydrogenic Stark channels was found to contribute dominantly to the linewidth of the recorded Stark resonances. In addition, a reformulation of this theory by McNicholl, Ivri, and Bergeman (unpublished) in terms of a configuration-interaction model was employed to analyze a particular avoided crossing of several Stark components. In this way recorded line profiles were parametrized within a limited model to obtain resonance energies, linewidths, and Fano q parameters.
We have studied experimentally and theoretically two-step photoionization through the 3P state of sodium in an electric field of up to 3.90 kV/cm. The apparatus uses an atomic beam crossed by two pulsed laser beams, one at 589 nm for the first step, and the other swept through the zero field threshold Eo near 409 nm for the ionization. We observe broad undulations in the photocurrent above Eo that narrow with decreasing energy and eventually sharpen into well-defined but asymmetric transitions to Stark-shifted Rydberg states. We calculate the oscillator strength density for the appropriate transitions using modified hydrogenic wave functions and find excellent agreement for the position and relative strength of all the spectral features. We model the asymmetries as Fano-type interferences between quasi-discrete and continuum ionization channels. Using appropriate core potentials, and taking into account core-induced coupling of both discrete-to-continuum and continuum-to-continuum states, we obtain estimates of Fano's q and Ɖ that agree reasonably well with our measurements.
The Stark splitting of the second excited level of atomic hydrogen (with principal quantum number
n=3) has been measured by pulsed laser spectroscopy in order to determine small electric fields by optical means. Doppler-free excitation with two counterpropagating laser beams at
205nm allows us to measure the
n=3 Stark spectra either by an optogalvanic signal after ionization by a third laser photon or by detection of the Balmer-$\ensuremath{\alpha}$ fluorescence photons emitted by the excited atoms. Three different cases of laser polarization have been investigated in order to evaluate the possibilities and limitations of this one-step laser excitation method for electric field determination, especially at field strengths below
200V∕cm. The method provides the best field sensitivity achieved with lower excited levels that can be reached directly by two-photon absorption from the ground state (in contrast to the more sensitive Rydberg levels). For this purpose, an advanced tunable pulsed uv laser with narrow bandwidth almost at the Fourier limit has been used. The high spectral resolution allowed us to deduce electric field strengths as small as
50V∕cm from the frequency shift between two selected isolated Stark components. As a main advantage, this simple analysis of the measured spectra does not rely on knowledge of the line intensities which may be strongly affected by the measuring conditions.