Stark Manifold Research Articles

Efficient optical excitation of the highest energy level of the N=17 Stark manifold in barium

The authors report on two-photon laser experiments on the n=17 Stark manifold of Ba in an electric field varying from 0 to 1170 V cm-1. The observed wavelengths and peak intensities in the manifold are compared with the predictions of the diagonalisation method developed by Zimmerman et al. (1978-1979). Efficient excitation of the highest energy level in the Stark manifold is shown to take place inside a narrow range of electric field strength. This feature turns out to be favourable for future preparation of circular atoms ( mod m mod =l=n-1).

Influence of the 3d 23P 0 and 3d 23P 2 valence states on the stark spectrum of the rydberg state of Ca

The Stark spectrum of the Ca atom has been investigated in the vicinity of the n = 10–13 transitions by using two-step excitation and photoionization methods with an applied electric field up to 8 kV/cm. The results indicate that the 3 d 2 3 P 0 and 3 d 2 3 P 2 valence states are repelled by the n = 12 Stark manifold. Interference has been observed for the 3 d 2 3 P 0 state and the Stark states and is enhanced as the electric field is increased. The crossing and anticrossing structures of levels among the zero-field non-degenerate states, valence states, and Stark states are also discussed.

Stark manifolds and electric-field-induced avoided level crossings in helium Rydberg states.

The linear Stark effect in 1snp $^{1}$,3P Rydberg states (n\ensuremath{\approxeq}40) of the fundamental two-electron atom helium was studied with the resolution of cw laser spectroscopy. The evolution of the angular-momentum manifolds was followed up to the regime where Stark states originating from different n values interact. Narrow avoided level crossings were detected with high precision. Stark manifolds were also calculated by diagonalization of the complete energy matrix in the presence of an electric field. In these calculations, even at moderate values of the field up to five n values have to be included to accurately reproduce the experimental data.

Interference and stabilization in the quasibound Stark spectrum.

Experimental studies of the quasibound Stark spectrum of cesium are reported with emphasis on the Stark redistribution of nonhydrogenic states onto the linear Stark manifold. We show that most characteristics of the spectra are understood with analytical models describing the interaction of one or several discrete states with one or several quasicontinua of discrete states. In particular, we give experimental evidence for the discrete versions of Fano profiles and stabilization of states due to interference effects. These are also important features of the continuum region which several experiments have recently demonstrated.

LEVEL STRUCTURE OF THE RYDBERG STATES OF CALCIUM ATOM IN ELECTRIC FIELD

The Stark spectrum of Ca atom with m = 0 in the vicinity of n = 10 to n = 13 have been obtained by using two-step excitation and photoionization methods in the applied electric field from 0 to 8 kV/cm. The experimental results show that the 3d2 3P0 and 3d2 3P2 valence states are repelled by n= 12 Stark manifold. The interaction among the zero-field non-degenerate states, valence states and Stark states are discussed. The interference phenomenon, in which valence state and Stark states take part, has been observed. The interference is enhanced when the electric field increase.

Stark spectroscopic measurement of spatially resolved electric field and electric field gradients in a glow discharge

Spatially resolved Stark spectra of triplet helium Rydberg states have been measured in the cathode fall region of a normal glow discharge. It is demonstrated that Stark spectral intensity distribution of a single Stark manifold provides both the electric field and the electric field gradient. The spectra of appropriate manifolds typically are sensitive to 20 V/cm change across the width of the probe laser beam. The experimental method of determining the electric field gradient locally means that one can measure space-charge distributions in sheaths adjacent to electrodes, probes, and plasma boundaries.

Stark-effect studies in xenon autoionizing Rydberg states using a tunable extreme-ultraviolet laser source.

The Stark spectra of autoionizing Rydberg states of Xe converging to the second ionization limit 5${p}^{5}$ $^{2}P_{1/2}$ have been investigated as a function of applied electric field over the range 26--2362 V/cm. Single-photon excitation from the Xe ground state was achieved using coherent radiation near 92.5 nm, generated by frequency tripling the pulsed output of a frequency-doubled dye laser in a free jet of rare-gas atoms. For the lowest electric field only the ns' and nd' series were observed. As the electric field was increased the np' series appeared because of the mixing of wave functions with different l values. Further increase of the electric field caused the appearance of hydrogenlike Stark manifolds. The Stark spectrum was simulated in a two-step procedure with no adjustable parameters. Using a jl-coupling basis set the Hamiltonian matrix was diagonalized to determine the energy levels and corresponding eigenfunctions for a given electric field strength. The intensities and line shapes were then calculated using the formalism developed by Fano for a many-discrete-level--single-continuum configuration interaction. This treatment was sufficient to reproduce the positions, widths, and shapes of most observed features. At field strengths between 1000 and 2000 V/cm, however, an additional modulation structure with a spacing of about 2.7 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$ appeared on top of the \ensuremath{\Vert}M\ensuremath{\Vert}=1 autoionizing resonances, which could not be explained by our simple theoretical model.

Microwave multiphoton transitions between Rydberg states of potassium.

Observations are reported of complete sequences of N-photon resonant microwave transitions, in potassium, from the (n+2)s state to the lowest energy state of the linear Stark manifold of principal quantum number n. The number N of photons absorbed ranges from 1 to as high as 30, and n is in the range from 16 to 19. A sequence is observed by scanning the static electric field, starting at the field at which the levels undergo an avoided crossing, until zero field is reached. The maximum number of photons absorbed is observed to be proportional to the microwave field amplitude, with an offset of two photons at zero field. Dynamic Stark shifts of the levels are observed to be proportional to the microwave power. The n dependence and absolute size of the shift are in agreement with Floquet calculations. The relation between the N-photon resonances and microwave ionization is discussed. In particular, resonances in microwave ionization spectra are seen to be due to dynamic-Stark-shifted multiphoton transitions.

ELECTRIC FIELD EFFECTS ON Sr ATOM RYDBERG STATES

Stark structure of Sr atom Rydberg states in the vicinity of n = 12 and n = 13 were me-asured by multistep excitation method with ππ polarized lasers. The Stark map exhibited the linear behaviour of Stark manifold of Sr atom in low electric field. The crossing and antic-rossing structure of levels, which depends on the quantum effects, were discussed.

Rydberg state Stark spectroscopic measurement of electric-field profile in a glow discharge

The electric-field profile in the cathode-fall region of a low-pressure helium gas discharge has been measured by high-level Rydberg state Stark spectroscopy using optogalvanic detection. The Stark manifolds of triplet atomic helium Rydberg states with principal quantum numbers n=15 up to 20 have been used to measure the electric-field vector using both Δmj=0 and ‖Δmj‖=1 laser polarizations. The absolute accuracy of the electric-field measurement was found to be 5% or better. The ‖Δmj‖=1 polarization Stark spectra exhibit pseudohydrogenic behavior in Stark splitting, as well as in the manifold intensity distribution. The Stark splitting of states corresponding to 1>4 was almost hydrogenic for all the measured principal quantum-number states and the intensity distribution became approximately hydrogenic for n≥16 at electric fields ≤700 V/cm.

Rydberg states with anisotropic ion cores: Stark effect.

We have measured the Stark spectra of 5${d}_{3/2}$8l autoionizing states in barium. Because of the anisotropic 5d ion core, the Stark manifolds at higher fields are considerably more complex than those for the analogous 6snl bound states. The electrostatic coupling of the Rydberg electron with the anisotropic core gives rise to relatively large fine-structure splittings. For nonpenetrating orbitals (${l}_{\mathrm{Ry}>{l}_{\mathrm{core}}}$), jK coupling is a useful representation and the number of fine-structure components due to this interaction with the core increases the number of eigenstates (2${j}_{\mathrm{core}+1}$)-fold. We present a theoretical model for the calculation of Stark spectra in jK coupling. Results for barium are in quantitative agreement with the experimental observations for both \ensuremath{\pi} and \ensuremath{\sigma} polarizations up to fields where there is extensive overlap between adjacent n manifolds. These fine-structure effects occur for any states with nonisotropic cores (${j}_{\mathrm{core}>(1/2)}$), i.e., the states of most atoms except for bound singly excited states of alkali-metal and alkaline-earth-metal atoms.

Stark manifolds of barium Rydberg states

In a CW laser-atomic beam experiment Stark manifolds in barium originating from the Rydberg states 6s40f1F3, 6s40g1,3G4,3G5 and 6s40h1,3H5 have been studied. Accurate quantum defect values for higher orbital angular momentum states (l=6, 7) have been determined. The Stark manifolds are also calculated by diagonalization of the energy matrix in the presence of an external electric field. Good agreement between experiment and calculations is obtained.

Effects of very low electric fields on narrow autoionizing states in gadolinium.

We have observed a narrow (0.075-cm/sup -1/) isolated autoionizing level to undergo a stepwide increase in width at an electric field strength --2 V/cm. At such low fields, classical field ionization or ''forced autoionization'' cannot account for this phenomena. We find that the autoionizing level is narrow because of its high angular momentum (J = 5). The level is energetically embedded in the Rydberg series converging to a nearby limit. The model we propose suggests that such narrow autoionizing levels will increase in width near a field F (a.u.) = (1/3)n/sup 5/ for n values of the Rydberg levels which lie nearby in energy. At this field (Ingliss-Teller limit), adjacent n Stark manifolds begin to overlap, resulting in the onset of complete ''l mixing.''

Anticrossing spectroscopy of K Rydberg atoms using 300-K blackbody radiation.

The avoided crossings in an electric field of K s and p states with the nearly hydrogenic Stark manifold states have been investigated using 300-K blackbody radiation. Anticrossings between states of the same \ensuremath{\Vert}${m}_{j}$\ensuremath{\Vert} for which the \ensuremath{\Vert}${m}_{l}$\ensuremath{\Vert} values are the same or differ by one are encountered. The anticrossings between states of the same \ensuremath{\Vert}${m}_{l}$\ensuremath{\Vert} are quite wide as they are due to core penetration and polarization effects. The anticrossings for which \ensuremath{\Vert}${m}_{l}$\ensuremath{\Vert} differs by one are produced by the spin-orbit interaction and are accordingly quite small. We present results for the ns states for n in the range 18\char21{}29 and for the np states for n in the range 19\char21{}23.

Microwave absorption by hydrogen atoms in high Rydberg states.

The behavior of Rydberg atoms in a recent experiment involving selective excitation in combined ac and dc electric fields is shown to be consistent with the predictions of a one-dimensional model incorporating only the extreme level of each Stark manifold. For low microwave powers, the excitation is resonant and is described qualitatively by multiphoton perturbation theory. For higher powers, an alternative stochastic theory predicts rapid ionization at all frequencies, as observed experimentally.

Analytical study of quasidiscrete Stark levels in Rydberg atoms

A theory of nonhydrogenic Stark spectra based on the hydrogen atom is specialized to quasidiscrete levels. Algebraic expressions for level positions ${\ensuremath{\epsilon}}_{r}$, widths ${\ensuremath{\Gamma}}_{r}$, and oscillator strengths ${f}_{r}^{F}$ are derived in terms of matrices ${\mathit{H}}^{F}$ and ${\mathit{h}}^{F}$, which represent the hydrogenic density of states in a Stark field $F$. Core effects appear through zero-field quantum defects ${\ensuremath{\mu}}_{l}$ and dipole matrix elements ${d}_{l}^{0}$. Normalized oscillator strengths ${\overline{f}}_{r}^{F}$ are defined which are independent of all ${d}_{l}^{0}$ for $s\ensuremath{\rightarrow}p$ transitions. Isolated and interacting Stark manifolds with $m=0 \mathrm{and} 1$ are examined for systems with two nonnegligible ${\ensuremath{\mu}}_{l}$. Extensive comparisons are made with experimental Li spectra and matrix-diagonalization calculations of Zimmerman, Littman, Kash, and Kleppner [Phys. Rev. A 20, 2251 (1979); ZLKK]. For small fields $F<\frac{1}{3{n}^{5}}$ level positions are given analytically with respect to H levels of fixed $n$; $m=0$ intensity distributions do not appear hydrogenic in Li since ${\ensuremath{\mu}}_{0}\ensuremath{\sim}\frac{1}{2}$. At $F>\frac{1}{3{n}^{5}}$, degenerate parabolic eigenstates from different manifolds are coupled by the spherical core and avoid crossing. The upper levels disappear at $m=1$ anticrossings in Li, as observed in ZLKK. For $m=0$ the lower levels usually vanish instead. A full Stark map of calculated intensities ${\overline{f}}_{r}^{F}$ is presented for Li ($m=0$) and agrees with experiment. Pseudocrossings occur at near triple degeneracies of hydrogen Stark states. Extensions to include $\mathrm{ls}$ coupling are indicated. Experimental ionization rates in He are analyzed in a companion paper by van de Water, Mariani, and Koch [Phys. Rev. A 30, 2399 (1984)].

Microwave ionization of Na Rydberg atoms

Electric field ionization of excited Na atoms by microwave fields between 12 and 15 GHz exhibits several interesting phenomena. The $|m|=0 \mathrm{and} 1$ states may be ionized with a very low microwave field, $\ensuremath{\sim}\frac{1}{{3n}^{5}}$, corresponding to the point at which the $n$ and $n+1$ Stark manifolds of principal quantum numbers $n$ and $n+1$ intersect. The ionization occurs by an atom's making a succession of Landau-Zener transitions to higher-lying states, finally reaching the classical ionization limit. The $|m|=2$ states, on the other hand, ionize at a very high microwave field, $\ensuremath{\sim}\frac{1}{{9n}^{4}}$. Both these observations and the more familiar static or low-frequency result of ionization by a field of $\ensuremath{\sim}\frac{1}{{16n}^{4}}$ are all consistent with ionization in a completely classical fashion. The apparent differences are due to the dynamics of passing from zero field to a high ionizing field.

Microwave Ionization of Na Rydberg Levels

The authors have observed the ionization of Na Rydberg states by strong microwave fields and have found that the field required for ionization is $\frac{1}{(3.7{n}^{5})}$ (in atomic units) for $n=20\ensuremath{-}37$. This field is close to the field $\frac{1}{(3{n}^{5})}$ at which the Stark manifolds of principal quantum numbers $n$ and $n+1$ intersect. The ionization can be shown to arise from transitions occurring near these intersections.

Time evolution of the fluorescence in EuP 5O 14 crystals

Time resolved laser induced fluorescence in EuP 5O 14 crystals reveals new emission bands in the 580–700 nm region. These bands are assigned as the 5D 1→ 7F 3, 7F 4, 7F 5, 7F 6 emission bands, which are predicted by theory to account for a large proportion of the 5D 1 fluorescence intensity, but have never been seen before due to their masking by the much stronger 5D 0→ 7F 2, 7F 1 emission bands or due to their weakness. Branching ratios and lifetimes of the 5D 0 and 5D 1 Stark manifolds have been measured. The experimental branching ratios disagree sometimes with Judd-Ofelt calculation by a factor of two. The disagreement for these 5D 1 values may partly be explained by selective cooperative relaxation processes. The ion pair emission process is particularly attractive.

Stark structure of the Rydberg states of alkali-metal atoms

The authors describe practical methods for calculating the Stark structure of Rydberg states of the alkali metals based on diagnolization of the energy matrix. A survey of Stark structures is presented for all of the alkali metals in the vicinity of $n=15$. Topics discussed include general methods for evaluating radial matrix elements, the treatment of fine structure, oscillator-strength distribution, scaling laws, the structure of a level anticrossing, and sources of error. Experimental Stark maps are compared with calculated results for lithium and cesium. Experimental studies of the oscillator-strength distribution within a Stark manifold and the structure of a level anticrossing are also presented.