The Stark effect in Rydberg atoms has potential applications in the areas of dipole-dipole interaction, quantum information, quantum control, and so on. Many reflevant theoretical calculations and experimental studies about the Stark effect of alkali metal and alkali earth metals have been reported, but the other atom’s Stark effect is studied still relatively less. Our goal in this paper is to reflearch the third main group atom’s Stark effect in a large electric field. First, according to the level data of gallium atom in zero-field, we obtain the quantum defects from the modified Ritz formula in each state by using a nonlinear least-squares-fitting algorithm. The quantum defects as a function of the principal quantum number are analyzed in detail. Influences of both the core polarization and the penetrating valence electron on the quantum defect are discussed according to the fitting results. Then we use the Numerov algorithm to calculate the radial wave functions of atomic gallium. Finally, the Stark structures of Rydberg states around n=7 and n=18 are numerically calculated by matrix diagonalization. Results show that at the levels above n=7 manifold states, (n+1)P is higher than nD state, and it is in contrast to the levels below the n=7 manifold states. This phenomenon is different from the usual Stark structure of alkali metal atoms, the level’s order of which does not change with the principal quantum number. The Stark levels with the identical |m| anti-cross each other, and those with different |m| cross. Our results give an important reflerence for related reflearches, and are of great significance for insight into the atomic structure and the interaction between the atomic core and the highly excited electrons.
This paper systematically studies the energy level shift (Stark effect) of the highly excited Rydberg state of cesium (Cs) atoms under the action of an electrostatic field. In view of the limitations of the traditional hydrogen atom Stark perturbation theory in describing alkali metal atoms, we propose a complete set of parametric approximation methods, which fully consider the correction of energy level structure by quantum number deficiency. By introducing the effective principal quantum number n* and the correction coefficient 𝛽l, we extend the fourth-order Stark perturbation formula for hydrogen atoms to the Cs atomic system. The study first reviewed the analytical theory of the Stark effect of hydrogen atoms and derived the fourth-order energy shift expression based on parabolic quantum numbers. Then, the quantum number depletion characteristics of Cs atoms and their influence on Stark matrix elements were analyzed; On this basis, the parametric correction rules of the system were established, including the replacement of the effective quantum number, the determination of the polarizability correction coefficient, and the conditional use of the linear term. We have developed corresponding computing programs that can quickly estimate the energy shift of different quantum states under any electric field. By comparing with the existing experimental data and precise numerical calculation results, the reliability and application scope of this method were verified. Research shows that for the high-Rydberg state with n>20, the relative error of this parametric method under moderate electric field intensity (10-100 V/cm) is very small, making it particularly suitable for rapid estimation in large-scale parameter scanning and experimental design. The work of this paper provides practical tools and theoretical basis for the theoretical research and experimental analysis of the Stark effect 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.
The Stark effects of the Rydberg states in the alkaline-earth atoms are studied theoretically. Using a method similar to the treatment of alkali atoms, the properties of the Stark states of Mg, Ca, Sr and Ba atoms in the regions far away from the perturbers are investigated. The Stark maps for Mg ( n = 16, M = 0), Ca ( n = 10, M = 0), Sr ( n = 12, M = 0) and Ba ( n = 13, | M | = 0, 1) are presented. Topics such as the general methods of calculation, the treatment of fine structure and the structure of level anti-crossings are discussed. The comparison between the theoretical and experimental Stark maps is satisfactory.
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
frF are derived in terms of matrices
HF and
hF, 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
dl0. Normalized oscillator strengths
frF are defined which are independent of all
dl0 for $s\ensuremath{\rightarrow}p$ transitions. Isolated and interacting Stark manifolds with
m=0and1 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<3n51 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>3n51, 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
frF is presented for Li (
m=0) and agrees with experiment. Pseudocrossings occur at near triple degeneracies of hydrogen Stark states. Extensions to include
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)].
Rydberg states of atoms and molecules are very sensitive to electric fields. This property makes them ideal electric-field sensors but is detrimental to applications of Rydberg states in quantum optics, quantum-information processing, and quantum simulation because of inhomogeneous Stark broadening and the resulting loss of quantum coherence. We demonstrate, with the example of Rydberg states of
39K, the existence of Rydberg-Rydberg transitions with extremely small differential dc Stark shifts, which we call dc-field-magic Rydberg-Rydberg transitions. These transitions hardly exhibit any Stark broadening, even when the electric-field strength varies by as much as $10\phantom{\rule{4pt}{0ex}}\mathrm{V}\phantom{\rule{4pt}{0ex}}{\mathrm{cm}}^{\ensuremath{-}1}$ over the experimental volume. We present a systematic study of dc-field-magic Rydberg-Rydberg transitions combining experiment and calculations and classify them in three main types, which should also be encountered in the other alkali-metal atoms, in alkaline-earth-metal atoms, and even in molecules. The observed insensitivity to dc electric fields does not reduce the interactions between Rydberg atoms, even if they are dominantly electric dipole-dipole in nature. Rydberg states coupled by dc-field-magic Rydberg-Rydberg transitions, therefore, have great potential as qubits.
Introduction Series of atomic spectral lines had been studied by emission from excited vapors even before Balmer described the regularity of the visible lines of hydrogen in 1884. However, direct excitation had been restricted to the few lowest-lying levels, particularly those accessible by electric dipole transitions from the ground state using classical light sources. The advent of tunable lasers in the 1970s changed such spectroscopic limitations enormonsly, allowing excitation to a very much larger number of states. Atoms in highly excited states, typically with principal quantum numbers n ≥ 10, are called Rydberg atoms. They are oversize, fragile states of significant intrinsic interest. They are very rare in nature because of their size and fragility, but they are found in interstellar space (H I regions). One of the best sources for comprehensive descriptions of Rydberg atoms and references to the literature describing their exploration is Ref. [120]. It describes their characteristic properties and behavior both classically and quantum mechanically, and especially their strongly enhanced interactions with external fields. The first thing to note is that Rydberg atoms are usually characterized by a single, highly excited electron while all the other electrons remain in their original states. Thus their properties are very nearly classical, and the atoms are much closer to the ideal hydrogen-like model of Chap. 7, along with appropriate quantum defects (see Chap. 10). The spectroscopy of such states is especially interesting because the active electron is much less perturbed by the other electrons in the atom than when it is in lower states. Moreover, there are some special circumstances in which the energy of a Rydberg state is degenerate with an atomic state having two electrons excited to lower levels, and such configurations yield further new information. Second, Rydberg atoms do not usually decay back to the ground state by emission of characteristic radiation, so their study is mediated by other techniques that reveal new and interesting properties. Such properties arise because Rydberg atoms have a huge dipole moment and very low binding energy resulting from the large average distance between the excited electron and the nucleus-plus-core of the rest of the atom with net charge e . Third, transitions between Rydberg states are quite different from those connecting to the ground state for at least three reasons.