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Journal of Physics B Atomic and Molecular Physics

Rydberg states of alkali-metal atoms in orthogonal electric and magnetic fields

Petr A. Braun

Published Nov 14, 1985• 11 citations
Publisher

Abstract

A study is made of the first-order splitting of the Rydberg levels of alkali-metal atoms in weak mutually orthogonal electric and magnetic fields. It is shown that the majority of perturbed states belong to highly degenerate sublevels with the same energy as in the case of atomic hydrogen. For the rest of the states a method of energy calculation is described which does not involve numerical diagonalisation of huge perturbation matrices.

DOI
10.1088/0022-3700/18/21/008

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Journal of Physics B Atomic and Molecular Physics•Oct 28, 1983•3 citations
A study is made of the first-order splitting of the Rydberg levels of alkali-metal atoms in weak mutually orthogonal electric and magnetic fields. It is shown that the majority of perturbed states belong to highly degenerate sublevels with the same energy as in the case of atomic hydrogen. For the rest of the states a method of energy calculation is described which does not involve numerical diagonalisation of huge perturbation matrices.
Second-order contributions of diamagnetic interaction to the energy shift and splitting are studied in the basis of the angular momentum eigenfunctions for two kinds of Rydberg states in atoms: (i) hydrogen-like degenerate states and (ii) nondegenerate Rydberg states with small magnetic quantum number, m ? 3, in many-electron atoms. General formulae are presented for calculations of higher order energy corrections in degenerate states with the use of reduced Green's function. The analytical expressions are derived for the second-order radial matrix elements of operator r2 and for the second-order diamagnetic susceptibilities of hydrogen-like states with m ? n-5. The quasiclassical quantum defect method is used to calculate the irreducible components ?nl(p) of the diamagnetic susceptibility ?nlm(2) for Rydberg states of alkali atoms. The numerical results are presented for susceptibilities of degenerate hydrogen substates, and for susceptibilities of alkali atoms in Rydberg s-, p-, d-states. The asymptotic dependence of susceptibilities in alkali atoms on the effective principal quantum number ? is determined numerically and the deviation from that of the hydrogen-like states is discovered. The data is also presented for the scaling parameters cl(p), determining the irreducible parts of the diamagnetic susceptibilities in states with high ?, according to the asymptotic formula ?nl(p) = cl(p)?11.
The spectrum of a Rydberg atom in crossed electric and magnetic fields has been calculated by the methods of classical perturbation theory. Much consideration is given to the region of almost degenerate frequencies, involving mutually normal orientations of fields of any relative value, and also the case when one of the fields is very weak. Strong anisotropy of the electric polarisability in a magnetic field is predicted. In particular, longitudinal and transverse polarisabilities have different signs. The magnetic polarisability in an electric field has been found.
I have calculated the energy spectrum of a highly excited atom which lies in parallel, static electric and magnetic fields. In parallel fields the Coulomb quantum numbers n and m are still "good" quantum numbers but 1 is not: the calculation is for n = 30, m = 1 atoms.;The eigenvalues were obtained by semi-classical quantisation of first-order classical perturbation theory and have been calculated for a large range of electric and magnetic field strengths. The results are in good agreement with those found from first-order degenerate quantum perturbation theory.;The semi-classical analysis provides a correlation diagram connecting the Stark effect states to those of the diamagnetic effect.
We study the spectra of diamagnetic rubidium Rydberg atoms in strong magnetic and weak electric parallel fields, in the nnn-mixing regime. Our emphasis is on isolated pairs of near-degenerate, opposite-parity, diamagnetic states that become mixed by the weak electric field. Such level pairs allow for the generation of nondegenerate states with large, tunable permanent electric dipole moments and large optical excitation cross sections from the atomic ground state. We investigate how the dipole moments and the zero-electric-field energy defects of these level pairs can be tuned using small variations of the electric and magnetic fields. Using calculations, we explore the abundance of such level pairs over wide spectral regions for several magnetic quantum numbers. Applications of polar, diamagnetic Rydberg states in Rydberg-atom interaction experiments are briefly discussed.
The quadratic Zeeman effect of Rydberg atoms is treated with the help of first-order perturbation theory and a special WKB approximation. The Bohr-Sommerfeld quantization leads to complete elliptic integrals. As a result we found that the spectrum is doubly degenerate if n2m2>5\frac{{n}^{2}}{{m}^{2}>5}m2>5n2​, this part exhibiting a linear Stark effect in an additional weak electric field; the rest of the spectrum (n2m2<5\frac{{n}^{2}}{{m}^{2}<5}m2<5n2​) is nondegenerate, exhibiting a quadratic Stark effect in an additional weak electric field.