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Rydberg Atoms In Parallel Electric And Magnetic Fields

Robert L. Waterland

Published Jan 1, 1986• 0 citations
Publisher

Abstract

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.

DOI
10.21220/s2-tmb6-kj63

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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.
For pt. I see ibid., vol.21, no.21, p.3473-98 (1988). The semiclassical approach based on the secular perturbation method, primarily introduced by Solov'ev (1982) to study the pure diamagnetism of hydrogen in the weak-field limit, is extended to the case where the atom is subjected to electric and magnetic fields both parallel to the 0z direction. The structure of the manifold of states with principal quantum number n is governed by the existence of an approximate constant of motion and the states can be classified into three groups. The semiclassical Bohr-Sommerfeld quantisation rule allows the energy of the states to be calculated. The main properties of the spectra and their evolution when one of the fields increases are analysed. An original comparison between the structure of the pure diamagnetic n multiplet with azimuthal quantum number M not=0 and the structure of the n, M=0 multiplet with parallel fields is proposed.
A spectroscopic study of Rydberg states of helium (n = 30 and 45) in magnetic, electric and combined magnetic and electric fields with arbitrary relative orientations of the field vectors is presented. The emphasis is on two special cases where (i) the diamagnetic term is negligible and both paramagnetic Zeeman and Stark effects are linear (n = 30, B ≤ 120 mT and F = 0-78 V cm⁻¹), and (ii) the diamagnetic term is dominant and the Stark effect is linear (n = 45, B = 277 mT and F = 0-8 V cm⁻¹). Both cases correspond to regimes where the interactions induced by the electric and magnetic fields are much weaker than the Coulomb interaction, but much stronger than the spin-orbit interaction. The experimental spectra are compared to spectra calculated by determining the eigenvalues of the Hamiltonian matrix describing helium Rydberg states in the external fields. The spectra and the calculated energy-level diagrams in external fields reveal avoided crossings between levels of different m ₗ values and pronounced m ₁-mixing effects at all angles between the electric- and magnetic-field vectors other than 0. These observations are discussed in the context of the development of a method to generate dense samples of cold atoms and molecules in a magnetic trap following Rydberg-Stark deceleration.
Abstract A spectroscopic study of Rydberg states of helium ( n = 30 and 45) in magnetic, electric and combined magnetic and electric fields with arbitrary relative orientations of the field vectors is presented. The emphasis is on two special cases where (i) the diamagnetic term is negligible and both paramagnetic Zeeman and Stark effects are linear ( n = 30, B ≤ 120 mT and F = 0–78 V cm −1 ), and (ii) the diamagnetic term is dominant and the Stark effect is linear ( n = 45, B = 277 mT and F = 0–8 V cm −1 ). Both cases correspond to regimes where the interactions induced by the electric and magnetic fields are much weaker than the Coulomb interaction, but much stronger than the spin–orbit interaction. The experimental spectra are compared to spectra calculated by determining the eigenvalues of the Hamiltonian matrix describing helium Rydberg states in the external fields. The spectra and the calculated energy-level diagrams in external fields reveal avoided crossings between levels of different m l values and pronounced m l -mixing effects at all angles between the electric- and magnetic-field vectors other than 0. These observations are discussed in the context of the development of a method to generate dense samples of cold atoms and molecules in a magnetic trap following Rydberg–Stark deceleration.
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.
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.