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Physical Review A

Rydberg atoms in weak magnetic fields

A. P. Kazantsev, V. L. Pokrovsky, János A. Bergou

Published Dec 1, 1983• 11 citations
Publisher

Abstract

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 $\frac{{n}^{2}}{{m}^{2}>5}$, this part exhibiting a linear Stark effect in an additional weak electric field; the rest of the spectrum ($\frac{{n}^{2}}{{m}^{2}<5}$) is nondegenerate, exhibiting a quadratic Stark effect in an additional weak electric field.

DOI
10.1103/physreva.28.3659

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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.

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Rydberg states of rubidium in crossed electric and magnetic fields

Francis Jean Penent, Dominique Delande, J. C. Gay

The results of an experimental study of the Rydberg spectrum of rubidium in crossed electric and magnetic fields are reported and compared with theoretical predictions. The present investigations have been conducted in the low-field regime in which the paramagnetic and linear Stark interactions are perturbations to the Coulomb energy. When quantum-defect corrections are negligible, the SO(4) symmetry of the Coulomb interaction organizes the hydrogenic energy spectrum according to the law ${\mathit{E}}_{\mathit{n}}$,k=-R/${\mathit{n}}^{2}$+\ensuremath{\Elzxh}k(${\mathrm{\ensuremath{\omega}}}_{\mathit{L}}^{2}$+${\mathrm{\ensuremath{\omega}}}_{\mathit{S}}^{2}$${)}^{1/2}$, where k is an integer such that -(n-1)\ensuremath{\le}k\ensuremath{\le}(n-1), and ${\mathrm{\ensuremath{\omega}}}_{\mathit{L}}$,${\mathrm{\ensuremath{\omega}}}_{\mathit{S}}$, are, respectively, the Larmor and linear Stark frequencies. The experimental evidence for such a quantization is presented in rubidium Rydberg series using Doppler-free two-photon spectroscopy. The role of quantum defects is incorporated into the theory and experimentally demonstrated.

Physical Review A•Jun 1, 1988•48 citations
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.
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.
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.
A Rydberg atom has a highly excited valence electron which is weakly bound and far from the nucleus. These atoms have exaggerated properties that make them attractive candidates for quantum computation and studies of fundamental quantum mechanics. The discrete energy levels of Rydberg atoms are shifted in the presence of an electric field by the Stark effect and are similarly shifted due to a magnetic field by the Zeeman effect. These effects couple the energy levels together, creating avoiding crossings. At these avoided crossings, an electron in one energy level can jump to the other. Our goal is to be able to use these avoided crossings to put the electron in a superposition state of both energy levels. In order to achieve this we created new software that enables us to calculate the energy levels of an electron in both a magnetic and an electric field. We present energy level maps visualizing the results of the Stark and Zeeman effects.
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.
The results of an experimental study of the Rydberg spectrum of rubidium in crossed electric and magnetic fields are reported and compared with theoretical predictions. The present investigations have been conducted in the low-field regime in which the paramagnetic and linear Stark interactions are perturbations to the Coulomb energy. When quantum-defect corrections are negligible, the SO(4) symmetry of the Coulomb interaction organizes the hydrogenic energy spectrum according to the law En{\mathit{E}}_{\mathit{n}}En​,k=-R/n2{\mathit{n}}^{2}n2+\ensuremath{\Elzxh}k(${\mathrm{\ensuremath{\omega}}}_{\mathit{L}}^{2}$+${\mathrm{\ensuremath{\omega}}}_{\mathit{S}}^{2}$)1/2{)}^{1/2})1/2, where k is an integer such that -(n-1)\ensuremath{\le}k\ensuremath{\le}(n-1), and ${\mathrm{\ensuremath{\omega}}}_{\mathit{L}}$,${\mathrm{\ensuremath{\omega}}}_{\mathit{S}}$, are, respectively, the Larmor and linear Stark frequencies. The experimental evidence for such a quantization is presented in rubidium Rydberg series using Doppler-free two-photon spectroscopy. The role of quantum defects is incorporated into the theory and experimentally demonstrated.