Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Journal of Physics B Atomic and Molecular Physics

Perturbation theory for highly-excited states (application to Rydberg atoms in the external magnetic field)

A. P. Kazantsev, V. L. Pokrovsky

Published Oct 28, 1983• 3 citations
Publisher

Abstract

A generalisation of the classical averaging over fast variables is proposed. The spectrum and wavefunctions of highly excited quantum states in weak external fields are found explicitly for the simplest cases of classically non-degenerate or twofold degenerate systems. The theory is applied to find the polarisability and linear Stark effect of Rydberg atoms in a relatively strong magnetic field and a weak electric field.

DOI
10.1088/0022-3700/16/20/001

Related papers

Rydberg atoms in crossed fields

A A Belov, A. P. Kazantsev, Dmitri V. Khveshchenko +1 more

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.

Journal of Physics B Atomic and Molecular Physics•Dec 28, 1985•5 citations

Rydberg Atoms In Parallel Electric And Magnetic Fields

Robert L. Waterland

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.

•Jan 1, 1986•0 citations

Multichannel quantum-defect theory of perturbed Rydberg atoms in external fields

K. T. Lu, A. R. P. Rau

The diamagnetic and Stark shifts of strongly perturbed Rydberg spectra such as those of the alkaline earths are expressed in terms of multichannel---quantum-defect parameters. The theory is applicable when the shifts produced by the external fields are smaller than the neighboring Rydberg separations. It is applied to evaluate the diamagnetic shifts in Ba, an atom in which Rydberg and doubly excited channels are strongly mixed. In such complex spectra, the diamagnetic effect can serve a useful purpose as a tool to disentangle the interacting series. The radial sizes and, therefore, the diamagnetic shifts are quite different for singly and doubly excited states even when they are at the same energy. In fact, for the field strengths considered ($\ensuremath{\simeq}40$ kG), the diamagnetic contribution of the doubly excited configuration is quite negligible. As a result, the observed shift is a direct measure of the amount of singly excited configuration in the state of interest. Exactly similar conclusions apply to Stark shifts. The last part of this paper considers states of very high excitation further up in the spectrum which are no longer in a perturbative regime. Spectra of atoms in a magnetic field have shown equally spaced resonances near the ionization threshold with characteristic spacings. By the consideration of the effects of electric fields which are also often simultaneously present, a criterion is established for the nature of these spacings depending on the relative strengths of the crossed electric and magnetic fields. The spacing seen in any particular experiment is shown to depend on the mass and quantum defect of the atom, the strengths of the external fields, and experimental conditions such as the temperature of the atomic vapor whose absorption spectrum is being studied.

Physical Review A•Nov 1, 1983•11 citations

Rydberg atoms in weak magnetic fields

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

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.

Physical Review A•Dec 1, 1983•11 citations

Oscillator strengths in the spectra of highly excited atomic hydrogen in crossed electric and magnetic fields

Petr A. Braun

A study is made of the spectra of a highly excited hydrogen atom in crossed external l-mixing electric and magnetic fields. A semiclassical model is suggested for the radiative transitions between the perturbed Rydberg levels and the low-lying levels of the atom. The emitted light is shown to be a superposition of radiation of two effective linear vibrators symmetrically placed with respect to the external fields' plane. The interference between the vibrators is the source of rapid oscillations of the observed line intensities and polarization accompanying even small variation of the external fields. The averaged spectral intensity is shown to be unchanged by the presence of the magnetic field, being the same as in Stark splitting.

Journal of Physics B Atomic Molecular and Optical Physics•May 14, 1991•2 citations

Highly polar states of Rydberg atoms in strong magnetic and weak electric fields

E. Paradis, Stefan Zigo, Georg A. Raithel

We study the spectra of diamagnetic rubidium Rydberg atoms in strong magnetic and weak electric parallel fields, in the $n$-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.

Physical Review A•Jan 14, 2013•10 citations
A generalisation of the classical averaging over fast variables is proposed. The spectrum and wavefunctions of highly excited quantum states in weak external fields are found explicitly for the simplest cases of classically non-degenerate or twofold degenerate systems. The theory is applied to find the polarisability and linear Stark effect of Rydberg atoms in a relatively strong magnetic field and a 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.
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 diamagnetic and Stark shifts of strongly perturbed Rydberg spectra such as those of the alkaline earths are expressed in terms of multichannel---quantum-defect parameters. The theory is applicable when the shifts produced by the external fields are smaller than the neighboring Rydberg separations. It is applied to evaluate the diamagnetic shifts in Ba, an atom in which Rydberg and doubly excited channels are strongly mixed. In such complex spectra, the diamagnetic effect can serve a useful purpose as a tool to disentangle the interacting series. The radial sizes and, therefore, the diamagnetic shifts are quite different for singly and doubly excited states even when they are at the same energy. In fact, for the field strengths considered ($\ensuremath{\simeq}40$ kG), the diamagnetic contribution of the doubly excited configuration is quite negligible. As a result, the observed shift is a direct measure of the amount of singly excited configuration in the state of interest. Exactly similar conclusions apply to Stark shifts. The last part of this paper considers states of very high excitation further up in the spectrum which are no longer in a perturbative regime. Spectra of atoms in a magnetic field have shown equally spaced resonances near the ionization threshold with characteristic spacings. By the consideration of the effects of electric fields which are also often simultaneously present, a criterion is established for the nature of these spacings depending on the relative strengths of the crossed electric and magnetic fields. The spacing seen in any particular experiment is shown to depend on the mass and quantum defect of the atom, the strengths of the external fields, and experimental conditions such as the temperature of the atomic vapor whose absorption spectrum is being studied.
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.
A study is made of the spectra of a highly excited hydrogen atom in crossed external l-mixing electric and magnetic fields. A semiclassical model is suggested for the radiative transitions between the perturbed Rydberg levels and the low-lying levels of the atom. The emitted light is shown to be a superposition of radiation of two effective linear vibrators symmetrically placed with respect to the external fields' plane. The interference between the vibrators is the source of rapid oscillations of the observed line intensities and polarization accompanying even small variation of the external fields. The averaged spectral intensity is shown to be unchanged by the presence of the magnetic field, being the same as in Stark splitting.
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.