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Physical Review A

Experimental observation and theoretical calculation of the diamagnetic spectrum of sodium Rydberg states

W. Gao, Haifeng Yang, Hong Cheng, X. J. Liu, Hongping Liu

Published Jul 31, 2012• 13 citations
Publisher

Abstract

We report diamagnetic spectra of sodium atoms observed in a strong magnetic field up to 3 T and compare them with theoretical calculations based on the formulation of an exact quantum-defect theory. We focus on one-photon absorption processes from the ground $3s$ state to the excited $np$ Rydberg states whose magnetic quantum numbers are determined by the polarization of the laser field. The calculations employ $B$-spline basis expansion and the complex spatial coordinate rotation technique, and their results agree well with the observed ones when atomic core effects are appropriately taken into account. When graphed against magnetic field, level anticrossings and core-induced interaction of the $np$ states provide clear signatures for studying the effects of quantum defect on the diamagnetic spectra.

DOI
10.1103/physreva.86.012517

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We report diamagnetic spectra of sodium atoms observed in a strong magnetic field up to 3 T and compare them with theoretical calculations based on the formulation of an exact quantum-defect theory. We focus on one-photon absorption processes from the ground 3s3s3s state to the excited npnpnp Rydberg states whose magnetic quantum numbers are determined by the polarization of the laser field. The calculations employ BBB-spline basis expansion and the complex spatial coordinate rotation technique, and their results agree well with the observed ones when atomic core effects are appropriately taken into account. When graphed against magnetic field, level anticrossings and core-induced interaction of the npnpnp states provide clear signatures for studying the effects of quantum defect on the diamagnetic spectra.
A theoretical calculation is carried out to investigate the spectrum of a barium Rydberg atom in an external magnetic field. Using an effective approach incorporating quantum defect into the centrifugal term in the Hamiltonian, we reexamine the reported spectrum of the barium Rydberg atom in a magnetic field of 2.89 T [ J. Phys. B 28 L537 (1995) ]. Our calculation employs B -spline basis expansion and complex coordinate rotation techniques. For single photon absorption from the ground 6s 2 to 6s n p Rydberg states, the spectrum is not influenced by quantum defects of channels n s and n d. The calculation is in agreement with the experimental observations until the energy reaches E = −60 cm −1 . Beyond this energy, closer to the threshold, the calculated and experimental results do not agree with each other. Possible reasons for their discrepancies are discussed. Our study affirms an energy range where the diamagnetic spectrum of the barium atom can be explained thoroughly using a hydrogen model potential.
We study the core effect of nonhydrogenic alkaline-earth-metal barium in its diamagnetic spectrum by one photon transition from the ground state 6s26{s}^{2}6s2 1S0{}^{1}\phantom{\rule{-0.16em}{0ex}}{S}_{0}1S0​ experimentally and theoretically. The non-Coulombic potential of the ion core introduces an extra energy shift compared with hydrogen and a level anticrossing between different nnn manifolds, characterized by the quantum defect of the concerned angular momentum states. With a complex rotation coordinate technique and a BBB-spline expansion method, we develop a matrix-form Hamiltonian based on an effective potential incorporating the angular-dependent quantum defect into the angular rotation term. The nonhydrogen core effects are investigated by sweeping the quantum defects of different channels in the calculation. Results show that quantum defects of ppp and fff states have a undeniable effect on the intensities and positions of the spectral lines, although barium is closely hydrogenlike in the energy range examined. The anticrossing spectral lines are also identified with the aid of theoretical calculations. The calculations are in good agreement with the experimental observations.
We have studied highly excited sodium in various electric fields, parallel electric and magnetic fields, with one σ and π photon irradiation, and even in a magnetic field with a complex laser polarization configuration. The σ spectra shows a simple linear Stark effect with the applied electric field, while the π spectra exhibits a strong non-linear dependence on the electric field. The π transitions in parallel fields show a similar behavior to that in a pure electric field but the spectra get more smooth due to the magnetic field. The diamagnetic spectrum with laser polarization angles between 0 and π /2 proves that it can be reproduced by simple linear combination of π and σ components, indicating there is no interference between the π and σ channels. A full quantum calculation considering the quantum defects accounts for all the observations. The quantum defects, especially for the channel n p, play an important role in the spectral profile.
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.
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.
We present an experimental survey of a group of Rydberg states of sodium in magnetic fields up to 6 T, where levels from different terms overlap and interact strongly. The observed energy levels and relative line intensities for even-parity ml=1{m}_{l}=1ml​=1 terms in the vicinity n=28n=28n=28 are in good agreement with calculations based on a numerical diagonalization using spherical basis states in the range $n=25\ensuremath{-}31$.