The well-known graphical representation called the Lu-Fano plot was originally developed for multi-channel Rydberg spectroscopy, especially in quantum defect theory. The present study shows some of the limitations of this traditional Lu-Fano plot that are desirable to improve on, when there are closely split ionization thresholds as in many current generation quantum information applications involving hyperfine-split thresholds, or when there are more than two ionization threshold energies. The modified representation introduced here is especially simplifying in the situation where one is exploring the bound states lying very far below those closely split thresholds. Moreover, it overcomes one limitation, namely that in contrast to the traditional Lu-Fano plot, the modified representation developed here can be utilized for problems where there more than two ionization thresholds. An example application to Rydberg series of the manganese atom illuminates its use in a practical problem.
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 present a study of the Rydberg spectrum in
166Er for series connected to the
4f12(3H6)6s,
Jc=13/2, and
Jc=11/2 ionic core states using an all-optical detection based on electromagnetically induced transparency in an effusive atomic beam. Identifying approximately 550 individual states, we find good agreement with a multichannel quantum defect theory (MQDT) which allows assignment of most states to
ns or
nd Rydberg series. We provide an improved accuracy for the lowest two ionization thresholds to ${E}_{\mathrm{IP},{J}_{c}=13/2}=49260.750(1)\phantom{\rule{0.28em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}1}$ and ${E}_{\mathrm{IP},{J}_{c}=11/2}=49701.184(1)\phantom{\rule{0.28em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}1}$ as well as the corresponding quantum defects for all observed series. We identify Rydberg states in five different isotopes, and states between the two lowest ionization thresholds. Our results open the way for future applications of Rydberg states for quantum simulation using erbium and exploiting its special open-shell structure.