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arXiv:2006.06199 · Physical Review Research

Crystal-field Paschen-Back effect on ruby in ultrahigh magnetic fields

Masaki Gen, Tomoki Kanda, Takashi Shitaokoshi, Yoshimitsu Kohama, Toshihiro Nomura

Published Aug 17, 2020• 4 citations
arXivHTMLPDF

Abstract

This paper reports the anomalous Zeeman effect of the R lines of ruby in megagauss region. This observation owes to the Paschen-Back effect, where the Zeeman energy overcomes the crystal-field energy splitting, resulting in the renormalization of the good quantum number.
DOI
10.1103/physrevresearch.2.033257

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Analytical expressions for the dependence of the intensity of Zeeman components of doublet lines on the magnetic field are obtained. Sharp changes of these function on passing from the anomalous Zeeman effect to the Paschen-Back effect lead to the disappearance of marginal lines and the equalization of intensities of remaining lines. In the region of the complete Paschen-Back effect, a strong influence on these dependences is produced by the dynamic atom-field interaction, which weakens the paramagnetic effect in the states with a positive magnetic quantum number m and enhances the effect in the states with a negative m . Simple analytical expressions are obtained that take into account the effect of the diamagnetic interaction on line intensities. The role of the diamagnetic interaction increases in Rydberg atomic states with a large spin-orbit splitting. For the states with m > 0, it can lead to the “diamagnetic reversal” of the Paschen-Back effect, i.e., the recovery of the anomalous Zeeman effect.
The Zeeman effect of R-absorption lines in ruby was observed in a high pulsed magnetic field up to 520 kOe using an optical multichannel analyzer. The experiment was done under a thermal equilibrium condition ( T =130 K) and the Zeeman line intensity is satisfactorily explained. When a magnetic field is applied perpendicular to the C 3 -axis, the excited \barE and 2\barA states show a level mixing and the observed pattern indicates a clear Paschen-Back effect The observed g // -values of the excited states are -2.49±0.05 and 1.49±0.05 for \barE and 2\barA, respectively. g ⊥ -values for these levels were estimated to be smaller than 0.1 at 500 kOe.
We precisely investigate the Zeeman and Paschen-Back effects of the hyperfine structure during the rubidium $5{\phantom{\rule{0.16em}{0ex}}}^{2}{S}_{1/2}\ensuremath{\rightarrow}5{\phantom{\rule{0.16em}{0ex}}}^{2}{D}_{5/2}$ two-photon transition. Owing to the high sensitivity of the DDD state of atoms to a magnetic field, the splittings of the spectra of the DDD state are sufficiently large in a weak magnetic field of <10<10<10 G. We experimentally observe how in the hyperfine coupling in the 52D5/25{\phantom{\rule{0.16em}{0ex}}}^{2}{D}_{5/2}52D5/2​ state is disrupted even in weak magnetic fields around 10 G and the energy levels are arranged according to their total angular momentum JJJ and nuclear spin III. The transient of the spectra known as the Paschen-Back effect is observed even in a weak magnetic field with an order of magnitude of several tens of gauss. The results of theoretical calculations for energy shifts and transition intensities under a magnetic field are in quantitative agreement with the experimental results.
The Zeeman effect of the B and R absorption lines of ruby was observed photographically with strong pulsed magnetic fields up to 230 kOe at 77°K. This was achieved by flashing a Xe-lamp at the time when a magnetic field reached its peak. The duration of the pulsed field was made to be about 1 m sec which was much longer than that of the pulsed light, about 20 µ sec. The g -values of the excited states responsible for the B and R lines were measured and the comparison was made with those reported by other authors. For the Zeeman patterns of the R lines with magnetic fields perpendicular to the optic axis, the Paschen-Back effect was calculated and compared with the observed patterns.
Simple and efficient λ-method and λ/2-method (λ is the resonant wavelength of laser radiation) based on a nanometric-thickness cell filled with rubidium (Rb) are implemented to study the splitting of hyperfine transitions of an Rb85 and Rb87D1 line in an external magnetic field in the range of B=0.5–0.7 T. It is experimentally demonstrated from 20 (12) Zeeman transitions allowed at low B-field in Rb85 (Rb87) spectra in the case of σ+ polarized laser radiation, only 6 (4) remain at B>0.5 T, caused by decoupling of the total electronic momentum J and the nuclear spin momentum I (hyperfine Paschen–Back regime). The expressions derived in the frame of completely uncoupled basis (J,mJ;I,mI) describe the experimental results extremely well for Rb85 transitions at B>0.6 T (that is a manifestation of hyperfine Paschen–Back regime). A remarkable result is that the calculations based on the eigenstates of the coupled (F,mF) basis, which adequately describe the system for a low magnetic field, also predict reduction of the number of transition components from 20 to 6 for Rb85 and from 12 to 4 for Rb87 spectrum at B>0.5 T. Also, the Zeeman transition frequency shifts, frequency intervals between the components and their slope versus B, are in agreement with the experiment.
We investigate experimentally and theoretically the Faraday effect in an atomic medium in the hyperfine Paschen–Back regime, where the Zeeman interaction is larger than the hyperfine splitting. We use a small permanent magnet and a micro-fabricated vapour cell, giving magnetic fields of the order of a tesla. We show that for low absorption and small rotation angles, the refractive index is well approximated by the Faraday rotation signal, giving a simple way to measure the atomic refractive index. Fitting to the atomic spectra, we achieve magnetic field sensitivity at the 10 −4 level. Finally we note that the Faraday signal shows zero crossings which can be used as temperature insensitive error signals for laser frequency stabilization at large detuning. The theoretical sensitivity for 87 Rb is found to be ∼40 kHz °C −1 .