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Physical Review A

Second-order Zeeman effect in the 5 2 S–3 2 Sand 4 2 D–3 2 Stwo-photon transitions of atomic sodium

Wolfgang Hüttner, P. Otto, M. Gamperling

Published Aug 1, 1996• 5 citations
Publisher

Abstract

We have observed the second-order, field-induced Zeeman effects of the Doppler-free two-photon transitions 5${\mathrm{}}^{2}$S--3${\mathrm{}}^{2}$S and 4${\mathrm{}}^{2}$D--3${\mathrm{}}^{2}$S of atomic sodium using fields up to 5 T. Using a suitable experimental configuration it was possible to avoid the appearance of first-order effects in the high-field limit. The remaining small field-induced shifts are of the order of magnitude of a few linewidths. They yield the differences of the diamagnetic susceptibilities of the connected atomic states. The method is therefore capable of providing data related to atomic electronic structure. \textcopyright{} 1996 The American Physical Society.

DOI
10.1103/physreva.54.1318

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We have observed the second-order, field-induced Zeeman effects of the Doppler-free two-photon transitions 52{\mathrm{}}^{2}2S--32{\mathrm{}}^{2}2S and 42{\mathrm{}}^{2}2D--32{\mathrm{}}^{2}2S of atomic sodium using fields up to 5 T. Using a suitable experimental configuration it was possible to avoid the appearance of first-order effects in the high-field limit. The remaining small field-induced shifts are of the order of magnitude of a few linewidths. They yield the differences of the diamagnetic susceptibilities of the connected atomic states. The method is therefore capable of providing data related to atomic electronic structure. \textcopyright{} 1996 The American Physical Society.
The technique of two-photon absorption without Doppler broadening has made possible the observation of the Zeeman splitting of a transition between two 2S^{2}S2S states. Selection rules are discussed. The observed pattern of hyperfine components is narrower in very high fields than in zero field, in agreement with the theory.
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In this paper, we describe two complementary nonlinear spectroscopy methods which both allow one to achieve Doppler-free spectra of atomic gases. First, saturated absorption spectroscopy is used to investigate the structure of the 5S 1/2 → 5P 3/2 transition in rubidium. Using a slightly modified experimental setup, Doppler-free two-photon absorption spectroscopy is then performed on the 5S 1/2 → 5D 5/2 transition in rubidium, leading to accurate measurements of the hyperfine structure of the 5D 5/2 energy level. In addition, electric dipole selection rules of the two-photon transition are investigated, first by modifying the polarization of the excitation laser, and then by measuring two-photon absorption spectra when a magnetic field is applied close to the rubidium vapour. All experiments are performed with the same grating-feedback laser diode, providing an opportunity to compare different high-resolution spectroscopy methods using a single experimental setup. Such experiments may acquaint students with quantum mechanics selection rules, atomic spectra and Zeeman effect.
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.
Experimental results of studying the spectrum of the microwave 37 P -37 S transition of Rydberg sodium atoms in a weak magnetic field (≤7 G) are reported. The populations of the Rydberg states were measured using the method of selective ionization with a pulsed electric field. When the magnetic field was parallel to the ionizing electric field, a good agreement between the calculated and experimental spectral shapes was observed, making it possible to determine the unknown polarization of the microwave radiation. In the case of the orthogonal configuration of the fields, the resonance structure was suppressed in the field ionization signals due to the strong influence of the magnetic field on the electron trajectories in the detection system.
We have used two-photon absorption from counterpropagating laser beams of different frequencies to measure Stark shifts and splittings of the 62S6^{2}S62S, 72S7^{2}S72S, 82S8^{2}S82S, 52D5^{2}D52D, and 62D6^{2}D62D states in sodium. Beams from a fixed-frequency, single-mode Ar+{\mathrm{Ar}}^{+}Ar+ laser and a tunable, single-frequency cw dye laser were focussed into a coarse sodium atomic beam and the fluorescence was monitored. The collimation of the atomic beam reduced the residual Doppler width inherent in using two different frequencies. Using the two lasers allowed two-photon transitions to be observed at frequencies unattainable with the dye laser alone, and enhanced the transition rates due to the near resonance of the dye laser with the strong Na $3^{2}S\ensuremath{\rightarrow}3^{2}P$ transition. Our experimental results for the scalar and tensor polarizabilities, ${\ensuremath{\alpha}}_{0}$ and ${\ensuremath{\alpha}}_{2}$, agree with calculations in the Bates and Damgaard Coulomb approximation within 2% for ${\ensuremath{\alpha}}_{0}$ and 9% for ${\ensuremath{\alpha}}_{2}$. As a by-product the hyperfine-interaction constants aaa for the SSS states and the fine-structure intervals $\ensuremath{\delta}\ensuremath{\nu}=\frac{({E}_{\frac{3}{2}}\ensuremath{-}{E}_{\frac{5}{2}})}{h}$ for the DDD states were obtained.