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Journal of the Optical Society of America B

Saturated-absorption spectroscopy of weak-field Zeeman splittings in rubidium: comment

J. B. Kim, H.A. Kim, Han Seb Moon, H. S. Lee

Published Nov 1, 1997• 2 citations
Publisher

Abstract

High-resolution saturated absorption spectroscopy of the 85RbD1 line has been used for observation of the Zeeman effect by use of a diode laser with a narrow linewidth. Experimental results were compared with both Breit–Rabi theory related to shifted resonant frequencies and Nakayama's single-cycle optical pumping theory related to signal magnitudes of signal [J. Opt. Soc. Am. B2, 1431 (1985)]. A comparison of our results with those of Bowie [J. Opt. Soc. Am. B12, 1839 (1995)], who used perturbation theory to obtain the energy-level shifts, yielded experimental results that differ significantly in some respects.

DOI
10.1364/josab.14.002946

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High-resolution saturated absorption spectroscopy of the 85RbD1 line has been used for observation of the Zeeman effect by use of a diode laser with a narrow linewidth. Experimental results were compared with both Breit–Rabi theory related to shifted resonant frequencies and Nakayama's single-cycle optical pumping theory related to signal magnitudes of signal [J. Opt. Soc. Am. B2, 1431 (1985)]. A comparison of our results with those of Bowie [J. Opt. Soc. Am. B12, 1839 (1995)], who used perturbation theory to obtain the energy-level shifts, yielded experimental results that differ significantly in some respects.
Using an external cavity-tuned diode laser in Doppler-free saturation spectroscopy, we are able to resolve the weak-field Zeeman splittings in the hyperfine levels of the rubidium D1 line. The number of lines observed in the Zeeman structure of rubidium and their measured energy-level splittings are as expected from theory. The measured amplitudes of the saturated-absorption signals, crossover resonances, and velocity-selective optical pumping signals are used in the analysis of various theories concerning saturated-absorption spectroscopy.
We observed saturated absorption spectra of the 87Rb atom under a magnetic field of several millitesla with a diode laser oscillating at 780 nm. The spectra were compared with the theoretical ones obtained on the basis of Nakayama's four-level model. We numerically computed Zeeman splittings of the 52 P 3/2 excited state of the atom. As the magnetic field increased to 5 mT, the absorption peak of the F=2→F'=3 transition shifted almost linearly up to about 62 MHz. The shift direction was reversed by changing the polarization combination of the pump and probe lasers. The measured frequency stability, when the laser was locked at the absorption peak, was better than σy(τ)= 1 ×10-11τ-1/2 for the sampling time of 0.01 s≤τ≤10 s.
Zeeman splitting in the D 2 line of rubidium atoms ( 87 Rb and 85 Rb) has been studied using 'Doppler broadened' as well as 'saturation absorption spectroscopy'. While a linearly polarized beam was used for the former experiment, in the latter case a (π, σ ± ) polarization configuration was employed for both pump and probe beams. Zeeman lines have been observed by applying a field up to 5 mT. The field variation of relative line intensities in Doppler-broadened spectrum was determined following Tremblay et al and Nakayama's four-level model. For the saturation spectrum, a four-level model was used. Because the enhancement of absorption at the field is as low as 1 mT, the F g = 2 to F e = 3 transition for 87 Rb can be used as the reference for laser locking. Level crossing is observed in 85 Rb at fields less than 5 mT.
The saturated absorption spectra of the 87Rb D2 line were observed in an almost-zero magnetic field, in the geomagnetic field, and in a magnetic field of 10 G. The relative magnitudes of the resonance signals were calculated and tabulated by application of Nakayama’s four-level model to the 87Rb D2 line. The observed spectra were in good agreement with the theoretical plots. However, it was found that in the case of the 10-G magnetic field it is necessary to calculate an exact splitting of Zeeman sublevels in order to fit the theoretical calculation to the observed spectra and that saturation spectroscopy can be used as a method for observing the Zeeman splitting.
This paper presents a simple analytical theory for the velocity-dependent pump-probe laser spectroscopy of 87Rb^{87}\mathrm{Rb}87Rb and 85Rb^{85}\mathrm{Rb}85Rb atoms where the pump and the probe beams are circularly or linearly polarized. The analytical solutions of the line shapes of the velocity-selective optical pumping spectroscopy [G. Moon and H. R. Noh, Phys. Rev. A 78, 032506 (2008)] and saturated absorption spectroscopy [G. Moon and H. R. Noh, J. Opt. Soc. Am. B 25, 701 (2008); 27, 1741 (2010)] obtained in the previous reports, expressed as a sum of several Lorentzian functions, could be approximated as one (or in some cases, two) Lorentzian function(s). In particular, the contributions of the saturation and optical pumping effects could be discriminated explicitly in these simple analytical solutions, which is not possible in existing theories such as Nakayama's model. The simple analytical results for the saturation spectroscopy were compared with experimental results, and good agreement between them was observed.
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.