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European Journal of Physics

The Zeeman effect and optical pumping in atomic rubidium: a teaching experiment in quantum physics

R.J. Butcher, Sarah Adams, G J Seddon, J A Golby, D R Massey

Published Oct 1, 1987• 1 citation
Publisher

Abstract

The authors describe an experiment developed recently in an undergraduate laboratory to measure the Zeeman splitting of the ground state of atomic rubidium. An optical pumping technique is employed and the magnetic field is calibrated by using free-electron spin resonance. Multiphoton absorption and power broadening of transitions are also investigated and a number of quantum principles introduced experimentally.

DOI
10.1088/0143-0807/8/4/004

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Physical Review A•Feb 1, 1972•265 citations
The authors describe an experiment developed recently in an undergraduate laboratory to measure the Zeeman splitting of the ground state of atomic rubidium. An optical pumping technique is employed and the magnetic field is calibrated by using free-electron spin resonance. Multiphoton absorption and power broadening of transitions are also investigated and a number of quantum principles introduced experimentally.
Abstract It is common for senior physics students at many universities to perform optical pumping experiments using a rubidium cell in an integrated apparatus. Such experiments provide an encounter with atomic structure in the context of a standard technique of modern atomic physics. Typically, students investigate radiofrequency resonances between Zeeman levels and measure hyperfine splitting. Despite its pivotal role in aligning the apparatus the so-called zero-field resonance is usually not investigated in such experiments. However it is instructive to look more closely at this phenomenon. We show that it is a consequence of a residual transverse magnetic field that is the result of the inability to align precisely the optical axis of the apparatus in the local N – S direction. The measured width and depth of the resonance-like minimum in transmission is found to be consistent with a very small relaxation rate for the rubidium atoms. In an appendix we show further that the measurements compare well with theory for the Hanle effect in the ground state for an arbitrary magnetic field direction relative to the optical axis of the experiment.
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.
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.
The theory of several experiments involving optical pumping is presented in a simplified form. Vector methods are employed to discuss the hyperfine energy levels of an atom in a weak magnetic field, and, for the purposes of considering relaxation time, the system is assumed to have only two effective levels. The Breit-Rabi equation for the ground-state hyperfine Zeeman energy levels of an alkali atom is derived from the Schrödinger equation to facilitate the interpretation of the quadratic Zeeman effect. A number of suggestions for practical optical pumping experiments are made.
Abstract : A method for the optical observation of nutational resonance in optically pumped rubidium vapor has been studied both experimentally and theoretically. The method consists of pulsemodulating an rf magnetic field a one of the Zeeman resonance frequencies of the vapor and observing the resulting damped transient modulation in the transmitted light intensity. Of particular interest is the application of this method to a study of the spin relaxation of vapor atoms as influenced by the physical parameters of the system, in the case where the applied steady magnetic field is intense enough to cause individual Zeeman intervals to become noticeably unequal. Both single and double quantum resonances at a wide spectrum of Zeeman transitions of Rb-85 vapor diffusing through neon and helium buffer gases have been observed and identified, and the damping of the transient nutations in light intensity has been recorded under a variety of conditions. (Author)
According to the quantum theory of the optical-pumping cycle, one can describe the effect of a nonresonant light beam on the different Zeeman sublevels of an atomic ground state by an effective Hamiltonian He{\mathcal{H}}_{e}He​ which depends on the polarization and spectral profile of the incident light. In order to check the structure of He{\mathcal{H}}_{e}He​, we have performed a detailed experimental study of the ground-state energy sublevels of various kinds of atoms perturbed by different types of nonresonant light beams. Attention is paid to the modification of the Zeeman structure due to He{\mathcal{H}}_{e}He​. We have been able to obtain experimentally in the ground state of 199Hg^{199}\mathrm{Hg}199Hg, 201Hg^{201}\mathrm{Hg}201Hg, and 87Rb^{87}\mathrm{Rb}87Rb, Zeeman light shifts that are larger than the width of the levels due to the thermal relaxation. The removal of the Zeeman degeneracy in zero external field, due to a nonresonant light irradiation, is observed by different optical-pumping techniques; the full Zeeman diagram of the perturbed atoms is also determined when a static field ${\stackrel{\ensuremath{\rightarrow}}{\mathrm{H}}}_{0}$ is added. We have checked that the effect of He{\mathcal{H}}_{e}He​ can be described in terms of fictitious static electric or magnetic fields. These fictitious fields can be used to act selectively on a given atomic level.