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Journal of Physics B Atomic and Molecular Physics

Radio-frequency Faraday effect in atomic hydrogen

Jack Finkel

Published Mar 28, 1985• 0 citations
Publisher

Abstract

Expressions for the angle of the Faraday rotation in atomic hydrogen, at radio frequencies, that are valid for all temperatures and magnetic field strengths are developed taking into account the electron-proton spin interactions. Simplified expressions for the rotation are also given for the special cases when the Zeeman splitting is much greater than or much smaller than the hyperfine splitting and when the two splittings are equal. A numerical result is given for the latter case at the hyperfine resonance frequency, 1420 MHz.

DOI
10.1088/0022-3700/18/6/009

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Expressions for the angle of the Faraday rotation in atomic hydrogen, at radio frequencies, that are valid for all temperatures and magnetic field strengths are developed taking into account the electron-proton spin interactions. Simplified expressions for the rotation are also given for the special cases when the Zeeman splitting is much greater than or much smaller than the hyperfine splitting and when the two splittings are equal. A numerical result is given for the latter case at the hyperfine resonance frequency, 1420 MHz.
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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 87Rb is found to be ∼40 kHz °C−1.
The identical spin rotation effect is the quantum mechanical collisional effect underlying the transverse nuclear spin waves recently seen in dilute non degenerate gases in Paris [3He] and at Cornell University [H↓]. This mechanism could in principle give rise, at low enough temperatures, to hydrodynamic oscillatory modes associated with any non diagonal elements of the atomic internal density matrix (generalized spin waves or coherences waves). Starting from a quantum Boltzmann equation recently derived for the study of 4-component atomic hydrogen, we show that the current of any transverse quantity (hyperfine or Zeeman coherence) does indeed precess around molecular exchange fields. Unhappily, in most cases, the oscillatory modes associated with these transverse quantities are heavily damped. The first intrinsic cause of damping of these waves is spin exchange. We study the conditions under which this damping is minimized in both zero field and in high magnetic field. Numerical values of all relevant parameters for the description of spin transport properties in atomic hydrogen are given in the appendices.
We show that the Faraday rotation (FR) in strong longitudinal magnetic fields is a convenient tool to study atomic transitions by using the D1 line in a Cs vapour confined in a nanocell of thickness L≈450 nm. We use strong magnetic fields ranging from 0.1 to 6 kG, in which Cs atomic transitions are split into a large number of components, and FR signals of spectral width of ∼ 50 MHz are frequency-resolved allowing the investigation of individual transitions. For magnetic fields of several kG, the hyperfine Paschen–Back regime is reached that is manifested by the presence in the spectrum of the eight FR components having the amplitudes of the same height and located with almost equidistant frequencies. A remarkable feature of FR spectrum is the proportionality of its amplitude to the probability of an atomic transition in a strong magnetic field. A theoretical model which agrees well with the experiment is developed.
Abstract The interaction of rubidium atoms with sapphire cell windows at an interwindow distance L = 40–100 nm is studied. For studies, we used the Faraday rotation (FR) effect (rotation of the plane of radiation polarization in a magnetic field) in a thin rubidium atom vapor column for D1, 2 lines. When L decreases from 100 to 40 nm, a red shift of the FR signal frequency is detected: it increases from 10 to 250 MHz, and the broadening of the low-frequency wing increases to ~1 GHz. The atomic transition Fg = 3 → Fe = 2 for the D1 line of 85Rb is shown to be convenient for such investigations, since it can be spectrally separated from other strongly broadened atomic transitions. Coefficients C3, which characterize the atom–surface interaction for the D1 and D2 lines of Rb, are determined. An additional red frequency shift takes place at a nanocell thickness L < 100 nm when the Rb atom density increases, and this shift is absent at large L. A practical application of an FR signal for measuring strong magnetic fields of several kilogausses is described.