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arXiv:physics/0509157 · Physical Review A

Polarization spectroscopy in rubidium and cesium

Margaret Harris, Charles S. Adams, Simon L. Cornish, I. C. McLeod, Edmund Tarleton, Ifan G. Hughes

Published Jun 29, 2006• 155 citations
arXivHTMLPDF

Abstract

We develop a theoretical treatment of polarization spectroscopy and use it to make predictions about the general form of polarization spectra in the alkali-metal atoms. Using our model, we generate theoretical spectra for the $D2$ transitions in $^{87}\mathrm{Rb}$, $^{85}\mathrm{Rb}$, and $^{133}\mathrm{Cs}$. Experiments demonstrate that the model accurately reproduces spectra of transitions from the upper hyperfine level of the ground state only. Among these, the closed transition $F\ensuremath{\rightarrow}{F}^{\ensuremath{'}}=F+1$ dominates, with a steep gradient through line center ideally suited for use as a reference in laser locking.

DOI
10.1103/physreva.73.062509

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Bulletin of the American Physical Society•Jun 11, 2015•0 citations
We develop a theoretical treatment of polarization spectroscopy and use it to make predictions about the general form of polarization spectra in the alkali-metal atoms. Using our model, we generate theoretical spectra for the D2D2D2 transitions in 87Rb^{87}\mathrm{Rb}87Rb, 85Rb^{85}\mathrm{Rb}85Rb, and 133Cs^{133}\mathrm{Cs}133Cs. Experiments demonstrate that the model accurately reproduces spectra of transitions from the upper hyperfine level of the ground state only. Among these, the closed transition F\ensuremath→F\ensuremath′=F+1F\ensuremath{\rightarrow}{F}^{\ensuremath{'}}=F+1F\ensuremath→F\ensuremath′=F+1 dominates, with a steep gradient through line center ideally suited for use as a reference in laser locking.
We present a theoretical and experimental study of polarization spectroscopy of rubidium atoms. All of the populations of the magnetic sublevels were calculated from the rate equations and used in the calculation of the polarization spectroscopy spectra. Using this model, we could generate theoretical line shapes of the polarization spectra on the D2{D}_{2}D2​ transitions of rubidium atoms. The experimental results demonstrated that our model accurately reproduced spectra for all transitions in hyperfine structures.
We study polarization spectroscopy of Rb vapour. A weak probe beam analyses the birefringence induced in a room temperature vapour by a strong counterpropagating circularly polarized pump beam. In contrast to most other work on polarization spectroscopy, we use a polarization beam splitting cube and two detectors (rather than a polarizer and one detector) to analyse the probe beam. The signal is in the form of a derivative of a Lorentzian. For theoretical analysis we study the closed atomic transition 5 2 S 1/2 ( F = 3) → 5 2 P 3/2 ( F ' = 4) in the D2 line of 85 Rb. We study the time needed to redistribute population among the m F states, derive an expression for the expected lineshape and present experimental data in excellent agreement with theory. The polarization spectrum provides an ideal error signal for frequency stabilization of a laser. We describe the geometry and parameters for optimizing the error signal.
Abstract We experimentally generate polarization spectroscopy (error) signals corresponding to the D2-line hyperfine transitions, F g = 2 → F e = 1 , 2 , 3 of 87Rb, and F g = 3 → F e = 2 , 3 , 4 of 85Rb, and show that the strongest error signals correspond to the closed hyperfine transitions (oscillator strength ∼ 0.7 ), F g = 2 → F e = 3 and F g = 3 → F e = 4 , respectively. We make the generated error signal robust to fluctuations in external parameters by finding optimum values for the vapor cell temperature and pump-probe intensities at two different beam diameters. We further employ these optimized error signals to directly (without the need for frequency/phase modulation) lock the laser frequency—reducing the rms drift/linewidth from ∼ 10 MHz to < 500 kHz, when measured over a ∼ 60 min duration. In addition, by comparing theoretically calculated and experimentally measured error signals for the pump intensities ranging from ∼ 0.1 I sat 0 − 10 I sat 0 (where, I sat 0 ∼ 1.6 mW cm−2 is the two-level saturation intensity for the Rb D2-line transitions), we discuss the applicability and limitations of existing numerical and analytical approaches based on a full multi-level rate equation model for polarization spectroscopy.
We realize the linear polarization spectroscopy on the D2 transitions of rubidium atoms and investigate the underlying physics with an analytical theory using the Nakayama model. We demonstrate that the strong birefringence in the rubidium atomic gas is induced by the π light optical pumping, which is distinguished from the conventional PS using circularly polarized light. The theory agrees with the experiment reasonably well, except for the upper hyperfine closed transitions where the saturation plays nontrivial roles. The effects of the misalignment of the polarization optics and the miscalibration of the pump intensity are also discussed.
An ongoing spectroscopic investigation of atomic rubidium utilizes a two-photon, single-laser excitation process. Transitions accessible with our tunable laser include 5P1/2 (F ′ ) ← 5S1/2 (F) and 5P3/2 (F ′ ) ← 5S1/2 (F). The laser is split into a pump and probe beam to allow for Doppler-free measurements of transitions between hyperfine levels. The pump and probe beams are overlapped in a counter-propagating geometry and the laser frequency scans over a transition. Absorption, fluorescence and polarization spectroscopy techniques are applied to this basic experimental setup. The temperature of the vapor cell and the power of the pump and probe beams have been varied to explore line broadening effects and signal-to-noise of each technique. This humble setup will hopefully grow into a more robust experimental arrangement in which double resonance, two-laser excitations are used to explore hyperfine state changing collisions between rubidium atoms and noble gas atoms. Rb-noble gas collisions can transfer population between hyperfine levels, such as 5P3/2 (F ′ = 3) Collision ←− 5P3/2 (F ′ = 2), and the probe beam couples 7S1/2 (F ′′ = 2) ← 5P3/2 (F ′ = 3). Polarization spectroscopy signal depends on the rate of population transfer due to the collision as well as maintaining the orientation created by the pump laser. Fluorescence spectroscopy relies only on transfer of population due to the collision. Comparison of these techniques yields information regarding the change of the magnetic sublevels, mF , during hyperfine state changing collisions.