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Physical Review A

Rb87 D1 isoclinic point

N. P. Wells, James C. Camparo

Published Dec 7, 2010• 14 citations

Abstract

In the research presented here, we reconsider the problem of obtaining stable resonant features in linear absorption spectroscopy, which has application to ultraminiature atomic physics where sub-Doppler spectroscopic techniques are not always optimal. In particular, we consider the applicability of isoclinic points for precision atomic spectroscopy. These are defined as ``[a] wavelength, wave number, or frequency at which the first derivative of an absorption spectrum of a sample does not change upon a chemical reaction or physical change of the sample,'' and we demonstrate the existence of isoclinic points in the ${D}_{1}$ spectra of $I=3/2$ alkali-metal isotopes, where $I$ is the nuclear spin. We then consider the ${D}_{1}$ isoclinic point of $^{87}\mathrm{Rb}$ in detail, showing that a slight $^{85}\mathrm{Rb}$ contamination in real $^{87}\mathrm{Rb}$ samples should have no significant effect on the frequency stability of the isoclinic point and that optical pumping by a linearly polarized laser should also not affect the isoclinic point's stability (i.e., the isoclinic point is insensitive to laser intensity). Finally, we perform an experiment demonstrating that the $^{87}\mathrm{Rb}$ ${D}_{1}$ isoclinic point has a temperature shift more than an order of magnitude smaller than that of the most isolated transition in the $^{87}\mathrm{Rb}$ ${D}_{1}$ spectrum.

DOI: 10.1103/physreva.82.062505

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For years, inelastic, fine-structure-changing collisions between excited alkali-metal atoms and noble-gas perturbers have been a source of information on the alkali-metal--noble-gas interaction. Here, we consider the role of elastic fine-structure-mixing collisions on alkali-metal absorption cross sections. Specifically, we consider the four optical hyperfine transitions of the ${D}_{1}$ absorption spectrum for $^{87}\mathrm{Rb}$, and in particular the doublet corresponding to $5^{2}S_{1/2}({F}_{g}=2)\ensuremath{-}5^{2}P_{1/2}({F}_{e}=1,2)$ transitions. Although ideally the amplitudes of the doublet's absorption cross sections are identical, we find that fine-structure mixing of ${D}_{2}$ oscillator strength into the ${D}_{1}$ spectrum breaks the cross sections' equality and leads to doublet asymmetry. We obtain a fine-structure mixing parameter $\ensuremath{\lambda}$ of $(5.4\ifmmode\pm\else\textpm\fi{}0.3)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}21}\phantom{\rule{0.16em}{0ex}}\mathrm{c}{\mathrm{m}}^{3}$, and estimate a $5^{2}P_{1/2}$ hyperfine-splitting density shift $\ensuremath{\zeta}$ in the $^{87}\mathrm{Rb}$-Xe system of $+0.71\ifmmode\pm\else\textpm\fi{}0.03\phantom{\rule{0.16em}{0ex}}\mathrm{GHz}/\mathrm{amagat}$. These results have implications for spectroscopic applications of the $^{87}\mathrm{Rb}$ isoclinic point, which we consider as part of our conclusions.

Physical Review A•Aug 13, 2015•6 citations

In the research presented here, we reconsider the problem of obtaining stable resonant features in linear absorption spectroscopy, which has application to ultraminiature atomic physics where sub-Doppler spectroscopic techniques are not always optimal. In particular, we consider the applicability of isoclinic points for precision atomic spectroscopy. These are defined as ``[a] wavelength, wave number, or frequency at which the first derivative of an absorption spectrum of a sample does not change upon a chemical reaction or physical change of the sample,'' and we demonstrate the existence of isoclinic points in the

{D}_{1}

spectra of

I=3/2

alkali-metal isotopes, where

I

is the nuclear spin. We then consider the

{D}_{1}

isoclinic point of

^{87}\mathrm{Rb}

in detail, showing that a slight

^{85}\mathrm{Rb}

contamination in real

^{87}\mathrm{Rb}

samples should have no significant effect on the frequency stability of the isoclinic point and that optical pumping by a linearly polarized laser should also not affect the isoclinic point's stability (i.e., the isoclinic point is insensitive to laser intensity). Finally, we perform an experiment demonstrating that the

^{87}\mathrm{Rb}

{D}_{1}

isoclinic point has a temperature shift more than an order of magnitude smaller than that of the most isolated transition in the

^{87}\mathrm{Rb}

{D}_{1}

spectrum.

In recent years, much work has been done in experimental studies to frequency lock laser diodes to atomic or molecular resonances.1 By such techniques it is possible to improve greatly the laser frequency stability and to define precisely its nominal value. For laser sources operating in the 0.8-μm range, rubidium is the preferred specie and each isotope offers two resonance lines, one at 780 nm (D2 line) and one at 795 nm (D1 line). Both linear and saturated absorption have been used, and laser frequency charcteristics are published.2,3

To overcome the temperature sensitivity of lasers locked to Doppler-broadened transitions, we propose a scheme in which the laser is locked to an isoclinic point of the atom's spectrum: a frequency at which the first derivative of the absorption spectrum does not change upon a physical change of the sample. Here, we demonstrate that an isoclinic point exists in the Rb87D1spectrum at 795 nm, and that it is located midway between the Fg=2 → Fe=1 and Fg=2 → Fe=2 transitions. Locking a VCSEL diode laser to this isoclinic point, we have been able to demonstrate a very low sensitivity of the locked laser's frequency to temperature variations of the atomic vapor.

We present and analyze a bichromatic version of the well-known saturation absorption spectroscopy technique used to stabilize lasers to atomic resonances without Doppler broadening. We show that the spectroscopic properties can be transferred between two transitions at very different wavelengths by spectral hole burning in a Doppler-broadened atomic ensemble. Specifically, we demonstrate that this technique can be used to stabilize a laser to the D1 line of Rb87 by obtaining a saturation absorption spectrum with a strong pump laser stabilized to the D2 line. This allows for more freedom in the choice of the probe laser frequency offsets compared to conventional saturation absorption spectroscopy. We compare our experimental results to an analytical model and numerical results based on rate equations.

Determination of the Raman Transition in Cold

^{87}

Rb Atoms by Using an Isotope Transition Line

For years, inelastic, fine-structure-changing collisions between excited alkali-metal atoms and noble-gas perturbers have been a source of information on the alkali-metal--noble-gas interaction. Here, we consider the role of elastic fine-structure-mixing collisions on alkali-metal absorption cross sections. Specifically, we consider the four optical hyperfine transitions of the

{D}_{1}

absorption spectrum for

^{87}\mathrm{Rb}

, and in particular the doublet corresponding to $5^{2}S_{1/2}({F}_{g}=2)\ensuremath{-}5^{2}P_{1/2}({F}_{e}=1,2)$ transitions. Although ideally the amplitudes of the doublet's absorption cross sections are identical, we find that fine-structure mixing of

{D}_{2}

oscillator strength into the

{D}_{1}

spectrum breaks the cross sections' equality and leads to doublet asymmetry. We obtain a fine-structure mixing parameter $\ensuremath{\lambda}$ of $(5.4\ifmmode\pm\else\textpm\fi{}0.3)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}21}\phantom{\rule{0.16em}{0ex}}\mathrm{c}{\mathrm{m}}^{3}$, and estimate a

5^{2}P_{1/2}

hyperfine-splitting density shift $\ensuremath{\zeta}$ in the

^{87}\mathrm{Rb}

-Xe system of $+0.71\ifmmode\pm\else\textpm\fi{}0.03\phantom{\rule{0.16em}{0ex}}\mathrm{GHz}/\mathrm{amagat}$. These results have implications for spectroscopic applications of the

^{87}\mathrm{Rb}

isoclinic point, which we consider as part of our conclusions.