Experimental investigation of spin noise spectroscopy of rubidium atomic ensemble
Authors: Yang Yu-Lin , Bai Le-Le , Zhang Lu-Lu , He Jun , Wen Xin , Wang Jun-Min ,   State Key Laboratory of Quantum Optics and Quantum Optics Devices, Institute of Opto-Electronics, Shanxi University, Taiyuan 030006, China,   Collaborative Innovation Center of Extreme Optics of Education of Ministry and Shanxi Province, Shanxi University, Taiyuan 030006, China,   Department of Physics, Tsinghua University, Beijing 100084, China
Published: December 2020

Spin noise spectroscopy is a very sensitive undisturbed spectroscopic technique for measuring atomic spin fluctuations by using a far-detuned probe laser beam. In this paper, we describe an experimental setup for measuring the spin noise spectroscopy. The spin noise spectra of Rubidium atomic vapor cell filled with 10 Torr of Neon gas and 20 Torr of Helium gas as buffer gas are investigated in a magnetically shielded environment. The dependence of the spin noise power spectral density, separately, on the probe beam’s intensity (<i>I </i>), the probe beam’s frequency detuning (<i>Δ</i>) and Rubidium atomic number density (<i>n</i>) are measured. The integrated power of Rubidium atomic spin noise spectra is scaled as<inline-formula><tex-math id="M1">\begin{document}$ {I^2}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="23-20201103_M1.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="23-20201103_M1.png"/></alternatives></inline-formula>. Owing to homogeneous broadening, the full width at half maximum of transmission spectrum of the same cell is broadened to <inline-formula><tex-math id="M2">\begin{document}$\Delta {\nu _t} = {\rm{6}}.{\rm{9}}\;{\rm{GH}}{\rm{z}}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="23-20201103_M2.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="23-20201103_M2.png"/></alternatives></inline-formula>. Center frequency of transmission spectrum is set to be <inline-formula><tex-math id="M3">\begin{document}$\varDelta = {\rm{0}}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="23-20201103_M3.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="23-20201103_M3.png"/></alternatives></inline-formula>. The probe beam’s frequency detuning is larger than the half width at half maximum of the transmission spectrum <inline-formula><tex-math id="M4">\begin{document}$\left| \varDelta \right| > {{\Delta {\nu _t}}}/{{\rm{2}}}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="23-20201103_M4.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="23-20201103_M4.png"/></alternatives></inline-formula>, so the integrated power of Rubidium atomic spin noise spectra is scaled as <inline-formula><tex-math id="M5">\begin{document}$\varDelta^{-1}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="23-20201103_M5.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="23-20201103_M5.png"/></alternatives></inline-formula>. And there is a dip for <inline-formula><tex-math id="M6">\begin{document}$|\varDelta| < {{\Delta {\nu _t}}}/{{\rm{2}}}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="23-20201103_M6.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="23-20201103_M6.png"/></alternatives></inline-formula> as a result of collisions between the buffer gas and Rubidium atoms. The integrated power of Rubidium atomic spin noise spectra is scaled as <inline-formula><tex-math id="M7">\begin{document}$ \sqrt n $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="23-20201103_M7.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="23-20201103_M7.png"/></alternatives></inline-formula>. The Rubidium atomic spin's transverse relaxation time becomes shorter while the temperature increases. Only at the condition of non-perturbative probe, including far-off-resonant laser, weak laser intensity and uniform transverse magnetic field, the measured full width at half maximum will be close to the intrinsic linewidth of spin noise spectrum. In this way, we can obtain the Rubidium atomic spin's transverse relaxation time. This work can be applied to the field of physical constants precision measurement, like Lande <i>g</i> factor and isotopic abundance ratio. In addition, it provides an important reference for developing the high signal-to-noise ratio and compact spin noise spectrometer.