Detection of spin coherence in cold atoms via Faraday rotation fluctuations

We report noninvasive detection of spin coherence in a collection Raman-driven cold atoms using dispersive Faraday rotation fluctuation measurements, which opens possibilities probing correlations quantum gases and other similar systems. demonstrate five orders magnitude enhancement the measured signal strength as compared to traditional noise spectroscopy with thermal equilibrium. Our observations are good agreement comprehensive theoretical modeling driven at various temperatures. The extracted relaxation rate rubidium atom number density $\ensuremath{\sim}10{\phantom{\rule{0.16em}{0ex}}}^{9}/{\mathrm{cm}}^{3}$ is order $3\phantom{\rule{0.16em}{0ex}}\ifmmode\times\else\texttimes\fi{}\phantom{\rule{0.16em}{0ex}}10{\phantom{\rule{0.16em}{0ex}}}^{3}\phantom{\rule{4pt}{0ex}}{\mathrm{s}}^{\ensuremath{-}1}$ 150 $\ensuremath{\mu}\mathrm{K}$, two less than $3\phantom{\rule{0.16em}{0ex}}\ifmmode\times\else\texttimes\fi{}\phantom{\rule{0.16em}{0ex}}10{\phantom{\rule{0.16em}{0ex}}}^{5}\phantom{\rule{4pt}{0ex}}{\mathrm{s}}^{\ensuremath{-}1}$ that atomic vapor $\ensuremath{\sim}10{\phantom{\rule{0.16em}{0ex}}}^{12}/{\mathrm{cm}}^{3}$ 373 K.