Detection of Spin Coherence in Cold Atoms via Faraday Rotation Fluctuations.

We report non-invasive detection of spin coherence in a collection of Raman-driven cold atoms using dispersive Faraday rotation fluctuation measurements, which opens up new possibilities of probing spin correlations in quantum gases and other similar systems. We demonstrate five orders of magnitude enhancement of the measured signal strength than the traditional spin noise spectroscopy with thermal atoms in equilibrium. Our observations are in good agreement with the comprehensive theoretical modeling of the driven atoms at various temperatures. The extracted spin relaxation rate of cold rubidium atoms with atom number density $\sim$10$^9/$cm$^3$ is of the order of 2$\pi\times$0.5 kHz at 150 $\mu$K, two orders of magnitude less than $\sim$ 2$\pi\times$50 kHz of a thermal atomic vapor with atom number density $\sim$10$^{12}/$cm$^3$ at 373 K.