%0 Journal Article %T Real-time vector field tracking with a cold-atom magnetometer %A Naeimeh Behbood %A Ferran Martin Ciurana %A Giorgio Colangelo %A Mario Napolitano %A Morgan W. Mitchell %A Robert J. Sewell %J Physics %D 2013 %I arXiv %R 10.1063/1.4803684 %X We demonstrate a fast three-axis optical magnetometer using cold, optically-trapped $^{87}$Rb gas as a sensor. By near-resonant Faraday rotation we record the free-induction decay following optical pumping along two orthogonal axes to obtain the three field components and one gradient component. A single measurement achieves shot-noise limited sub-nT sensitivity in 1 ms, with transverse spatial resolution of $\sim$ 20 $\mu$m. We make a detailed analysis of the shot-noise-limited sensitivity. %U http://arxiv.org/abs/1303.2312v2