Optical Precursor Polarization Rotation in a Magnetic Field

We apply a magnetic field to an ultracold gas and by applying light turned on faster than the atomic dipole response time, we observe the time development of polarization rotation through the Faraday effect. The details of the time development depend on the atomic dipole lifetime, the optical thickness of the gas, the spin polarization of the gas, and the strength of the applied magnetic field. Experimental and theory results are presented.