When a gas of ultracold atoms is suddenly illuminated by light that is nearly resonant with an atomic transition, the atoms cannot respond instantaneously. This non-instantaneous response means the gas is initially more transparent to the applied light than in steady-state. The timescale associated with the development of light absorption is set by the atomic excited state lifetime. Similarly, the index of refraction in the gas also requires time to reach a steady-state value, but the development of the associated phase response is expected to be slower than absorption effects. Faraday rotation is one manifestation of differing indices of refraction for orthogonal circular light polarization components. We have performed experiments measuring the time-dependent development of polarization rotation in an ultracold gas subjected to a magnetic field. Our measurements match theoretical predictions based on solving optical Bloch equations. We are able to identify how parameters such as steady-state optical thickness and applied magnetic field strength influence the development of Faraday rotation.
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