  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.
