  An anomalous light shift in the precession of a ground-state Zeeman coherence
is observed: the Larmor frequency increases with the strength of a drive that
is blue (red) detuned from a transition out of the lower (upper) energy level.
Our measurements are made on Rb 85 atoms traversing an optical cavity
containing a few photons; shifts as large as 1% per photon are recorded. The
anomalous shift arises from an accumulation of phase driven by quantum jumps.
It is stochastic and accompanied by broadening.
