  Recent time-resolved differential transmission and Faraday rotation
measurements of long-lived electron spin coherence in quantum wells displayed
intriguing parametric dependencies. For their understanding we formulate a
microscopic theory of the optical response of a gas of optically incoherent
excitons whose constituent electrons retain spin coherence, under a weak
magnetic field applied in the quantum well's plane. We define a spin beat
susceptibility and evaluate it in linear order of the exciton density. Our
results explain the many-body physics underlying the basic features observed in
the experimental measurements.
