  We demonstrate control over the spin state of a semiconductor quantum dot
exciton using a polarized picosecond laser pulse slightly detuned from a
biexciton resonance. The control pulse follows an earlier pulse, which
generates an exciton and initializes its spin state as a coherent superposition
of its two non-degenerate eigenstates. The control pulse preferentially couples
one component of the exciton state to the biexciton state, thereby rotating the
exciton's spin direction. We detect the rotation by measuring the polarization
of the exciton spectral line as a function of the time-difference between the
two pulses. We show experimentally and theoretically how the angle of rotation
depends on the detuning of the second pulse from the biexciton resonance.
