  We demonstrate optical control of the geometric phase acquired by one of the
spin states of an electron confined in a charge-tunable InAs quantum dot via
cyclic 2pi excitations of an optical transition in the dot. In the presence of
a constant in-plane magnetic field, these optically induced geometric phases
result in the effective rotation of the spin about the magnetic field axis and
manifest as phase shifts in the spin quantum beat signal generated by two
time-delayed circularly polarized optical pulses. The geometric phases
generated in this manner more generally perform the role of a spin phase gate,
proving potentially useful for quantum information applications.
