We investigate ultrafast refractive index dynamics in a multiquantum-well InGaAsP-InGaAs semiconductor optical amplifier that is operated in the gain regime by using a pump-and-probe approach. The pump-and-probe pulses are cross-linearly polarized. We observe a phase shift of 200 degrees if the amplifier is pumped with 120 mA of current but find that the phase shift vanishes if the injection current is increased to 160 mA. Our results indicate a contribution of two-photon absorption to the nonlinear phase shift that opposes the phase shift introduced by the gain. Finally, we observe that the phase shift comes up and disappears within a picosecond.