  We measure the collective excitation spectrum of a spin-orbit coupled
Bose-Einstein condensate using Bragg spectroscopy. The spin-orbit coupling is
generated by Raman dressing of atomic hyperfine states. When the Raman detuning
is reduced, mode softening at a finite momentum is revealed, which provides
insight towards a supersolid-like phase transition. We find that for the
parameters of our system, this softening stops at a finite excitation gap and
is symmetric under a sign change of the Raman detuning. Finally, using a moving
barrier that is swept through the BEC, we also show the effect of the
collective excitation on the fluid dynamics.
