Probing supersolidity through excitations in a spin-orbit-coupled Bose-Einstein condensate

Spin-orbit-coupled Bose-Einstein condensates are a flexible experimental platform to engineer synthetic quantum many-body systems. In particular, they host the so-called stripe phase, an instance of a supersolid state of matter. The peculiar excitation spectrum of the stripe phase, a definite footprint of its supersolidity, has been difficult to measure experimentally. Here, we perform in situ imaging of the stripes and directly observe both superfluid and crystal excitations. We investigate superfluid hydrodynamics and reveal a stripe compression mode, thus demonstrating that the system possesses a compressible crystalline structure. Through the frequency softening of this mode, we locate the supersolid transition point. Our results establish spin-orbit-coupled supersolids as ideal systems to investigate supersolidity and its rich dynamics.