Spin-orbit-coupled Bose-Einstein condensates in a one-dimensional optical lattice.

We investigate a spin-orbit-coupled Bose-Einstein condensate loaded into a translating optical lattice. We experimentally demonstrate the lack of Galilean invariance in the spin-orbit-coupled system, which leads to anisotropic behavior of the condensate depending on the direction of translation of the lattice. The anisotropy is theoretically understood by an effective dispersion relation. We experimentally confirm this theoretical picture by probing the dynamical instability of the system.