Lattice Dynamics and Galilean Symmetry in a Zeeman Lattice

Spin-orbit coupling and optical lattices are two powerful yet distinct cornerstones of modern quantum gas experiments. While optical lattices break translation symmetry, spin-orbit coupling in the plane-wave regime does not directly lead to a periodic lattice structure and breaks Galilean invariance. Here we demonstrate that starting with a spin-orbit coupled BEC and adding an additional radio-frequency field can lead to an emergent lattice structure even though neither of the two ingredients are periodic in space. We discuss the band structure of such a Zeeman lattice and show that Galilean symmetry can be restored. In our experiments, we demonstrate that Bloch oscillations can be driven in the Zeman lattice and also discuss the application of other experimental techniques such as lattice shaking for band spectroscopy. This line of research opens the door to an exploration of spin-selectivity and flat-band properties exploiting Zeeman lattices.