Stabilizing period-doubled density waves by spin-orbit coupling in Bose-Einstein condensates in optical lattices

In atomic Bose-Einstein condensates in optical lattices, mean-field energy can support the existence of period-doubled density waves, which are similar to Bloch waves but have the double periodicity of the underlying lattice potentials. However, they are dynamically unstable. Here, we propose to use the spin-orbit coupling to stabilize the period-doubled density waves. The stabilization mechanism is revealed to relate to interaction-induced spontaneous symmetry breaking of the spin-flip parity symmetry.