Stripe phase in a spin-orbit coupled Bose-Einstein condensate with attractive interstate interactions*

Supersolids are an exotic phase of matter combining the contrasting characteristics of rigidity in crystalline solids and frictionless flow in superfluids. In spin-orbit coupled Bose-Einstein condensates, the double minimum structure of the dispersion at small coupling enables the existence of a supersolid-like stripe phase. The stability of the stripe phase is limited by the miscibility of the components of the spin-orbit coupled system. We present a scheme to exploit highly tunable interactions in potassium-39 to enter a highly stable stripe phase with attractive interstate interactions. The characteristic density modulation can be imaged directly using matterwave optics. Furthermore, we investigate the effect of highly imbalanced intrastate interactions on the phase diagram and the excitation spectrum of the system.