Tunable spin-orbit coupling and magnetic superstripe phase in a Bose-Einstein condensate

Superstripe phases in Bose-Einstein condensates (BECs), possessing both crystalline structure and superfluidity, open a new avenue for exploring exotic quantum matters-supersolids. However, conclusive detection and further exploration of a superstripe is still challenging in experiments because of its short period, low visibility, fragility against magnetic-field fluctuation, or short lifetime. Here we propose a scheme in a spin-orbit coupled BEC which overcomes these obstacles and generates a robust magnetic superstripe phase, with only spin-density (no total density) modulation due to the magnetic translational symmetry, ready for direct real-space observation. In the scheme, two hyperfine spin states are individually Raman coupled with a largely detuned third state, which induce a momentum-space separation between two lower band dispersions, yielding an effective spin-1/2 system with tunable spin-orbit coupling and Zeeman fields. Without effective Zeeman fields, spin-dependent interaction dominates, yielding a magnetic superstripe phase with a long tunable period and high visibility. Our scheme provides a platform for observing and exploring exotic properties of superstripe phases as well as novel physics with tunable spin-orbit coupling.