Tunable spin-orbit coupling and long-period magnetic superstripe phase in Bose-Einstein condensates

Superstripe phases in Bose-Einstein condensates, possessing both crystalline structure and superfluidity, opens a new avenue for exploring exotic quantum matters---supersolids. However, complete detection and exploration of superstripes are still challenging in experiments because of the short period, low visibility and external factors such as magnetic field fluctuations or heating issues. Here we propose a scheme in a spin-orbit coupled BEC which overcomes these obstacles and generates a robust magnetic superstripe phase [i.e., only spin (no total) density modulation] with a long period and high visibility, 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.