Spin-superstripe phase in helicoidal spin-orbit coupled Bose-Einstein condensates

The stripe phase in Bose-Einstein condensates (BECs) features both superfluidity and crystalline order, offering a promising platform to reveal exotic supersolidity of quantum matters. However, the stripe phase in BECs can exist only in a narrow parameter region favored by weak spin-spin interaction, making the stripes showing a low visibility and difficult to observe experimentally. Here, we propose an experimentally feasible model to break these limits and realize a prevalent spin-superstripe phase with crystal spin-density configuration favored by both weak and strong spin-spin interaction. We consider a highly tunable and spatially nonuniform helicoidal spin-orbit (SO) coupling, which locks the momentum of the atoms to two types of SO coupling and provides superior-advantages for generating the tunable superstripe phase. Without the Zeeman field, the system supports strong interplay of helicoidal SO coupling and atomic interactions. In this case, the spin-spin interaction dominates the phase diagram and hosts the spin-superstripe phase. The spin-superstripe phase is prevalent in the system. Particularly, the helicoidal SO coupling makes the two spin states orthogonal and the spin-spin interaction dominates the phase diagram, high-contrast (≈100%) spin-superstripe phase is realized. When the Zeeman field is present, both spin-superstripe phase and total density modulated superstripe phase are also predicted. The period and visibility of the superstripe phase can be well manipulated by the helicoidal gauge field. The helicoidal SO coupled BECs provide an ideal scheme to observe and study the exotic properties of the supersolids.