By exploring the spin-orbit-coupled rotating pseudo-spin-1/2 Bose-Einstein condensates with the stochastic projected Gross-Pitaevskii equations, we prove the existence of the circular-hyperbolic skyrmion, which possesses two extreme values of ${S}_{z}$ . The nonequal intraspecies interactions and interspecies interactions cause the two components to be wholly disproportionate when the system reaches the equilibrium state. The circular-hyperbolic skyrmion results from the vortex-dipole structure. For the miscible condensates, the increase of spin-orbit coupling enhances the creation of the circular-hyperbolic skyrmion, and makes them link one after another locally. In particular, the circular-hyperbolic skyrmion even can form a chain when the spin-orbit coupling is only in one direction. For the immiscible condensates, the hyperbolic skyrmion occurs at the center, while the circular-hyperbolic skyrmion occurs at the outskirts of the condensates. The increase of the spin-orbit coupling restricts the creation of the hyperbolic skyrmion and enhances the creation of the circular-hyperbolic skyrmion.By exploring the spin-orbit-coupled rotating pseudo-spin-1/2 Bose-Einstein condensates with the stochastic projected Gross-Pitaevskii equations, we prove the existence of the circular-hyperbolic skyrmion, which possesses two extreme values of ${S}_{z}$. The nonequal intraspecies interactions and interspecies interactions cause the two components to be wholly disproportionate when the system reaches the equilibrium state. The circular-hyperbolic skyrmion results from the vortex-dipole structure. For the miscible condensates, the increase of spin-orbit coupling enhances the creation of the circular-hyperbolic skyrmion, and makes them link one after another locally. In particular, the circular-hyperbolic skyrmion even can form a chain when the spin-orbit coupling is only in one direction. For the immiscible condensates, the hyperbolic skyrmion occurs at the center, while the circular-hyperbolic skyrmion occurs at the outskirts of the condensates. The increase of the spin-orbit coupling restricts the creation of the hyperbolic skyrmion and enhances the creation of the circular-hyperbolic skyrmion.

Physical Review ANov 19, 201259 citations

Spin–orbit-coupled Bose–Einstein condensates

Y.-J. Lin, Karina Jiménez-García, Ian B. Spielman

arXiv:1103.3522NatureMar 1, 20112,101 citations

Spin-orbit coupled Bose-Einstein condensates

Brandon Anderson, Tudor D. Stanescu, Victor M. Galitski

Bulletin of the American Physical SocietyMar 17, 20090 citations

Phase separation in a spin-orbit-coupled Bose-Einstein condensate

Sandeep Gautam, Sadhan K. Adhikari

We study a spin-orbit (SO)-coupled hyperfine spin-1 Bose-Einstein condensate (BEC) in a quasi-one-dimensional trap. For an SO-coupled BEC in a one-dimensional box, we show that in the absence of the Rabi term, any nonzero value of SO coupling will result in a phase separation among the components for a ferromagnetic BEC, like $^{87}\mathrm{Rb}$ . On the other hand, SO coupling favors miscibility in a polar BEC, like $^{23}\mathrm{Na}$ . In the presence of a harmonic trap, which favors miscibility, a ferromagnetic BEC phase separates, provided that the SO-coupling strength and number of atoms are greater than some critical value. The Rabi term favors miscibility irrespective of the nature of the spin interaction: ferromagnetic or polar.We study a spin-orbit (SO)-coupled hyperfine spin-1 Bose-Einstein condensate (BEC) in a quasi-one-dimensional trap. For an SO-coupled BEC in a one-dimensional box, we show that in the absence of the Rabi term, any nonzero value of SO coupling will result in a phase separation among the components for a ferromagnetic BEC, like $^{87}\mathrm{Rb}$. On the other hand, SO coupling favors miscibility in a polar BEC, like $^{23}\mathrm{Na}$. In the presence of a harmonic trap, which favors miscibility, a ferromagnetic BEC phase separates, provided that the SO-coupling strength and number of atoms are greater than some critical value. The Rabi term favors miscibility irrespective of the nature of the spin interaction: ferromagnetic or polar.

arXiv:1409.6211Physical Review AOct 20, 201454 citations

{S}_{z}

. The nonequal intraspecies interactions and interspecies interactions cause the two components to be wholly disproportionate when the system reaches the equilibrium state. The circular-hyperbolic skyrmion results from the vortex-dipole structure. For the miscible condensates, the increase of spin-orbit coupling enhances the creation of the circular-hyperbolic skyrmion, and makes them link one after another locally. In particular, the circular-hyperbolic skyrmion even can form a chain when the spin-orbit coupling is only in one direction. For the immiscible condensates, the hyperbolic skyrmion occurs at the center, while the circular-hyperbolic skyrmion occurs at the outskirts of the condensates. The increase of the spin-orbit coupling restricts the creation of the hyperbolic skyrmion and enhances the creation of the circular-hyperbolic skyrmion.

^{87}\mathrm{Rb}

. On the other hand, SO coupling favors miscibility in a polar BEC, like

^{23}\mathrm{Na}

. In the presence of a harmonic trap, which favors miscibility, a ferromagnetic BEC phase separates, provided that the SO-coupling strength and number of atoms are greater than some critical value. The Rabi term favors miscibility irrespective of the nature of the spin interaction: ferromagnetic or polar.