Spatial order in a two-dimensional spin–orbit-coupled spin-1/2 condensate: superlattice, multi-ring and stripe formation

Abstract

We demonstrate the formation of stable spatially-ordered states in a uniform and also trapped quasi-two-dimensional (quasi-2D) Rashba or Dresselhaus spin-orbit (SO) coupled pseudo spin-1/2 Bose-Einstein condensate using the mean-field Gross-Pitaevskii equation. For weak SO coupling, one can have a circularly-symmetric (0, +1)or (0, −1)-type multi-ring state with intrinsic vorticity, for Rashba or Dresselhaus SO coupling, respectively, where the numbers in the parentheses denote the net angular momentum projection in the two components, in addition to a circularly-asymmetric degenerate state with zero net angular momentum projection. For intermediate SO couplings, in addition to the above two types, one can also have states with stripe pattern in component densities with no periodic modulation in total density. The stripe state continues to exist for large SO coupling. In addition, a new spatially-periodic state appears in the uniform system: a superlattice state, possessing some properties of a supersolid, with a square-lattice pattern in component densities and also in total density. In a trapped system the superlattice state is slightly different with multi-ring pattern in component density and a square-lattice pattern in total density. For an equal mixture of Rashba and Dresselhaus SO couplings, in both uniform and trapped systems, only stripe states are found for all strengths of SO couplings. In a uniform system all these states are quasi-2D solitonic states.

Stable stripe and vortex solitons in two-dimensional spin-orbit coupled Bose–Einstein condensates

“…We also systematically study their existence and stability regions. Compared to previous solitons in attractive interaction systems [26][27][28], the solitons we found have better stability. In addition, we find that the stripe bright solitons transform into a vortex array under a rotating frame, and we also find the stable range.…”

“…This novel system has incorporated various elements, such as artificial magnetic fields, optical lattices [13][14][15][16][17], and dipole interactions [18][19][20], introducing a plethora of physical phenomena in BEC. Examples include the emergence of plane-wave (PW) phases [21,22], stripe phases [18,[23][24][25][26][27][28], vortices [29][30][31][32], lattice phases [27,33], topological superfluid phases [34,35] and supersolid phases [36,37]. Researchers have conducted interesting dynamic studies on the abundant solitons in these BECs [38][39][40].…”

Supersolid-like solitons in two-dimensional nonmagnetic spin-orbit coupled spin-1 and spin-2 condensates

“…The presence of the SO-coupling terms with first derivatives, mixing the components, are the necessary ingredients for the emergence of different types of spatially-periodic solitons. In conclu-sion, it is strongly suggestive that the spatially-periodic supersolid-like states found in SO-coupled pseudo spin-1/2 [1,3,4], spin-1 [5], and spin-2 [7] spinor BECs are not a consequence of spinor interactions but are a consequence of multicomponent nature of these states in presence of SO coupling.…”

“…A quasi-one-dimensional (quasi-1D) and quasitwo-dimensional (quasi-2D) spin-orbit-coupled (SOcoupled) spin-1/2, spin-1, or spin-2 trapped or trapless Bose-Einstein condensates (BECs) can produce spatially-periodic structures in component or total density [1,2,3,4,5,6,7]. A spin-1 or spin-2 spinor BEC may have distinct magnetic phases, like, ferromagnetic, anti-ferromagnetic, cyclic, etc.…”