Spontaneous spatial order in two-dimensional ferromagnetic spin-orbit coupled uniform spin-1 condensate solitons

Abstract

We demonstrate spontaneous spatial order in stripe and super-lattice solitons in a Rashba spin-orbit (SO) coupled spin-1 uniform quasi-two-dimensional (quasi-2D) ferromagnetic Bose-Einstein condensate. For weak SO coupling, the solitons are of the (−1, 0, +1) or (0, +1, +2) type with intrinsic vorticity, where the numbers in the parentheses denote angular momentum in spin components F z = +1, 0, −1, respectively. For intermediate SO coupling, three types of solitons are found: (a) circularly-asymmetric solitons, (b) circularly-symmetric (−1, 0, +1)and (c) (0, +1, +2)-type multi-ring solitons maintaining the above-mentioned vortices in respective components. For large SO coupling, quasidegenerate stripe and super-lattice solitons are found in addition to the circularly-asymmetric solitons. A super-lattice soliton forms a 2D square lattice structure in the total density as in a super-solid; in component densities it may have either (i) a 1D stripe pattern or (ii) a 2D square lattice structure.

Supersolid-like states in a two-dimensional trapped spin–orbit-coupled spin-1 condensate

“…For example, we will see that, in the antiferromagnetic phase, the superstripe state is the ground state, the multi-ring state is an excited state, viz figures 4(g)-(i) and 5, and the superlattice state is unstable. However, we established in [22] that in a uniform spin-1 SO-coupled BEC the superlattice state can appear in both ferromagnetic as well as antiferromagnetic phases. In the ferromagnetic phase, the circularly asymmetric state is the ground state, viz figure 2.…”

“…The search of such a spatially-periodic state in this system is an interesting topic of future investigation. A superlattice state was first predicted in a quasi-2D SO-coupled spin-1 uniform BEC [22].…”

“…It is remarkable that the superlattice states first found in a uniform system [22] survives under a strong harmonic trap. These states are dynamically robust and deserve further theoretical, and also experimental, investigation.…”

“…A superstripe state has an 1D periodic pattern in density, whereas a superlattice state has a 2D periodic square-lattice pattern in density. In a quasi-1D and a quasi-2D uniform SO-coupled spin-1 spinor BEC, superstripe [23] and superlattice [22] states have also been predicted.…”

“…In the ferromagnetic phase, the circularly-symmetric state is the ground state. These spatially-periodic states in an SO-coupled BEC, sharing some properties of a supersolid, have their own names [20], e.g., superstripe [21] and superlattice [22] states. A superstripe state has an 1D periodic pattern in density, whereas a superlattice state has a 2D periodic square-lattice pattern in density.…”