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

Abstract

We study supersolid-like states in a quasi-two-dimensional trapped Rashba and Dresselhaus spin–orbit (SO) coupled spin-1 condensate. For small strengths of SO coupling γ (γ ⪅ 0.75), in the ferromagnetic phase, circularly-symmetric (0, ±1, ±2)- and (∓1, 0, ±1)-type states are formed where the numbers in the parentheses denote the angular momentum of the vortex at the center of the components and where the upper (lower) sign correspond to Rashba (Dresselhaus) coupling; in the antiferromagnetic phase, only (∓1, 0, ±1)-type states are formed. For large strengths of SO coupling, supersolid-like superlattice and superstripe states are formed in the ferromagnetic phase. In the antiferromagnetic phase, for large strengths of SO coupling, supersolid-like superstripe and multi-ring states are formed. For an equal mixture of Rashba and Dresselhaus SO couplings, only a superstripe state is found. All these states are found to be dynamically stable and hence accessible in an experiment and will enhance the fundamental understanding of crystallization onto radially periodic states in solids.

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

“…For a small γ, the solitonic states in a uniform SO-coupled BEC have very large spatial extension. All these states are dynamically stable, as we verified by real-time simulation over a long period of time as in the case of an SO-coupled spin-1 quasi-2D BEC [23,24] (result not presented in this paper). Superlattice states were also found in an SO-coupled spin-1 spinor BEC [23].…”

“…Previous considerations were limited to a stripe state in a quasi-1D pseudo spin-1/2 SO-coupled spinor BEC [21,22]. In a quasi-2D trap, different types of spatially-ordered 2D lattice states seem likely in an SO-coupled pseudo spin-1/2 spinor BEC, specially after the confirmation of such states in an SO-coupled quasi-2D spin-1 spinor BEC [23,24]. We will consider both uniform (trapless) and trapped states in this study under the action of Rashba or Dresselhaus SO coupling, in addition to an equal mixture of Rashba and Dresselhaus couplings.…”

“…For strong SO coupling two types of degenerate solitonic states appear: a state with stripe pattern in density without any modulation in total density and a superlattice state with square-lattice pattern in both component and total densities. The present solitons with a 2D square-lattice structure in total density [21], viz figures 6(d)-(f ), sharing properties with, and more closely related to, a conventional supersolid, will be termed superlattice solitons in the following as suggested in references [21][22][23][24]. The multi-ring, viz figures 5(a)-(c), and stripe solitons, viz figures 6(a)-(c), only exhibit a spatially-periodic pattern in the component densities without any periodic pattern in the total density.…”

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

“…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.…”

“…[8]. Distinct periodic structures are obtained in different magnetic phases of SO-coupled spin-1 or spin-2 BECs [5,6,7]. Hence, the spatially-periodic structures are generally thought to be associated with these magnetic phases.…”