Effective potentials in a rotating spin-orbit-coupled spin-1 spinor condensate

Abstract

We theoretically study the stationary-state vortex lattice configurations of rotating spin-orbit- and coherently-coupled spin-1 Bose-Einstein condensates trapped in quasi-two-dimensional harmonic potentials. The combined effects of rotation, spin-orbit and coherent couplings are analyzed systematically from the single-particle perspective. Through the single-particle Hamiltonian, which is exactly solvable for one-dimensional coupling, under specific coupling and rotation strengths, we illustrate that a boson in these rotating spin-orbit- and coherently-coupled condensates are subjected to effective toroidal, symmetric double-well, or asymmetric double-well potentials. In the presence of mean-field interactions, using the coupled Gross-Pitaevskii formalism at moderate to high rotation frequencies, the analytically obtained effective potential minima and the numerically obtained coarse-grained density maxima position are in excellent agreement. On rapid rotation, we further find that the spin-expectation per particle of an antiferromagnetic spin-1 Bose-Einstein condensate approaches unity indicating a similarity in the response with ferromagnetic spin-orbit-coupled condensates.

Vortex Formation in Spin-Orbit Coupled Spin-1 Bose Condensates with Magnetic Field

“…The characteristic of a vortex necklace is that vortices link up with each other in a ring. Moreover, we note that this configuration is also observed in antiferromagnetic SOC spin-1 BECs [33] and rotating binary BECs [34]. When the magnetic field strength is increased, the difference occurs in density profiles.…”

FORTRESS: FORTRAN programs to solve coupled Gross-Pitaevskii equations for spin-orbit coupled spin-f Bose-Einstein condensate with spin f = 1 or 2

“…The densities profiles obtained by the variational method for non-interacting systems are in excellent agreement with the numerical results (not shown here) and so as the corresponding energies. The rotating spin-2 BEC in the presence of ansitropic SO-coupling coupling is exactly solvable [16]. The ansatz presented here is an exact analytic solution to a one-dimensional SO coupling Hamiltonian under rotation.…”

“…The effective potential incurred by the boson can be evaluated by calculating the vector and scalar potentials as discussed in ref. [6,16]. With the definition given in [6], the effective potential for rotating SO-coupled spin-2 system calculated in Appendix.…”

“…The interplay of isotropic SO coupling and rotation resulting in the emergence of half-skyrmion excitations in rotating and rapidly quenched spin-1 BECs using stochastic projected Gross-Pitaevskii equations have been studied in [11][12][13][14][15]. Rotating spin-1 BEC also supports many interesting solutions in the presence of an isotropic [13,16] as well as anisotropic, [11,12,16] SO coupling. Moreover, numerical studies on rotating SO-coupled BEC has been done in toroidal traps [14], with Weyl SO coupling [15], and SU(3) coupling [17].…”