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arXiv:1512.06385 · Physical Review A

Coupled spin-vortex pair in dipolar spinor Bose-Einstein condensates

Tiantian Li, Su Yi, Yunbo Zhang

Published Dec 1, 2015• 9 citations
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Abstract

We investigate the ground-state and magnetic properties of a dipolar spin-1 Bose-Einstein condensate trapped in a symmetric double-well potential. In particular, we focus on the spin-vortex states by assuming that each potential well is highly pancake shaped. We show that the presence of the double-well potential gives rise to two different spin configurations for the spin-vortex pair states. We also study the response of the coupled spin-vortex pair to static transverse magnetic fields.

DOI
10.1103/physreva.92.063603

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We investigate the ground-state and magnetic properties of a dipolar spin-1 Bose-Einstein condensate trapped in a symmetric double-well potential. In particular, we focus on the spin-vortex states by assuming that each potential well is highly pancake shaped. We show that the presence of the double-well potential gives rise to two different spin configurations for the spin-vortex pair states. We also study the response of the coupled spin-vortex pair to static transverse magnetic fields.
The collisional and magnetic field quench dynamics of a coupled spin-vortex pair in dipolar spinor Bose-Einstein condensates in a double-well potential are numerically investigated in the mean-field theory. Upon a sudden release of the potential barrier the two layers of condensates collide with each other in the trap center with the chirality of the vortex pair exchanged after each collision, showing the typical signature of in-phase collision for the parallel spin-vortex phase, and out-of-phase collision for the antiparallel phase. When quenching the transverse magnetic field, the vortex center in the single-layered condensate starts to make a helical motion with oval-shaped trajectories and the displacement of the center position is found to exhibit a damped simple harmonic oscillation with an intrinsic frequency and damping rate. The oscillation mode of the spin-vortex pair may be tuned by the initial magnetic field and the height of the Gaussian barrier; e.g., the gyrotropic motions for a parallel spin-vortex pair are out of sync with each other in the two layers, while those for the antiparallel pair exhibit a double-helix structure with the vortex centers moving opposite to each other with the same amplitude.
We theoretically study the stationary-state vortex lattice configurations of rotating spin-orbit (SO)- and coherently-coupled spin-1 Bose-Einstein condensates (BECs) trapped in quasi-two-dimensional harmonic potentials. The combined effects of rotation, SO and coherent couplings are analyzed systematically from the single-particle perspective. Through the single-particle Hamiltonian, which is exactly solvable for one-dimensional coupling, we illustrate that a boson in these rotating SO- and coherently-coupled condensates are subjected to effective toroidal, symmetric double-well, or asymmetric double-well potentials under specific coupling and rotation strengths. 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 BEC approaches unity indicating a similarity in the response with ferromagnetic SO-coupled condensates.
We have calculated the F=1 ground state of a spinor Bose-Einstein condensate trapped harmonic potential with an applied Ioffe-Pitchard magnetic field. The vortex phase diagram is found in the plane spanned by perpendicular and longitudinal magnetic fields. The ferromagnetic condensate has two vortex phases which differ by winding number in the spinor components. The two vortices for the F(z)=-1 antiferromagnetic condensate are separated in space. Moreover, we considered an average local spin |<S-->>| to testify to what extent it is parallel to magnetic field (the nonadiabatic effects). We have shown that the effects are important at vortex cores.
Under many circumstances, the only important two-body interaction between atoms in ultracold dilute atomic vapors is the short-ranged isotropic s-wave collision. Recent studies have shown, however, that situations may arise where the dipolar interaction between atomic magnetic or electric dipole moments can play a significant role. The long-range anisotropic nature of the dipolar interaction greatly enriches the static and dynamic properties of ultracold atoms. In the case of dipolar spinor condensates, the interplay between the dipolar interaction and the spin exchange interaction may lead to nontrivial spin textures. Here we pay particular attention to the spin vortex state that is analogous to the magnetic vortex found in thin magnetic films.
Motivated by the recent experimental realization of a Bose-Einstein condensate (BEC) of europium atoms, we investigate the self-bound droplet state for a dipolar BEC with spin degrees of freedom. Under a sufficiently weak magnetic field, the droplet has a torus shape with circulating spin vectors, which is referred to as a magnetic vortex. The ground state transforms from a torus to a cigar shape through bistability with increasing magnetic field. Dynamical change of the magnetic field causes the torus to rotate due to the Einstein–de Haas effect. The magnetic vortices form a supersolid in a confined system. Published by the American Physical Society 2024
Extended Gross-Pitaevskii equations for the rotating F=2F=2F=2 condensate in a harmonic trap are solved both numerically and variationally using trial functions for each component of the wave function. Axially symmetric vortex solutions are analyzed and energies of polar and cyclic states are calculated. The equilibrium transitions between different phases with changing of the magnetization are studied. We show that at high magnetization the ground state of the system is determined by interaction in ``density'' channel, and at low magnetization spin interactions play a dominant role. Although there are five hyperfine states, all the particles are always condensed in one, two, or three states. Two interesting types of vortex structures are also discussed.