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arXiv:cond-mat/0212539 · Physical Review Letters

Coreless Vortex Formation in a Spinor Bose-Einstein Condensate

A. E. Leanhardt, Yong-il Shin, D. Kielpinski, David E. Pritchard, Wolfgang Ketterle

Published Apr 9, 2003• 296 citations
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Abstract

Coreless vortices were phase imprinted in a spinor Bose-Einstein condensate. The three-component order parameter of F=1 sodium condensates held in a Ioffe-Pritchard magnetic trap was manipulated by adiabatically reducing the magnetic bias field along the trap axis to zero. This distributed the condensate population across its three spin states and created a spin texture. Each spin state acquired a different phase winding which caused the spin components to separate radially.

DOI
10.1103/physrevlett.90.140403

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Coreless vortices were phase imprinted in a spinor Bose-Einstein condensate. The three-component order parameter of F=1 sodium condensates held in a Ioffe-Pritchard magnetic trap was manipulated by adiabatically reducing the magnetic bias field along the trap axis to zero. This distributed the condensate population across its three spin states and created a spin texture. Each spin state acquired a different phase winding which caused the spin components to separate radially.
Vortices were imprinted in a Bose-Einstein condensate using topological phases. Sodium condensates held in a Ioffe-Pritchard magnetic trap were transformed from a nonrotating state to one with quantized circulation by adiabatically inverting the magnetic bias field along the trap axis. Using surface wave spectroscopy, the axial angular momentum per particle of the vortex states was found to be consistent with 2 variant Planck's over 2pi or 4 variant Planck's over 2pi, depending on the hyperfine state of the condensate.
We investigate an experimental method for imprinting Skyrmion spin textures in a spinor Bose–Einstein condensate by rapidly moving the zero-field center of a three-dimensional (3D) quadrupole magnetic field through the condensate. Various excitations such as 2D Skyrmions and coreless vortices were created in spin-1 sodium condensates, initially prepared in a uniform polar or ferromagnetic phase. The spin textures were characterized with the spatial distribution of the spin tilt angle, which is found to be in good quantitative agreement with the local description of single spins under the field rotation. We demonstrate the creation of a highly charged Skyrmion in a trapped condensate by applying the imprinting process multiple times.
We theoretically investigate vortex-lattice phases of rotating spinor Bose-Einstein condensates (BEC's) with a ferromagnetic spin interaction by numerically solving the Gross-Pitaevskii equation. The spinor BEC under slow rotation can sustain a rich variety of exotic vortices due to the multicomponent order parameters, such as Mermin-Ho and Anderson-Toulouse coreless vortices (the two-dimensional Skyrmion and meron) and nonaxisymmetric vortices with shifting vortex cores. Here, we present the spin texture of various vortex-lattice states at higher rotation rates and in the presence of an external magnetic field. In addition, the vortex phase diagram is constructed in the plane of the total magnetization MMM and the external rotation frequency $\ensuremath{\Omega}$ by comparing the free energies of possible vortices. It is shown that the vortex phase diagrams in the $M\text{\ensuremath{-}}\ensuremath{\Omega}$ plane may be divided into two categories: (i) the coreless vortex lattice formed by the several types of Mermin-Ho vortices and (ii) the vortex lattice filling in the cores with the pure polar (antiferromagnetic) state. In particular, it is found that the type-(ii) state forms composite lattices of coreless and polar-core vortices. The difference between type (i) and type (ii) results from the existence of the singularity of the spin textures, which may be experimentally confirmed by the spin imaging within polarized light recently proposed by Carusotto and Mueller. We also discuss the stability of triangular and square lattice states for rapidly rotating condensates.
We study the energetic and dynamic stability of coreless vortices in nonrotated spin-1 Bose-Einstein condensates, trapped with a three-dimensional optical potential and a Ioffe-Pritchard field. The stability of stationary vortex states is investigated by solving the corresponding Bogoliubov equations. We show that the quasiparticle excitations corresponding to axisymmetric stationary states can be taken to be eigenstates of angular momentum in the axial direction. Our results show that coreless vortex states can occur as local or global minima of the condensate energy or become energetically or dynamically unstable depending on the parameters of the Ioffe-Pritchard field. The experimentally most relevant coreless vortex state containing a doubly quantized vortex in one of the hyperfine spin components turned out to have very nontrivial stability regions, and especially a quasiperiodic dynamic instability region which corresponds to splitting of the doubly quantized vortex.
The low-lying excitations of coreless vortex states in F=1F=1F=1 spinor Bose-Einstein condensates (BECs) are theoretically investigated using the Gross-Pitaevskii and Bogoliubov--de Gennes equations. The spectra of the elementary excitations are calculated for different spin-spin interaction parameters and ratios of the number of particles in each sublevel. There exist dynamical instabilities of the vortex state which are suppressed by ferromagnetic interactions, and, conversely, enhanced by antiferromagnetic interactions. In both of the spin-spin interaction regimes, we find vortex-splitting instabilities in analogy with scalar BECs. In addition, a phase-separating instability is found in the antiferromagnetic regime.
The formation of vortices by topological phase engineering has been realized experimentally to create the first two- and four-quantum vortices in dilute atomic Bose-Einstein condensates. We consider a similar system, but in addition to the Ioffe-Pritchard magnetic trap we employ an additional hexapole field. By controlling cyclically the strengths of these magnetic fields, we show that a fixed amount of vorticity can be added to the condensate in each cycle. In an adiabatic operation of this vortex pump, the appearance of vortices into the condensate is interpreted as the accumulation of a local Berry phase. Our design can be used as an experimentally realizable vortex source for possible vortex-based applications of dilute Bose-Einstein condensates.