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arXiv:1601.01541 · Physical Review A

Fractional-charge vortex in a spinor Bose-Einstein condensate

Sandeep Gautam, Sadhan K. Adhikari

Published Jan 29, 2016• 11 citations
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Abstract

We classify all possible fractional charge vortices of charge less than unity in spin-1 and spin-2 polar and cyclic Bose-Einstein condensates (BECs) with zero magnetization. Statics and dynamics of these vortices in quasi-two-dimensional spinor BECs are studied employing an accurate numerical solution and a Lagrange variational approximation. The results for density and collective-mode oscillation are illustrated using the fractional-charge BEC vortex of $^{23}\mathrm{Na}$ and $^{87}\mathrm{Rb}$ atoms with realistic interaction and trapping potential parameters.

DOI
10.1103/physreva.93.013630

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We classify all possible fractional charge vortices of charge less than unity in spin-1 and spin-2 polar and cyclic Bose-Einstein condensates (BECs) with zero magnetization. Statics and dynamics of these vortices in quasi-two-dimensional spinor BECs are studied employing an accurate numerical solution and a Lagrange variational approximation. The results for density and collective-mode oscillation are illustrated using the fractional-charge BEC vortex of 23Na^{23}\mathrm{Na}23Na and 87Rb^{87}\mathrm{Rb}87Rb atoms with realistic interaction and trapping potential parameters.
We theoretically and numerically investigate the generation of fractional-charge vortex dipoles in spinor condensates with non-zero magnetization. We find that in the antiferromagnetic phase of spin-1 and spin-2 and the cyclic phase of spin-2 condensate with non-zero magnetization coupling of the density (phonon) and a spin-excitation mode results in two critical speeds for vortex-antivortex pair creation in the condensate. As a result, a Gaussian obstacle potential moving across the antiferromagnetic spin-1 or spin-2 and cyclic spin-2 spinor condensates with non-zero magnetization can lead to the creation of fractional-charge vortex dipoles. On the other hand, for zero magnetization, the two modes get decoupled, which is illustrated by a single critical speed for vortex-antivortex pair creation in the condensate due to the phonon excitation mode.
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.
Quantum vortices in the multi-component Bose-Einstein condensation (BEC) are investigated theoretically. It is found that three kinds of the vortex configurations are possible and their physical properties are discussed in details, including the density distribution and the spin texture. By using the Bogoliubov theory extended to the three component BEC, the collective modes for these vortices are evaluated. The local vortex stability for these vortices are examined in light of the existence of the negative eigenvalue, yielding a narrow magnetization window for the local intrinsic stable region where the multi-components work together to stabilize a vortex in a self-organized way.
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.
We have studied collective modes of quasi-2D Bose-Einstein condensates with multiply-charged vortices using a variational approach. Two of the four collective modes considered exhibit coupling between the vortex dynamics and the large-scale motion of the cloud. The vortex presence causes a shift in all frequencies of collective modes even for the ones that do not couple dynamically with the vortex-core. The coupling between vortex and large-scale collective excitations can induce the multi-charged vortex to decay into singly-charged vortices with the quadrupole mode being one possible channel for such a decay. Therefore a thorough study was done about the possibility to prevent the vortex decay by applying a Gaussian potential with its width proportional to the vortex-core radius and varying its height. In such way, we created a stability diagram of height versus interaction strength which has stable regions due the static Gaussian potential. Furthermore, by using a sinusoidal time-modulation around the average height of the Gaussian potential, we have obtained a diagram for the parametric resonance which can prevent the vortex decay in regions where static potential can not.
We propose methods to create fractional vortices in the cyclic state of an F=2F=2F=2 spinor Bose-Einstein condensate by manipulating its internal spin structure using pulsed microwave and laser fields. The stability of such vortices is studied as a function of the rotation frequency of the confining harmonic trap both in pancake- and cigar-shaped condensates. We find a range of parameters for which the so-called 13\frac{1}{3}31​ vortex state is energetically favorable. Such fractional vortices could be created in condensates of 87Rb^{87}\text{R}\text{b}87Rb atoms using current experimental techniques facilitating probing of topological defects with non-Abelian statistics.