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arXiv:0812.1439 · Physical Review A

Vortex-splitting and phase-separating instabilities of coreless vortices in F=1 spinor Bose-Einstein condensates

Masahiro O. Takahashi, Ville Pietilä, Mikko Möttönen, Takeshi Mizushima, K. Machida

Published Feb 17, 2009• 23 citations
arXivHTMLPDF

Abstract

The low-lying excitations of coreless vortex states in $F=1$ 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.

DOI
10.1103/physreva.79.023618

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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.
We investigate the dynamical stability of the coreless vortex state in F = 1 spinor Bose-Einstein condensates, by numerically solving the Gross-Pitaevskii and Bogoliubov-de Gennes equations. We cover both ferromagnetic and antiferromagnetic interaction regions and the magnetizations per particle M from -1 to +1. It is found that the coreless vortex state is dynamically stable in large parameter regions of magnetization M . At M = -1, the hyperfine spin component with vortex winding 2 is dominant, and hence the coreless vortex can spontaneously decay even without dissipation. However, it is found that in the ferromagnetic case, the spin-spin interactions tend to stabilize the state. In the antiferromagnetic case, we find new dynamical instability modes which are not obtained in the ferromagnetic interaction region. In the antiferromagnetic interaction region, the spin-spin interactions can stimulate dynamical instabilities, while there still remains a large stability area in the parameter M . This is because of certain restrictions in inducing dynamical instability.
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.
Summary form only given. I present results of the detailed asymptotic and numerical results on stability of unit and higher order vortices in coupled Gross-Pitaevskii equations, which model the experimental work. Low lying eigenfrequencies, including ones generating instability of the unit vortex placed in one component of a binary mixture of BEC, have been calculated applying perturbative theory in the limit of the weak interparticle interaction. Results of the perturbative theory have been verified and significantly extended using numerical analysis of the linearised equations for excitations and direct numerical simulation of the coupled Gross-Pitaevskii equations. Two main instability mechanisms have been identified and their dependencies on the relative number of the particles in the condensates and on the strength of the inter-species interaction have been studied. The first mechanism is the drift instability induced by the vortex free component of the condensate and resulting in the motion of the vortex out of the condensate center to its periphery. The second mechanism is the splitting of the higher order vortices into unit ones. Absolute and/or relative increase of the number of particles in the vortex free condensate component has been found to have stabilizing effect on both drift and splitting instabilities. Different scenarios of the splitting instabilities have been found.
Motivated by recent experiments [Chen et al., Phys. Rev. Lett. 121, 113204 (2018); Chen et al., Phys. Rev. Lett. 121, 250401 (2018)], we investigate the low-lying excitation spectrum of the ground-state phases of spin-orbital-angular-momentum-coupled (SOAM-coupled) spin-1 condensates. At vanishing detuning, a ferromagnetic SOAM-coupled spin-1 Bose-Einstein condensate (BEC) can have two ground-state phases, namely, coreless and polar-core vortex states, whereas an antiferromagnetic BEC supports only polar-core vortex solution. The angular momentum per particle, longitudinal magnetization, and excitation frequencies display discontinuities across the phase boundary between the coreless vortex and polar-core vortex phases. The low-lying excitation spectrum evaluated by solving the Bogoliubov--de Gennes equations is marked by avoided crossings and hence the hybridization of the spin and density channels. The spectrum is further confirmed by the dynamical evolution of the ground state subjected to a perturbation suitable to excite a density or a spin mode and a variational analysis for the density-breathing mode.
We theoretically study counterflow instability and turbulence in a spin-1 spinor Bose-Einstein condensate by the Gross-Pitaevskii equation and the Bogoliubov-de Gennes equation. Our study considers (i) the dynamics induced by the counterflow of two components with different magnetic quantum numbers, which leads to turbulence with spin degrees of freedom, and (ii) the properties of the turbulence. For (i), the behavior of the condensate induced by the counterflow strongly depends on whether the spin-dependent interaction is ferromagnetic or antiferromagnetic, leading to different behaviors for the dispersion relation and the spin density vector, etc. For (ii), we numerically calculate the spectrum of the spin-dependent interaction energy, which also depends on the spin-dependent interaction. The spectrum of the spin-dependent interaction energy in the ferromagnetic case clearly exhibits a $\ensuremath{-}7/3$ power law, which can be explained by scaling analysis. The spectrum in the antiferromagnetic case seems to show some power law too, but the power exponent cannot be estimated as definitely as the ferromagnetic case.