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Physical Review Letters

Two different vortex states in rotating A3 observed by use of negative ions

Juha Simola, L. Skrbek, Kaj K. Nummila, J. S. Korhonen

Published Mar 2, 1987• 88 citations
Publisher

Abstract

First experiments suggesting the presence of singular vortices in rotating $^{3}\mathit{A}$ are reported. Our studies on the interaction between negative ions and vortex textures verify the existence of the continuous vortices seen earlier by NMR, but evidence for a new vortex state with high ion mobility along the core is also found. The nucleation of the new vortex depends on the external magnetic field and the rotation history of the sample.

DOI
10.1103/physrevlett.58.904

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arXiv:cond-mat/0407684•Physical Review A•Oct 12, 2004•92 citations
First experiments suggesting the presence of singular vortices in rotating 3A^{3}\mathit{A}3A are reported. Our studies on the interaction between negative ions and vortex textures verify the existence of the continuous vortices seen earlier by NMR, but evidence for a new vortex state with high ion mobility along the core is also found. The nucleation of the new vortex depends on the external magnetic field and the rotation history of the sample.
The interaction between negative ions and 3 He superfluids was studied by using a time-of-flight spectrometer having a 10−3 relative resolution. The ions guided through a sample of rotating3He-A were found to be focused into the cores of the vortices present in this rotating superfluid. Two different types, with different core structures and presumably different numbers of circulation quanta associated with them, were found. The ion mobility along the vortex cores, μ c , observed in the absence of external magnetic field, can be explained by the mobility anisotropy of the A phase, which indicates that the vortices are continuous, i.e., consist of the A phase even in the core. In finite magnetic fields, a qualitatively similar continuous vortex structure was found, a result compatible with the earlier nuclear magnetic resonance (NMR) experiments, but also a new vortex type with an anomalously high μ c was seen when the vortex sample was prepared “adiabatically.” The observed strong ion focusing indicates broken w-symmetry in the core textures. This is in contradiction with the earlier numerical calculations on the optimal continuous vortex texture. Experiments to observe trapping of ions into the vortex cores were performed both in A and B phases. No trapping could be detected. Mobility measurements in stationary liquid were extended down toT=0.3T c . Comparison with the calculated transport coefficients yieldsΔ A (T)=1.32Δ BCS (T) for the maximal A phase gap atP=29.3 bar, andΔ B (T)=1.12Δ BCS (T) for the B phase gap at 4.8 bar. In the normal Fermi liquid a shallow minimum of ion mobility was detected aroundT≃2T c =5 mK.
Experiments with negative ions in rotating superfluid $^{3}\mathrm{He}\ensuremath{-}A$ show strong retardation and deformation of ion pulses drifting parallel to the angular velocity $\ensuremath{\Omega}$. This is caused by the interaction between the ions and the l\mathbf{l}l texture in the soft cores of AAA-phase vortices. The interaction is mediated by the anisotropic ion mobility: $\mathbf{v}={\ensuremath{\mu}}_{\ensuremath{\perp}}\mathbf{E}\ensuremath{-}\ensuremath{\Delta}\ensuremath{\mu}(\mathbf{E}\ifmmode\cdot\else\textperiodcentered\fi{}\mathbf{l})\mathbf{l}$. The ($\ensuremath{\Omega},T$) dependence of the retardation is explained by a model that assumes focusing of ions into the vortex cores, along which the mobility ${\ensuremath{\mu}}_{c}$ is lower than that in the bulk liquid, ${\ensuremath{\mu}}_{\ensuremath{\perp}}$. We find ${\ensuremath{\mu}}_{c}={\ensuremath{\mu}}_{\ensuremath{\perp}}\ensuremath{-}0.6\ensuremath{\Delta}\ensuremath{\mu}$.
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.