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arXiv:2004.05583 · Journal of Experimental and Theoretical Physics Letters

Spin Vortex Lattice in the Landau Vortex-Free State of Rotating Superfluids

Григорий Ефимович Воловик

Published May 1, 2020• 5 citations
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Abstract

We show that the Landau vortex-free state in rotating container may give rise to the lattice of spin vortices. We consider this effect on example of spin vortices in magnon Bose-Einstein condensate (the phase coherent spin precession) in the B-phase of superfluid 3 He, and on example of spin vortices in the polar phase of 3 He.
DOI
10.1134/s0021364020100045

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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.
Quantized vortices play a key role in superfluidity and superconductivity. We have observed the formation of highly ordered vortex lattices in a rotating Bose-condensed gas. These triangular lattices contained over 100 vortices with lifetimes of several seconds. Individual vortices persisted up to 40 seconds. The lattices could be generated over a wide range of rotation frequencies and trap geometries, shedding light on the formation process. Our observation of dislocations, irregular structure, and dynamics indicates that gaseous Bose-Einstein condensates may be a model system for the study of vortex matter.
We observe interlaced square vortex lattices in rotating dilute-gas spinor Bose-Einstein condensates (BEC). After preparing a hexagonal vortex lattice in a one-component BEC in an internal atomic state |1, we coherently transfer a fraction of the superfluid to a different state |2. The subsequent evolution of this pseudo-spin-1/2 superfluid towards a state of offset square lattices involves an intriguing interplay of phase-separation and -mixing dynamics, both macroscopically and on the length scale of the vortex cores, and a stage of vortex turbulence. The stability of the square structure is proved by its response to applied shear perturbations. An interference technique shows the spatial offset between the two vortex lattices. Vortex cores in either component are filled by fluid of the other component, such that the spin-1/2 order parameter forms a Skyrmion lattice.
The spin superfluidity -- superfluidity in the magnetic subsystem of a condensed matter - is manifested as the spontaneous phase-coherent precession of spins first discovered in 1984 in 3He-B. This superfluid current of spins - spin supercurrent - is one more representative of superfluid currents known or discussed in other systems, such as the superfluid current of mass and atoms in superfluid 4He; superfluid current of electric charge in superconductors; superfluid current of hypercharge in Standard Model of particle physics; superfluid baryonic current and current of chiral charge in quark matter; etc. Spin superfluidity can be described in terms of the Bose condensation of spin waves - magnons. We discuss different phases of magnon superfluidity, including those in magnetic trap; and signatures of magnons superfluidity: (i) spin supercurrent, which transports the magnetization on a macroscopic distance more than 1 cm long; (ii) spin current Josephson effect which shows interference between two condensates; (iii) spin current vortex - a topological defect which is an analog of a quantized vortex in superfluids, of an Abrikosov vortex in superconductors, and cosmic strings in relativistic theories; (iv) Goldstone modes related to the broken U(1) symmetry - phonons in the spin-superfluid magnon gas; etc. We also touch the topic of spin supercurrent in general including spin Hall and intrinsic quantum spin Hall effects.
When a vessel containing a superfluid is set in rotational motion, the superfluid does not rotate uniformly with it; instead, quantized vortices develop. Vortices have been observed in a range of superfluids, including helium, atomic Bose-Einstein condensates, and type II superconductors in a magnetic field. Freilich et al. (p. [1182][1]) visualized real-time vortex dynamics in the most tunable of superfluid systems, an atomic Bose-Einstein condensate. A small section of condensate was displaced from the trap and imaged as it fell in the gravitational field. The technique is applicable to exploring other complex dynamic systems, such as vortex reconnections and the role of vortices in quantum turbulence. [1]: /lookup/doi/10.1126/science.1191224