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EPFL Press eBooks

Unconventional Vorticity

Konstantinos G. Lagoudakis

Published Dec 2, 2013• 0 citations
Publisher

Abstract

Quantized vorticity is a property of quantum fluids that has been widely studied in various types of superfluids, either with or without spin [77],[86],[87] and Chapter 6. Superfluids with a two component (spinor) order parameter are characterized by a different type of vortex than those found in conventional scalar superfluids [99]-[102]. This new type of vortex is the so called half quantum vortex (HQV). HQVs have lower energy with respect to full vortices and constitute the elementary excitations of spinor superfluids. When circumventing their core, the phase and the polarization vector experience a ±π rotation. In this sense, HQV can be understood as a half phase vortex combined with a half polarization vortex [99]. In 4He superfluids, the HQV cannot be formed as the spin degree of freedom is absent. However, in 3He [99],[100] or in triplet superconductors [101],[102], the order parameter has two or more components, so that the formation of HQV is possible. So far, experiments have not presented any direct evidence for HQV in 3He [103], while more reliable indications of existence of HQV have been reported in cuprate superconductors [104].

DOI
10.1201/b15531-11

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•Dec 2, 2025•0 citations
Quantized vorticity is a property of quantum fluids that has been widely studied in various types of superfluids, either with or without spin [77],[86],[87] and Chapter 6. Superfluids with a two component (spinor) order parameter are characterized by a different type of vortex than those found in conventional scalar superfluids [99]-[102]. This new type of vortex is the so called half quantum vortex (HQV). HQVs have lower energy with respect to full vortices and constitute the elementary excitations of spinor superfluids. When circumventing their core, the phase and the polarization vector experience a ±π rotation. In this sense, HQV can be understood as a half phase vortex combined with a half polarization vortex [99]. In 4He superfluids, the HQV cannot be formed as the spin degree of freedom is absent. However, in 3He [99],[100] or in triplet superconductors [101],[102], the order parameter has two or more components, so that the formation of HQV is possible. So far, experiments have not presented any direct evidence for HQV in 3He [103], while more reliable indications of existence of HQV have been reported in cuprate superconductors [104].
Triple-Core Structure of the Double-Core Vortex in Superfluid 3^33He-B
Abstract The order parameter of superfluid 3^33 3 He involves nine complex components, and the multicomponent structure allows quantized vortices in superfluid 3^33 3 He to have complicated cores. One of the vortices found in the B phase is the double-core vortex, which has been often described as a pair of two half-quantum vortices (HQVs) connected by a domain wall. Our numerical calculations of the core structure suggest an alternative representation of the vortex as a combination of three vortices, one in each component of the spin-triplet superfluid. Based on the results we present a qualitative analytical model for the triple-core structure of the double-core vortex. Additionally we numerically calculate the structure of a double-core vortex stretched between pinning sites, and show that the HQV picture becomes more applicable when separation between subcores becomes large.
This doctoral thesis consists of experimental studies on rotating superfluid helium-3 at millikelvin temperatures. Superfluid 3He provides an example of ordered systems where quantum phenomena are visible on a macroscopic scale. The order parameter is described by a 3x3 complex matrix leading to different superfluid phases with different properties. The A and B phases support topologically different kinds of defects, most notably vortex lines. Vortex lines are most easily created and studied in uniform rotation. Because of quantum nature, the circulation around the vortices is quantized in units of κ0 = h/2m3.\n\nIn superfluid 3He nuclear magnetic resonance (NMR) provides a means to distinguish between different types of vortices and count them one by one. During the course of this work the sensitivity of the NMR spectrometer was improved by an order of magnitude, which enabled the direct measurement of the circulation of a vortex in the A phase that carries two circulation quanta (2κ0). Up to now the circulation of the known quantized vortex types in other quantum fluids, which include superfluid 4He, superconductors, and Bose-Einstein -condensates, has been singly quantized.\n\nOther NMR experiments reported in the thesis are: (1) The first qualitative measurements of vortex annihilation in the A and B phases of 3He. These measurements tell the lowest rotation velocity that stabilizes an array of vortex lines with a given number of vortices, and how it depends on the type of the defect. (2) Studies of vortex arrays with both singly and doubly quantized A phase vortex lines coexisting in the experimental container. 3He-A provides a unique system in which this kind of arrangement can be done. (3) In order to improve the vortex detection sensitivity in the B phase even further, the response of different nonlinear spin precession modes to superfluid-normal fluid counterflow was studied. A new mode, where the orbital angular momentum is oriented transverse to the external magnetic field, was found.
Triple-core structure of the double-core vortex in superfluid 3^33He-B
The order parameter of superfluid 3^33He involves nine complex components, and the multicomponent structure allows quantized vortices in superfluid 3^33He to have complicated cores. One of the vortices found in the B phase is the double-core vortex, which has been often described as a pair of two half-quantum vortices (HQVs) connected by a domain wall. Our numerical calculations of the core structure suggest an alternative representation of the vortex as a combination of three vortices, one in each component of the spin-triplet superfluid. Based on the results we present a qualitative analytical model for the triple-core structure of the double-core vortex. Additionally we numerically calculate the structure of a double-core vortex stretched between pinning sites, and show that the HQV picture becomes more applicable when separation between subcores becomes large.
Quantum vortices with half the quantum circulation, known as half-quantum vortices (HQVs), have been observed in various spinor superfluid systems recently. Because of their nonsingular cores, the interaction of HQVs is expected to be different from that of vortices in a conventional scalar superfluid, which can lead to a new class of superfluid dynamics. Here, we report on a collision experiment of two HQV pairs in an antiferromagnetic spinor Bose-Einstein condensate. The observed scattering motions of the HQVs reveal the short range interactions that arise from their ferromagnetic cores. Additionally, we investigate the relaxation dynamics of turbulent superflow containing many HQVs to find that spin wave excitations are generated and maintained by the collisional motions of the HQVs during dissipative evolution. These results provide new insight into the vortex dynamics in spinor superfluids.
The half quantum vortex (HQV) in condensates has been studied, since it was predicted by Volovik and Mineev, and independently by Cross and Brinkman in superfluid 3 He-A phase. However, no experimental evidence for its existence has been reported until recently. Motivated by a recent experimental report by Yamashita et al. ( AIP Conf. Proc. , 850 (2006) 185; private communication) we study the HQVs in superfluid 3 He confined between two parallel plates with a gap D ∼10 μm in the presence of a magnetic field H ∼26 mT perpendicular to the parallel plates. We find that the bound HQVs are more stable than the singular vortices and free pairs of HQVs, when the rotation perpendicular to the parallel plates is below the critical speed, Ω c =2∼12 rad/s, if the magnetic healing length, ξ H is about 2–5 μm. The bound pair of HQVs accompanies the tilting of -vector out of the plane, which leads to an additional absorption in NMR spectra. Our study appears to describe the temperature and rotation dependence of the observed satellite NMR signal, which supports the existence of the HQVs in 3 He.
Abstract Chapter 4 addresses the progress of studies on superfluid dynamics, mainly related to the dynamics of quantized vortices, in cold-atom BECs. First, we give a minimal description of the physics of cold atoms, e.g. cooling, trapping, control of interatomic interactions by external fields. We then turn to the argument of superfluid hydrodynamics in a scalar BEC characterized by a single-component order parameter. The properties of the vortices can be well described on the basis of the GP model, which allows a quantitative comparison between theory and experiment. We will discuss topics such as single vortex dynamics, interacting dynamics of a few vortices, vortex lattice formation in a rotating BEC, and collective properties of a vortex lattice in a rapidly rotating BEC, which have been unraveled experimentally by direct visualization of vortices in condensed gases. Next, we will discuss the properties of vortices in multicomponent BECs characterized by the multicomponent order parameters. We will first explain the vortex physics in two-component BECs as a simple case, finding that their structures and dynamics are highly nontrivial due to the presence of the intercomponent interaction; we will cover the topics of vortex structure composed of two-component order parameters, dynamics of composite vortices, exotic vortex lattices, and hydrodynamic instabilities associated with the interface dynamics between immiscible condensates. Finally, we explain the vortices in a spinor BEC. The vortex structures are extremely rich due to the complicated order parameter manifold, which is clarified by the discussion on vortices in spin-1 and spin-2 spinor BECs.