Lexicon of Topological Defects in He-3 Superfluids (original) (raw)

Topological superfluid defects with discrete point group symmetries

Nature Communications, 2022

Discrete symmetries are spatially ubiquitous but are often hidden in internal states of systems where they can have especially profound consequences. In this work we create and verify exotic magnetic phases of atomic spinor Bose-Einstein condensates that, despite their continuous character and intrinsic spatial isotropy, exhibit complex discrete polytope symmetries in their topological defects. Using carefully tailored spinor rotations and microwave transitions, we engineer singular line defects whose quantization conditions, exchange statistics, and dynamics are fundamentally determined by these underlying symmetries. We show how filling the vortex line singularities with atoms in a variety of different phases leads to core structures that possess magnetic interfaces with rich combinations of discrete and continuous symmetries. Such defects, with their non-commutative properties, could provide unconventional realizations of quantum information and interferometry. Symmetry plays a critical role in the scientific and mathematical descriptions of the universe. Symmetries can be continuous, as in rotations of a circular cylinder about its axis; or discrete, as in end-forend exchanges of the cylinder about its midpoint. Discrete polytope symmetries appear in diverse and widespread systems, including crystals, molecular bonds, and the familiar morphologies of honeycombs, snowflakes, and flower petals. They can also be hidden in the internal states of otherwise continuous and isotropic systems, where they can have profound and unusual consequences; for example, the discrete symmetries of charge conjugation, parity, and time-reversal play important roles in particle and condensed matter physics and serve as a touchstone for grand unified theories. Complex discrete symmetries also appear in spatially uniform condensed matter systems and, intriguingly, in spinor superfluids. In quantum mechanics, the internal symmetries of a spin-F system can be conveniently described in a geometrical representation due to Majorana, wherein a state corresponds to a constellation of 2F points on the unit sphere 1,2. Each point is related to the state of an independent spin-1/2 system 3 , and the polytopes with vertices established by the representative points display the discrete symmetries of the order parameter that describes the system 4-6. The stationary, dynamically stable states that share a given constellation are known as magnetic phases, whose richness of internal symmetries is illustrated by the examples in Fig. 1. In contrast to the ubiquity of their crystalline counterparts, condensed matter systems exhibiting discrete polytope symmetries within their internal degrees of freedom are relatively unusual, with examples appearing in exotic contexts such as d-wave superconductors 7 , 3 P 2 neutron star superfluids 8 , and biaxial nematic liquid crystals 9. Spinor Bose-Einstein condensates (BECs) 10 with spin F ≥ 2 provide an exciting pristine system with unprecedented experimental control. They are described by an order parameter whose complex broken internal symmetries lead to magnetic phases with polygonal (e.g., Fig. 1f), tetrahedral (e.g., Fig. 1g), octahedral (F ≥ 3), and icosahedral (F ≥ 6) Majorana symmetries. Previous experimental studies have examined phenomena associated with spinor BECs in simple magnetic phases that lack such symmetries, including topological defects 11-14 and textures 15-19 , spontaneous pattern formation 20,21 , dipolar interactions 22 ,

Symmetry protected topological superfluid (3)He-B

Journal of physics. Condensed matter : an Institute of Physics journal, 2015

Owing to the richness of symmetry and well-established knowledge of bulk superfluidity, the superfluid (3)He has offered a prototypical system to study intertwining of topology and symmetry. This article reviews recent progress in understanding the topological superfluidity of (3)He in a multifaceted manner, including symmetry considerations, the Jackiw-Rebbi's index theorem, and the quasiclassical theory. Special focus is placed on the symmetry protected topological superfuidity of the (3)He-B confined in a slab geometry. The (3)He-B under a magnetic field is separated to two different sub-phases: the symmetry protected topological phase and non-topological phase. The former phase is characterized by the existence of symmetry protected Majorana fermions. The topological phase transition between them is triggered by the spontaneous breaking of a hidden discrete symmetry. The critical field is quantitatively determined from the microscopic calculation that takes account of magnet...

Quantized Vorticity in Superfluid 3He-A: Structure and Dynamics

Lecture Notes in Physics, 2001

Superfluid 3 He-A displays the largest variety in vortex structure among the presently known coherent quantum systems. The experimentally verified information comes mostly from NMR measurements on the rotating fluid, from which the orderparameter texture can often be worked out. The various vortex structures differ in the topology of their order-parameter field, in energy, critical velocity, and in their response to temporal variations in the externally applied flow. They require different experimental conditions for their creation. When the flow is applied in the superfluid state, the structure with the lowest critical velocity is formed. In 3 He-A this leads to the various forms of continuous (or singularity-free) vorticity. Which particular structure is created depends on the externally applied conditions and on the global order-parameter texture.

Non-linear Spin Waves on Topological Defects of Texture in Superfluid 3He-B

1998

We have observed non-linear behaviour of stationary spin waves localised on textural topological defects. We can explain our results in the framework of the Schrodinger equation with feedback. The new method gives us the ability to see many topological defects, which are undistinguished by traditional methods of NMR. We have found that some of the non-linear spin wave modes can be responsible for the extremely long lived induction decay signals called "Persistent signals". PACS number:67.57.Lm 51 0022-2291/98/0100-0051$15.00/0

A topological defect model of superfluid vortices

Physica D: Nonlinear Phenomena, 1996

This paper introduces a nonlinear Schrrdinger model for superfluid that captures the process of mutual friction between the superfluid and normal fluid components of helium II. Superfluid vortices are identified as topological defects in the solution of this equation. A matched asymptotic analysis of Neu is adapted to derive an asymptotic dynamics for the vortices in the case they are widely separated compared with their core size. This motion agrees with the classical Hall and Vinen motion in which phenomenological drag terms are added, ad hoc, to the motion of vortices in an inviscid fluid. Several simple examples are considered to illustrate the unique character of the motion of superfluid vortices. Finally, the motion of vortices in uniformly rotating helium II is considered, and a continuum approximation to their dynamics is obtained in the case of very many vortices.

Superfluid phase of 3 He-B near the boundary

Journal of Physics: Conference Series, 2009

Following our analysis of some older and most recent transverse sound experiments in superfluid 3 He-B we have been able to solve one of the long-existing problem of superfluid quantum liquids in confined geometry, namely, answer a question what is the boundary state of 3 He-B. We have devoted specific attention to the differences between transverse sound experiments data from that obtained in longitudinal sound experiments. In our analysis, we have considered several potentially possible explanations of the above experimental data: existence of a new superfluid phase in the vicinity of the boundary; excitation of different branches of squashing mode by longitudinal and transverse sounds and, finally, deformation of the B-phase near the boundary. The last possibility seems to be the most likely explanation implying that the boundary state of 3 He-B is, in fact, the deformed Bphase, as was first suggested by Brusov and Popov about two decades ago for a case of presence of external perturbations such as a magnetic and an electric fields. Our result implies that influence of a wall or, in other words, a confined geometry does not lead to the existence of a new phase near the boundary, as had been suggested many years ago, but, instead, similarly to the case of other external perturbations (such as magnetic, electric fields etc.), the wall deforms the order parameter of the B-phase and this deformation leads to several very important consequences. For example, frequencies of the collective modes in the vicinity of the boundary change by up to about 20 percent.

Quantized Vorticity in Superfluid 3He-A

2000

Superfluid 3He-A displays the largest variety in vortex structure among the presently known coherent quantum systems. The experimentally verified information comes mostly from NMR measurements on the rotating fluid, from which the order-parameter texture can often be worked out. The various vortex structures differ in the topology of their order-parameter field, in energy, critical velocity, and in their response to temporal variations in the externally applied flow. They require different experimental conditions for their creation. When the flow is applied in the superfluid state, the structure with the lowest critical velocity is formed. In 3He-A this leads to the various forms of continuous (or singularity-free) vorticity. Which particular structure is created depends on the externally applied conditions and on the global order-parameter texture.

SuperfluidHe3in very confined regular geometries

Physical Review B, 1988

Superfluid 3He in very narrow slab and cylindrical geometries is studied using the Ginzburg-Landau approach. It is found that, in the case of very narrow slabs, the effect of the boundary is to favor the formation of the A phase. At lower temperatures, this A phase is unstable against a deformed B phase. Both states are locally stable and can be supercooled or superheated. The phase diagram for 'He in a narrow slab resembles that of He in a magnetic field. The superfluid densities along the channel for both diffusive and specular boundary conditions are computed. Similar results are obtained for a cylindrical geometry. In addition, we present an analytic scheme for determining the order parameter in other geometries in the "very strongly confined" limit.

Core Phase Transitions for Embedded Topological Defects

Vortices in superfluid 3He-B have been observed to undergo a core transition. We discuss the analog phenomenon in relativistic field theories which admit embedded global domain walls, vortices and monopoles with a core phase structure. They are present in scalar field theories with approximate global symmetries which are broken both spontaneously and in parts explicitly. For a particular range of parameters their symmetric core exhibits an instability and decays into the nonsymmetric phase.

“Cosmological” Scenario for A-B Phase Transition in Superfluid 3He

Physical Review Letters, 1998

At a very rapid superfluid transition in 3 He, follows after a reaction with single neutron, the creation of topological defects (vortices) has recently been demonstrated in accordance with the Kibble-Zurek scenario for the cosmological analogue. We discuss here the extension of the Kibble-Zurek scenario to the case when alternative symmetries may be broken and different states nucleated independently. We have calculated the nucleation probability of the various states of superfluid 3 He during a superfluid transition. Our results can explain the transition from supercooled A phase to the B phase, triggered by nuclear reaction. The new scenario is an alternative to the well-known "baked Alaska" scenario. 64.60.Qb, 98.80.Cq Superfluid 3 He has an order parameter which describe the simultaneous spin, orbital and gauge symmetries which are broken at the superfluid transition. This transition can be regarded as the closest condensed matter analogy to the cosmological grand unification transition. This analogy have been utilised in the experimental test of the Kibble cosmological mechanism of cosmic strings creation. According to this mechanism [1], at the transition separate regions of the Universe are independently nucleated with a random orientation of the gauge field in each region. The size of these initial regions (domains) depends strongly on the rapidity with which the transition is traversed. According to Zurek [2] the fundamental distance between the independently-created coherent domains (in the language of [2] the distance between the ensuing vortices Z) is of the order of Z = ξ 0 (τ Q /τ 0 ) 1/4 , where ξ 0 is the zero temperature coherence, τ 0 = (ξ 0 /v F ) is the characteristic time constant of the superfluid, and τ Q is the characteristic time for cooling through the phase transition. As the domains grow and make contact with their neighbours, the resulting gauge field cannot be uniform. The subsequent order-parameter "glass" forces a distribution of topological defects leading to a tangle of quantized vortex lines. The first quantitative tests of defect creation during a gauge symmetry transformation have been recently performed in superfluid 3 He.

Visualizing Pure Quantum Turbulence in Superfluid 3^{3}3He

2015

Superfluid 3 He-B in the zero-temperature limit offers a unique means of studying quantum turbulence by the Andreev reflection of quasiparticle excitations by the vortex flow fields. We validate the experimental visualization of turbulence in 3 He-B by showing the relation between the vortex-line density and the Andreev reflectance of the vortex tangle in the first simulations of the Andreev reflectance by a realistic 3D vortex tangle, and comparing the results with the first experimental measurements able to probe quantum turbulence on length scales smaller than the intervortex separation.

Universal Impurity-Induced Bound State in Topological Superfluids

We predict a universal midgap bound state in topological superfluids, induced by either nonmagnetic or magnetic impurities in the strong scattering limit. This universal state is similar to the lowest-energy Caroli-de Gennes-Martricon bound state in a vortex core, but is bound to localized impurities. We argue that the observation of such a universal bound state can be a clear signature for identifying topological superfluids. We theoretically examine our argument for a spin-orbit coupled ultracold atomic Fermi gas trapped in a two-dimensional harmonic potential by performing extensive self-consistent calculations within the mean-field Bogoliubov-de Gennes theory. A realistic scenario for observing a universal bound state in ultracold 40 K atoms is proposed.

Superfluid Interfaces in Quantum Solids

Physical Review Letters, 2005

One scenario for the non-classical moment of inertia of solid 4 He discovered by Kim and Chan [Nature, 427, 225 (2004)] is the superfluidity of micro-crystallite interfaces. On the basis of the most simple model of a quantum crystal-the checkerboard lattice solid-we show that the superfluidity of interfaces between solid domains can exist in a wide range of parameters. At strong enough interparticle interaction, a superfluid interface becomes an insulator via a quantum phase transition. Under the conditions of particle-hole symmetry, the transition is of the standard U (1) universality class in 3D, while in 2D the onset of superfluidity is accompanied by the interface roughening, driven by fractionally charged topological excitations. Recent observation by Kim and Chan [1] of nonclassical moment of inertia (NCMI) of 4 He at pressures significantly higher than the solidification point is a breathtaking result, especially striking in view of the theorem-like theoretical arguments against existence of commensurate supersolids . The fact of commensurability-equivalently, one may put it as the fact of absence of vacancies, or interstitials, or both-of the equilibrium solid 4 He at T = 0 is supported by an extensive experimental work over the past several decades (for review, see, e.g., [3]), as well as by the most recent experimental and numeric studies . The commensurability of solid 4 He rules out NCMI based on Bose-Einstein condensation of vacancies . Two of us have proposed recently [2] that NCMI might be due to the superfluidity of interfaces between 4 He crystallites. At present, the weak point of this hypothesis is the absence of a theoretical analysis and/or direct experimental evidence of the superfluidity in the walls separating insulating domains.

Experiments on the Twisted Vortex State in Superfluid 3He-B

Journal of Low Temperature Physics, 2008

We have performed measurements and numerical simulations on a bundle of vortex lines which is expanding along a rotating column of initially vortexfree 3 He-B. Expanding vortices form a propagating front: Within the front the superfluid is involved in rotation and behind the front the twisted vortex state forms, which eventually relaxes to the equilibrium vortex state. We have measured the magnitude of the twist and its relaxation rate as function of temperature above 0.3 T c . We also demonstrate that the integrity of the propagating vortex front results from axial superfluid flow, induced by the twist.

Topological Matter: Graphene and Superfluid ^3$$ 3 He

Journal of Low Temperature Physics, 2014

The physics of graphene and of the superfluid phases of 3 He have many common features. Both systems are topological materials where quasiparticles behave as relativistic massless (Weyl, Majorana or Dirac) fermions. We formulate the points where these features are overlapping. This will allow us to use graphene to study the properties of superfluid 3 He, to use superfluid 3 He to study the properties of graphene, and to use both of them in combination to study the physics of topological quantum vacuum. We suggest also some particular experiments with superfluid 3 He using graphene as an atomically thin membrane impenetrable for He atoms but allowing for spin, momentum and energy transfer.

Defect Formation in Quench-Cooled Superfluid Phase Transition

Physical Review Letters, 1998

We use neutron absorption in rotating 3 He-B to heat locally a ∼ 10 µm-size volume into normal phase. When the heated region cools back in µsecs, vortex lines are formed. We record with NMR the number of lines as a function of superflow velocity and compare to the Kibble-Zurek theory of vortex-loop freeze-out from a random network of defects. The measurements confirm the calculated loop-size distribution and show that also the superfluid state itself forms as a patchwork of competing A and B phase blobs. This explains the A→B transition in supercooled neutron-irradiated 3 He-A.

Textures and Exotic Vortices in Neutral Fermion Superfluids

2010

There has been intense interest in various Fermion superfluids in neutral atom liquids and gases, including chiral p-wave pairing in 3 He-A phase and Feshbach-resonanced 6 Li atom gases and d-wave pairing in atom gases. It is particularly interesting to find exotic vortices and associated low-lying Fermionic excitations under rotation. Here we report on our efforts of those topics: (1) Majorana Fermion in chiral superfluids near a p-wave Feshbach resonance. (2) Possible half-quantum vortices in p-wave superfluids of trapped Fermion atom gases. (3) Stability of a halfquantum vortex in rotating superfluid 3 He-A between parallel plates. (4) Majorana bound state in rotating superfluid 3 He-A between parallel plates. (5) Non-Abelian Fractional vortex in d-wave Feshbach resonance superfluids. We will summarize some of those works in a coherent manner in order to bridge the understanding between cold atom community and superfluid 3 He community by stressing the importance of cross fertilization between them.

Topological Defects : from Simplicity to Complexity

2017

On the one hand simple systems and simple rules can enable surprisingly complex patterns in nature. On the other hand several fundamental questions on natural behavior remain unanswered. For example, dark matter and dark energy have been introduced to explain observed structure and dynamics of the universe. However, their existence is not experimentally supported at fundamental level. It might be that difficulties in understanding of some basic phenomena of the nature arise because we are trying to present it from wrong perspective. There are strong evidences that in physics the fields are fundamental entities of nature and not particles. If this is the case then topological defects (TDs) might play the role of fundamental particles. An adequate testing ground to study and gain fundamental understanding of TDs are nematic liquid crystals. In this paper we present TDs in simple two-dimensional nematics emphasizing their particle-like behavior. We demonstrate strong interactions betwe...