arXiv subjects

William T. M. Irvine

Publications and source records attributed to William T. M. Irvine.

31 records · Page 2Linked to original sources

arXiv2015

How superfluid vortex knots untie

Knotted and tangled structures frequently appear in physical fields, but so do mechanisms for untying them. To understand how this untying works, we simulate the behavior of 1,458 superfluid vortex knots of varying complexity and scale in the Gross-Pitaevskii equation. Without exception, we find that the knots untie efficiently and completely, and do so within a predictable time range. We also observe that the centerline helicity -- a measure of knotting and writhing -- is partially preserved even as the knots untie. Moreover, we find that the topological pathways of untying knots have simple descriptions in terms of minimal 2D knot diagrams, and tend to concentrate in states along specific maximally chiral pathways.

physics.flu-dyn↗

arXiv2015

Topological mechanics of gyroscopic metamaterials

Topological mechanical metamaterials are artificial structures whose unusual properties are protected very much like their electronic and optical counterparts. Here, we present an experimental and theoretical study of an active metamaterial -- comprised of coupled gyroscopes on a lattice -- that breaks time-reversal symmetry. The vibrational spectrum of these novel structures displays a sonic gap populated by topologically protected edge modes which propagate in only one direction and are unaffected by disorder. We present a mathematical model that explains how the edge mode chirality can be switched via controlled distortions of the underlying lattice. This effect allows the direction of the edge current to be determined on demand. We envision applications of these edges modes to the design of loss-free, one-way, acoustic waveguides and demonstrate this functionality in experiment.

cond-mat.soft↗

arXiv2014

Helicity conservation by flow across scales in reconnecting vortex links and knots

The conjecture that helicity (or knottedness) is a fundamental conserved quantity has a rich history in fluid mechanics, but the nature of this conservation in the presence of dissipation has proven difficult to resolve. Making use of recent advances, we create vortex knots and links in viscous fluids and simulated superfluids and track their geometry through topology changing reconnections. We find that the reassociation of vortex lines through a reconnection enables the transfer of helicity from links and knots to helical coils. This process is remarkably efficient, owing to the anti-parallel orientation spontaneously adopted by the reconnecting vortices. Using a new method for quantifying the spatial helicity spectrum, we find that the reconnection process can be viewed as transferring helicity between scales, rather than dissipating it. We also infer the presence of geometric deformations which convert helical coils into even smaller scale twist, where it may ultimately be dissipated. Our results suggest that helicity conservation plays an important role in fluids and related fields, even in the presence of dissipation.

physics.flu-dyn↗

arXiv2014

Orientation-dependent handedness and chiral design

Chirality occupies a central role in fields ranging from biological self-assembly to the design of optical metamaterials. The definition of chirality, as given by Lord Kelvin, associates chirality with the lack of mirror symmetry: the inability to superpose an object on its mirror image. While this definition has guided the classification of chiral objects for over a century, the quantification of handed phenomena based on this definition has proven elusive, if not impossible, as manifest in the paradox of chiral connectedness. In this work, we put forward a quantification scheme in which the handedness of an object depends on the direction in which it is viewed. While consistent with familiar chiral notions, such as the right-hand rule, this framework allows objects to be simultaneously right and left handed. We demonstrate this orientation dependence in three different systems - a biomimetic elastic bilayer, a chiral propeller, and optical metamaterial - and find quantitative agreement with chirality pseudotensors whose form we explicitly compute. The use of this approach resolves the existing paradoxes and naturally enables the design of handed metamaterials from symmetry principles.

cond-mat.soft↗

arXiv2013

The Life of a Vortex Knot

The idea that the knottedness (hydrodynamic Helicity) of a fluid flow is conserved has a long history in fluid mechanics. The quintessential example of a knotted flow is a knotted vortex filament, however, owing to experimental difficulties, it has not been possible until recently to directly generate knotted vortices in real fluids. Using 3D printed hydrofoils and high-speed laser scanning tomography, we generate vortex knots and links and measure their subsequent evolution. In both cases, we find that the vortices deform and stretch until a series of vortex reconnections occurs, eventually resulting several disjoint vortex rings. This article accompanies a fluid dynamics video entered into the Gallery of Fluid Motion at the 66th Annual Meeting of the APS Division of Fluid Dynamics.

physics.flu-dyn↗

arXiv2013

Fractionalization of Interstitials in Curved Colloidal Crystals

Understanding the out-of equilibrium behaviour of point defects in crystals, yields insights into the nature and fragility of the ordered state, as well as being of great practical importance. In some rare cases defects are spontaneously healed - a one-dimensional crystal formed by a line of identical charged particles, for example, can accommodate an interstitial (extra particle) by a re-adjusting all particle positions to even out the spacing. In sharp contrast, particles organized into a perfect hexagonal crystal in the plane cannot accommodate an interstitial by a simple re-adjustment of the particle spacing - the interstitial remains instead trapped between lattice sites and diffuses by hopping, leaving the crystal permanently defected. Here we report on the behavior of interstitials in colloidal crystals on curved surfaces. Using optical tweezers operated independently of three dimensional imaging, we insert a colloidal interstitial in a lattice of similar particles on flat and curved (positively and negatively) oil-glycerol interfaces and image the ensuing dynamics. We find that, unlike in flat space, the curved crystals self-heal through a collective rearrangement that re-distributes the increased density associated with the interstitial. The self-healing process can be interpreted in terms of an out of equilibrium interaction of topological defects with each other and with the underlying curvature. Our observations suggest the existence of "particle fractionalization" on curved surface crystals.

cond-mat.soft↗

arXiv2013

Tying knots in light fields

We construct a new family of null solutions to Maxwell's equations in free space whose field lines encode all torus knots and links. The evolution of these null fields, analogous to a compressible flow along the Poynting vector that is both geodesic and shear-free, preserves the topology of the knots and links. Our approach combines the Bateman and spinor formalisms for the construction of null fields with complex polynomials on $\mathbb{S}^3$. We examine and illustrate the geometry and evolution of the solutions, making manifest the structure of nested knotted tori filled by the field lines.

math-ph↗

arXiv2011

Linked and knotted beams of light, conservation of helicity and the flow of null electromagnetic fields

Maxwell's equations allow for some remarkable solutions consisting of pulsed beams of light which have linked and knotted field lines. The preservation of the topological structure of the field lines in these solutions has previously been ascribed to the fact that the electric and magnetic helicity, a measure of the degree of linking and knotting between field lines, are conserved. Here we show that the elegant evolution of the field is due to the stricter condition that the electric and magnetic fields be everywhere orthogonal. The field lines then satisfy a `frozen field' condition and evolve as if they were unbreakable filaments embedded in a fluid. The preservation of the orthogonality of the electric and magnetic field lines is guaranteed for null, shear-free fields such as the ones considered here by a theorem of Robinson. We calculate the flow field of a particular solution and find it to have the form of a Hopf fibration moving at the speed of light in a direction opposite to the propagation of the pulsed light beam, a familiar structure in this type of solution. The difference between smooth evolution of individual field lines and conservation of electric and magnetic helicity is illustrated by considering a further example in which the helicities are conserved, but the field lines are not everywhere orthogonal. The field line configuration at time t=0 corresponds to a nested family of torus knots but unravels upon evolution.

physics.optics↗

arXiv2006

Strong coupling between single photons in semiconductor microcavities

We discuss the observability of strong coupling between single photons in semiconductor microcavities coupled by a chi(2) nonlinearity. We present two schemes and analyze the feasibility of their practical implementation in three systems: photonic crystal defects, micropillars and microdisks, fabricated out of GaAs. We show that if a weak coherent state is used to enhance the chi(2) interaction, the strong coupling regime between two modes at different frequencies occupied by a single photon is within reach of current technology. The unstimulated strong coupling of a single photon and a photon pair is very challenging and will require an improvement in mirocavity quality factors of 2-4 orders of magnitude to be observable.

quant-ph↗

arXiv2005

Bloch theory of entangled photon generation in non-linear photonic crystals

We present a quantum mechanical description of parametric down-conversion and phase-matching of Bloch-waves in non-linear photonic crystals. We discuss the theory in one-dimensional Bragg structures giving a recipe for calculating the down-converted emission strength and direction. We exemplify the discussion by making explicit analytical predictions for the emission amplitude and direction from a one-dimensional structure that consists of alternating layers of Al0.4Ga0.6As and Air. We show that the emission is suitable for the extraction of polarization-entangled photons.

quant-ph↗

arXiv2004

Realisation of Hardy's Thought Experiment

We present an experimental realisation of Hardy's thought experiment [Phys. Rev. Lett. {\bf 68}, 2981 (1992)], using photons. The experiment consists of a pair of Mach-Zehnder interferometers that interact through photon bunching at a beam splitter. A striking contradiction is created between the predictions of quantum mechanics and local hidden variable based theories. The contradiction relies on non-maximally entangled position states of two particles.

quant-ph↗

arXiv2004

Non-linear photonic crystals as a source of entangled photons

Non-linear photonic crystals can be used to provide phase-matching for frequency conversion in optically isotropic materials. The phase-matching mechanism proposed here is a combination of form birefringence and phase velocity dispersion in a periodic structure. Since the phase-matching relies on the geometry of the photonic crystal, it becomes possible to use highly non-linear materials. This is illustrated considering a one-dimensional periodic Al$_{0.4}$Ga$_{0.6}$As / air structure for the generation of 1.5 $μ$m light. We show that phase-matching conditions used in schemes to create entangled photon pairs can be achieved in photonic crystals.

quant-ph↗

arXiv2004

Robust long-distance entanglement and a loophole-free Bell test with ions and photons

Two trapped ions that are kilometers apart can be entangled by the joint detection of two photons, each coming from one of the ions, in a basis of entangled states. Such a detection is possible with linear optical elements. The use of two-photon interference allows entanglement distribution without interferometric sensitivity to the path length of the photons. The present method of creating entangled ions also opens up the possibility of a loophole-free test of Bell's inequalities.

quant-ph↗