Creating, imaging, and transforming the topological charge 1,2 in a superconductor 3 , a superfluid 4,5 , a system of cold atoms 6 , or a soft ferromagnet 7-9 is a di cult-if not impossible-task because of the shortness of the length scales and lack of control. The length scale and softness of defects in liquid crystals allow the easy observation of charges, but it is di cult to control charge creation. Here we demonstrate full control over the creation, manipulation and analysis of topological charges that are pinned to a microfibre in a nematic liquid crystal. Oppositely charged pairs are created through the Kibble-Zurek mechanism 10,11 by applying a laser-induced local temperature quench in the presence of symmetry-breaking boundaries. The pairs are long-lived, oppositely charged rings or points that either attract and annihilate, or form a long-lived, charge-neutral loop made of two segments with a fractional topological charge.Topological charge 1,2 is a conserved quantity that is associated with point, string or loop-like topological singularities of physical fields. It is assigned to topological defects in systems of various natures and length scales, such as Abrikosov vortices in type-II superconductors 3 , superfluid vortices 4,5 in 3 He and Bose-Einstein condensates 6 , quasiparticles in the fractional quantum Hall effect 12 , cold fermionic atoms in optical lattices 13 , and in field theories 14 . Integer or fractional topological charge is important for magnetization switching in soft ferromagnets [7][8][9] . In optical vortex beams the topological charge is a measure of the phase singularities of the optical field, and describes the orbital angular momentum of light 15 . Topological defects in liquid crystals 16,17 are the carriers of topological charge, which are produced as transients by a rapid pressure or temperature quench 18,19 and made stable either by colloidal inclusions 20,21 , or by confining the liquid crystal to cavities of various geometries and surface properties. One such example is liquid-crystalline droplets 22,23 .Full control over the topological charge creation and manipulation in a nematic liquid crystal (NLC) is achieved by using laser tweezers to induce a thermal microquench of the NLC around an inserted thin fibre (a few µm in diameter). We use a focused laser beam to locally 'melt' and quench the NLC, which leaves behind isolated topological defects that are stabilized by the fibre. The defects appear in the form of singular points or closed loops, which can be drawn, manipulated, cut and fused together with a laser under an optical microscope. We demonstrate a direct measurement of the topological charge using the charge-induced colloidal forces. This makes inclusions in nematic liquid crystals an ideal system for studying topological charge in soft matter.The experiments were performed on a glass fibre, a few µm in diameter, that was immersed in a thin layer of pentylcyanobiphenyl (5CB) NLC, sandwiched between two glass plates. The NLC molecules were aligned uniformly par...

A family of acrylate-based isotropic Liquid Crystal Elastomers (LCEs) exhibit stress-and strain-optic coefficients orders of magnitude greater than conventional polymeric and photoelastic materials. The three materials, composed of liquid crystalline and nonliquid crystalline monomers, show no nematic phase at any temperature. One of the materials has previously been synthesized with nematic symmetry, but here is instead templated with isotropic symmetry, demonstrating a previously unrealized idea proposed by de Gennes in 1969. Uniaxial strains applied to each material induce nematic ordering which we quantify using dye-absorption spectra and polarized Raman Spectroscopy. We deduce the coupling constants between the nematic liquid crystal order parameter and applied strain varies between 0.37 ± 0.02 and 0.66 ± 0.02values large compared to other LCE systems. The combination of high strain-optic coefficients (0.048 ± 0.003 to 0.11 ± 0.01) and high compliances (245 ± 18 to 1900 ± 100 GPa −1 ) demonstrates that isotropic LCEs are exciting candidates for photoelastic coatings for assessing deformations across soft devices and biomaterials.

We use the laser tweezers to create isolated pairs of topological point defects in a form of radial and hyperbolic hedgehogs, located close and attracted to a thin fiber with perpendicular surface orientation of nematic liquid crystal molecules in a thin planar nematic cell. We study the time evolution of the interaction between the two monopoles by monitoring their movement and reconstructing their trajectories and velocities. We find that there is a crossover in the pair interaction force between the radial and hyperbolic hedgehog. At small separation d, the elastic force between the opposite monopoles results in an increase of the attractive force with respect to the far field, and their relative velocity v scales as a v(d)∝d^{-2±0.2} power law. At large separations, the two oppositely charged monopoles can either attract or repel with constant interaction force. We explain this strange far-field behavior by the experimental inaccuracy in setting the fiber exactly perpendicular to the cell director.

We present a detailed analysis of topological binding and elastic interactions between a long, and micrometer-diameter fiber, and a microsphere in a homogeneously aligned nematic liquid crystal. Both objects are surface treated to produce strong perpendicular anchoring of the nematic liquid crystal. We use the opto-thermal micro-quench of the laser tweezers to produce topological defects with prescribed topological charge, such as pairs of a Saturn ring and an anti-ring, hyperbolic and radial hedgehogs on a fiber, as well as zero-charge loops. We study the entanglement and topological charge interaction between the topological defects of the fiber and sphere and we observe a huge variety of different entanglement topologies and defect-mediated elastic bindings. We explain all observed phenomena with simple topological rule: like topological charges repel each other and opposite topological charges attract. These binding mechanisms not only demonstrate the fascinating topology of nematic colloids, but also open a novel route to the assembly of very complex topological networks of fibers, spheres and other objects for applications in liquid crystal photonics.

Nanoparticles levitated by optical fields under vacuum conditions have applications in quantum science, the study of nanothermodynamics and precision sensing. The existing techniques for loading optical traps require ambient conditions and often involve dispersion in liquids, which can contaminate delicate optics and lead to enhanced optical absorption and heating. Here, we present a clean, dry and generic mechanism for directly loading optical traps at pressures down to 1 mbar, exploiting Laser Induced Acoustic Desorption and allowing for the rapid and efficient trapping of nanoparticles.

The momentum carried by structured light fields exhibits a rich array of surprising features. In this work, we generate transverse orbital angular momentum (TOAM) in the interference field of two parallel and counter-propagating linearly-polarised focused beams, synthesising an array of identical handedness vortices carrying intrinsic TOAM. We explore this structured light field using an optomechanical sensor, consisting of an optically levitated silicon nanorod, whose rotation is a probe of the optical angular momentum, which generates an exceptionally large torque. This simple creation and direct observation of TOAM will have applications in studies of fundamental physics, the optical manipulation of matter and quantum optomechanics.

We study topological defect annihilation on a glass fibre with homeotropic surface anchoring of nematic liquid crystal molecules. The fibre is set parallel to the nematic director of a planar cell with variable thickness and we create pairs of Saturn ring and Saturn anti-ring using the laser tweezers. In thick cells we observe in the whole region of defect separation a Coulomb-like pair attraction with no background force, [Formula: see text] with [Formula: see text]. In cells with thickness comparable to glass fibre diameter, we observe the Coulomb-like attraction only at small separations of the defect pair. For separations larger than the fibre diameter, the pair interaction force is independent of separation. This string-like force is attributed to the formation of defect lines, connecting both monopoles and are indeed visible only on extremely confined fibre, where the fibre diameter is practically equal to the nematic layer thickness. Numerical simulations confirm the formation of defect lines connecting both rings.

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