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We study elastic interactions between colloidal particles and deformation landscapes of undulations in a cholesteric liquid crystal under an electric field applied normal to cholesteric layers. The onset of undulation instability is influenced by the presence of colloidal inclusions and, in turn, layers' undulations mediate the spatial patterning of particle locations. We find that the bending of cholesteric layers around a colloidal particle surface prompts the local nucleation of an undulations lattice at electric fields below the well-defined threshold known for liquid crystals without inclusions, and that the onset of the resulting lattice is locally influenced, both dimensionally and orientationally, by the initial arrangements of colloids defined using laser tweezers. Spherical particles tend to spatially localize in the regions of strong distortions of the cholesteric layers, while colloidal nanowires exhibit an additional preference for multistable alignment offset along various vectors of the undulations lattice. Magnetic rotation of superparamagnetic colloidal particles couples with the locally distorted helical axis and undulating cholesteric layers in a manner that allows for a controlled three-dimensional translation of these particles. These interaction modes lend insight into the physics of liquid crystal structure-colloid elastic interactions, as well as point the way towards guided self-assembly of reconfigurable colloidal composites with potential applications in diffraction optics and photonics.

We explore the dynamics of topological point defects on surfaces of magnetically responsive colloidal microspheres in a uniformly aligned nematic liquid crystal host. We show that pinning of the liquid crystal director to a particle surface with random nanostructured morphology results in unexpected translational dynamics of both particles and topological point defects on their surfaces when subjected to rotating magnetic fields. We characterize and quantify the "stick-slip" motion of defects as a function of field rotation rates as well as temperature, demonstrating the roles played by the competition of elastic forces, surface anchoring, and magnetic torques on the sphere as well as random-surface-mediated pinning of the easy axis of the nematic director on colloidal microspheres. We analyze our findings through their comparison to similar dynamic processes in other branches of science.

Metastable configurations formed by defects, inclusions, elastic deformations and topological solitons in liquid crystals are a promising choice for building photonic crystals and metamaterials with a potential for new optical applications. Local optical modification of the director or introduction of colloidal inclusions into a moderately chiral nematic liquid crystal confined to a homeotropic cell creates localized multistable chiral solitons. Here we induce solitons that "dress" the dispersed spherical particles treated for tangential degenerate boundary conditions, and perform controlled switching of their state using focused optical beams. Two optically switchable distinct metastable states, toron and hopfion, bound to colloidal spheres into structures with different topological charges are investigated. Their structures are examined using Q-tensor based numerical simulations and compared to the profiles reconstructed from the experiments. A topological explanation of observed multistability is constructed.

Nematic and cholesteric liquid crystals are three-dimensional fluids that possess long-range orientational ordering and can support both topological defects and chiral superstructures. Implications of this ordering remain unexplored even for simple dynamic processes such as the ones found in so-called "fall experiments," or motion of a spherical inclusion under the effects of gravity. Here we show that elastic and surface anchoring interactions prompt periodic dynamics of colloidal microparticles in confined cholesterics when gravity acts along the helical axis. We explore elastic interactions between colloidal microparticles and confining surfaces as well as with an aligned ground-state helical structure of cholesterics for different sizes of spheres relative to the cholesteric pitch, demonstrating unexpected departures from Stokes-like behavior at very low Reynolds numbers. We characterize metastable localization of microspheres under the effects of elastic and surface anchoring periodic potential landscapes seen by moving spheres, demonstrating the important roles played by anchoring memory, confinement, and topological defect transformation. These experimental findings are consistent with the results of numerical modeling performed through minimizing the total free energy due to colloidal inclusions at different locations along the helical axis and with respect to the confining substrates. A potential application emerging from this work is colloidal sorting based on particle shapes and sizes.

Particle shape and medium chirality are two key features recently used to control anisotropic colloidal self-assembly and dynamics in liquid crystals. Here, we study magnetically responsive gourd-shaped colloidal particles dispersed in cholesteric liquid crystals with periodicity comparable or smaller than the particle's dimensions. Using magnetic manipulation and optical tweezers, which allow one to position colloids near the confining walls, we measured the elastic repulsive interactions of these particles with confining surfaces and found that separation-dependent particle-wall interaction force is a non-monotonic function of separation and shows oscillatory behavior. We show that gourd-shaped particles in cholesterics reside not on a single sedimentation level, but on multiple long-lived metastable levels separated by a distance comparable to cholesteric periodicity. Finally, we demonstrate three-dimensional laser tweezers assisted assembly of gourd-shaped particles taking advantage of both orientational order and twist periodicity of cholesterics, potentially allowing new forms of orientationally and positionally ordered colloidal organization in these media.

Despite the recent progress in physical control and manipulation of various condensed matter, atomic, and particle systems, including individual atoms and photons, our ability to control topological defects remains limited. Recently, controlled generation, spatial translation, and stretching of topological point and line defects have been achieved using laser tweezers and liquid crystals as model defect-hosting systems. However, many modes of manipulation remain hindered by limitations inherent to optical trapping. To overcome some of these limitations, we integrate holographic optical tweezers with a magnetic manipulation system, which enables fully holonomic manipulation of defects by means of optically and magnetically controllable colloids used as "handles" to transfer forces and torques to various liquid crystal defects. These colloidal handles are magnetically rotated around determined axes and are optically translated along three-dimensional pathways while mechanically attached to defects, which, combined with inducing spatially localized nematic-isotropic phase transitions, allow for geometrically unrestricted control of defects, including previously unrealized modes of noncontact manipulation, such as the twisting of disclination clusters. These manipulation capabilities may allow for probing topological constraints and the nature of defects in unprecedented ways, providing the foundation for a tabletop laboratory to expand our understanding of the role defects play in fields ranging from subatomic particle physics to early-universe cosmology.

Stable optical trapping and manipulation of high-index particles in low-index host media is often impossible due to the dominance of scattering forces over gradient forces. Here we explore optical manipulation in liquid crystalline structured hosts and show that robust optical manipulation of high-index particles, such as GaN nanowires, is enabled by laser-induced distortions in long-range molecular alignment, via coupling of translational and rotational motions due to helicoidal molecular arrangement, or due to elastic repulsive interactions with confining substrates. Anisotropy of the viscoelastic liquid crystal medium and particle shape give rise to a number of robust unconventional trapping capabilities, which we use to characterize defect structures and study rheological properties of various thermotropic liquid crystals.

String theory is the most promising approach to the long-sought unified description of the four forces of nature and the elementary particles, but direct evidence supporting it is lacking. The theory requires six extra spatial dimensions beyond the three that we observe; it is usually supposed that these extra dimensions are curled up into small spaces. This 'compactification' induces 'moduli' fields, which describe the size and shape of the compact dimensions at each point in space-time. These moduli fields generate forces with strengths comparable to gravity, which according to some recent predictions might be detected on length scales of about 100 microm. Here we report a search for gravitational-strength forces using planar oscillators separated by a gap of 108 micro m. No new forces are observed, ruling out a substantial portion of the previously allowed parameter space for the strange and gluon moduli forces, and setting a new upper limit on the range of the string dilaton and radion forces.