Micromechanical resonators, when cooled down to near their ground state, can be used to explore quantum effects such as superposition and entanglement at a macroscopic scale. Previously, it has been proposed to use electronic feedback to cool a high frequency (10 MHz) resonator to near its ground state. In other work, a low frequency resonator was cooled from room temperature to 18 K by passive optical feedback. Additionally, active optical feedback of atomic force microscope cantilevers has been used to modify their response characteristics, and cooling to approximately 2 K has been measured. Here we demonstrate active optical feedback cooling to 135 +/- 15 mK of a micromechanical resonator integrated with a high-quality optical resonator. Additionally, we show that the scheme should be applicable at cryogenic base temperatures, allowing cooling to near the ground state that is required for quantum experiments--near 100 nK for a kHz oscillator.

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-composed of coupled gyroscopes on a lattice-that breaks time-reversal symmetry. The vibrational spectrum displays a sonic gap populated by topologically protected edge modes that 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 demonstrate this functionality in experiment and envision applications of these edge modes to the design of oneway acoustic waveguides.topological mechanics | gyroscopic metamaterial | metamaterial A vast range of mechanical structures, including bridges, covalent glasses, and conventional metamaterials, can be ultimately modeled as networks of masses connected by springs (1-6). Recent studies have revealed that despite its apparent simplicity, this minimal setup is sufficient to construct topologically protected mechanical states (7-11) that mimic the properties of their quantum analogs (12). This follows from the fact that, irrespective of its classic or quantum nature, a periodic material with a gapped spectrum of excitations can display topological behavior as a result of the nontrivial topology of its band structure (13-21).All such mechanical systems, however, are invariant under time reversal because their dynamics are governed by Newton's second law, which, unlike the Schrödinger equation, is second order in time. If time-reversal symmetry is broken, as in recently suggested acoustic structures containing circulating fluids (16), theoretical work (13) has suggested that phononic chiral topological edge states that act as unidirectional waveguides resistant to scattering off impurities could be supported. In this paper, we show that by creating a coupled system of gyroscopes, a "gyroscopic metamaterial," we can produce an effective material with intrinsic time-reversal symmetry breaking. As a result, our gyroscopic metamaterials support topological mechanical modes analogous to quantum Hall systems, which have robust chiral edge states (22)(23)(24). We demonstrate these effects by building a real system of gyroscopes coupled in a honeycomb lattice. Our experiments show long-lived, unidirectional transport along the edge, even in the presence of significant defects. Moreover, our theoretical analysis indicates that direction of edge propagation is controlled both by the gyroscope spin and the geometry of the underlying lattice. As a result, deforming the lattice of gyroscopes allows one to control the edge mode direction, offering unique opportunities for engineering novel materials.Much of the counterintuitive behavior of rapidly spinning objects originates from their large angular momentum, which endows th...

Knots and links have been conjectured to play a fundamental role in a wide range of physical fields, including plasmas and fluids, both quantum and classical. In fluids, the fundamental knottedness-carrying excitations occur in the form of linked and knotted vortex loops, which have been conjectured to exist for over a century. Although they have been the subject of considerable theoretical study, their creation in the laboratory has remained an outstanding experimental goal. Here we report the creation of isolated trefoil vortex knots and pairs of linked vortex rings in water using a new method of accelerating specially shaped hydrofoils. Using a high-speed scanning tomography apparatus, we measure their three-dimensional topological and geometrical evolution in detail. In both cases we observe that the linked vortices stretch themselves and then deform-as dictated by their geometrically determined energy-towards a series of local vortex reconnections. This work establishes the existence and dynamics of knotted vortices in real fluids.

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 antiparallel 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 that 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.helicity | fluid topology | vortex reconnections | superfluid vortices | topological fields

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Knots and links often occur in physical systems, including shaken strands of rope 1 and DNA (ref. 2), as well as the more subtle structure of vortices in fluids 3 and magnetic fields in plasmas 4 . Theories of fluid flows without dissipation predict these tangled structures persist 5 , constraining the evolution of the flow much like a knot tied in a shoelace. This constraint gives rise to a conserved quantity known as helicity 6,7 , o ering both fundamental insights and enticing possibilities for controlling complex flows. However, even small amounts of dissipation allow knots to untie by means of 'cutand-splice' operations known as reconnections 3,4,8-11 . Despite the potentially fundamental role of these reconnections in understanding helicity-and the stability of knotted fields more generally-their e ect is known only for a handful of simple knots 12 . Here we study the evolution of 322 elemental knots and links in the Gross-Pitaevskii model for a superfluid, and find that they universally untie. We observe that the centreline helicity is partially preserved even as the knots untie, a remnant of the perfect helicity conservation predicted for idealized fluids. Moreover, we find that the topological pathways of untying knots have simple descriptions in terms of minimal two-dimensional knot diagrams, and tend to concentrate in states which are twisted in only one direction. These results have direct analogies to previous studies of simple knots in several systems, including DNA recombination 2 and classical fluids 3,12 . This similarity in the geometric and topological evolution suggests there are universal aspects in the behaviour of knots in dissipative fields.Tying a knot has long been a metaphor for creating stability, and for good reason: untangling even a common knotted string requires either scissors or a complicated series of moves. This persistence has important consequences for filamentous physical structures such as DNA, the behaviour of which is altered by knots and links 9,13 . An analogous effect can be seen in physical fields, for example, magnetic fields in plasmas or vortices in fluid flow; in both cases knots never untie in idealized models, giving rise to new conserved quantities 6,14 . At the same time, there are numerous examples in which forcing real (non-ideal) physical systems causes them to become knotted: vortices in classical or superfluid turbulence 15,16 , magnetic fields in the solar corona 4 , and defects in condensed matter phases 10 . This presents a conundrum: why doesn't everything get stuck in a tangled web, much like headphone cords in a pocket 1 ?In all of these systems, 'reconnection events' allow fields to untangle by cutting and splicing together nearby lines/structures ( Fig. 1a; refs 3,4,8-11). As a result, the balance of knottedness, and its fundamental role as a constraint on the evolution of physical systems, depends critically on understanding if and how these mechanisms cause knots to untie.Previous studies of the evolution of knotted fields have been restricted ...

Helicity, a topological measure of the intertwining of vortices in a fluid flow, is a conserved quantity in inviscid fluids but can be dissipated by viscosity in real flows. Despite its relevance across a range of flows, helicity in real fluids remains poorly understood because the entire quantity is challenging to measure. We measured the total helicity of thin-core vortex tubes in water. For helical vortices that are stretched or compressed by a second vortex, we found conservation of total helicity. For an isolated helical vortex, we observed evolution toward and maintenance of a constant helicity state after the dissipation of twist helicity by viscosity. Our results show that helicity can remain constant even in a viscous fluid and provide an improved basis for understanding and manipulating helicity in real flows.

For magnetite spherical nanoparticles, the orientation of the dipole moment in the crystal does not affect the morphology of either zero field or field induced structures. For non-spherical particles however, an interplay between particle shape and direction of the magnetic moment can give rise to unusual behaviors, in particular when the moment is not aligned along a particle symmetry axis. Here we disclose for the first time the unique magnetic properties of hematite cubic particles and show the exact orientation of the cubes' dipole moment. Using a combination of experiments and computer simulations, we show that dipolar hematite cubes self-organize into dipolar chains with morphologies remarkably different from those of spheres, and demonstrate that the emergence of these structures is driven by competing anisotropic interactions caused by the particles' shape anisotropy and their fixed dipole moment. Furthermore, we have analytically identified a specific interplay between energy, and entropy at the microscopic level and found that an unorthodox entropic contribution mediates the organization of particles into the kinked nature of the dipolar chains.