Topology has journeyed from the purely mathematical arena to feature throughout physics.

]]>Author: Manuel Asorey

An old branch of mathematics has paved the way for discovering new phases of matter.

]]>Authors: Carlo Beenakker & Leo Kouwenhoven

Topological matter can host low-energy quasiparticles, which, in a superconductor, are Majorana fermions described by a real wavefunction. The absence of complex phases provides protection for quantum computations based on topological superconductivity.

]]>Author: Sebastian D. Huber

Electronic topological insulators have inspired the design of new mechanical systems that could soon find real-life applications.

]]>Authors: Yaacov E. Kraus & Oded Zilberberg

The topological state of matter depends on its dimension. Remarkably, topological properties of quasiperiodic systems are found to emerge from higher dimensions.

]]>Authors: Ling Lu, John D. Joannopoulos & Marin Soljačić

Optics played a key role in the discovery of geometric phase. It now joins the journey of exploring topological physics, bringing bosonic topological states that equip us with the ability to make perfect photonic devices using imperfect interfaces.

]]>Author: Mark Buchanan

]]>Author: Abigail Klopper

]]>Author: Andreas H. Trabesinger

]]>Author: Iulia Georgescu

]]>Author: Bart Verberck

]]>Author: Andrea Taroni

]]>Author: Frédéric Mila

The topological degeneracy associated with Majorana edge states has been measured in a spin-1/2 chain of cobalt atoms, thereby opening new avenues in low-dimensional quantum magnetism.

]]>Authors: Jeroen Elzerman & Mark Buitelaar

A frequency comb technique used in NMR spectroscopy reveals the dynamics of the nuclear spin bath in self-assembled quantum dots.

]]>Author: Desika Narayanan

When it comes to star formation, dwarf galaxies perform very poorly. A possible explanation for this behaviour involves photoelectric electrons heating the star-forming gas.

]]>Authors: James S. Bennett & Warwick P. Bowen

Radiation pressure noise from squeezed light constrains the precision of sensing devices such as improved gravitational wave interferometers.

]]>Authors: N. Goldman, J. C. Budich & P. Zoller

]]>Authors: Carolyn Meldgin, Ushnish Ray, Philip Russ, David Chen, David M. Ceperley & Brian DeMarco

The disordered Bose–Hubbard model—a paradigm for strongly correlated and disordered bosonic systems—is central to our understanding of quantum phase transitions. Despite extensive theoretical work on the disordered Bose–Hubbard model, little is known about the impact of temperature, the dynamical behaviour of quantum phases, and how equilibrium is affected during quantum phase transitions. These issues are critically important to applications such as quantum annealing and electronics based on quantum phase transitions. Here, we use a quantum quench of disorder in an ultracold lattice gas to dynamically probe the superfluid–Bose glass quantum phase transition at non-zero temperature ( Fig. 1). By measuring excitations generated during the quench, we provide evidence for superfluid puddles in the Bose glass phase and produce a superfluid–Bose glass phase diagram consistent with completely constrained, finite temperature, and equilibrium quantum Monte Carlo simulations. The residual energy from the quench, which is an efficacy measure for optimization through quantum annealing, is unchanged for quench times spanning nearly a hundred tunnelling times.

]]>Authors: Dustin Kleckner, Louis H. Kauffman & William T. M. Irvine

Knots and links often occur in physical systems, including shaken strands of rope and DNA (ref. ), as well as the more subtle structure of vortices in fluids and magnetic fields in plasmas. Theories of fluid flows without dissipation predict these tangled structures persist, 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, offering both fundamental insights and enticing possibilities for controlling complex flows. However, even small amounts of dissipation allow knots to untie by means of ‘cut-and-splice’ operations known as reconnections. Despite the potentially fundamental role of these reconnections in understanding helicity—and the stability of knotted fields more generally—their effect is known only for a handful of simple knots. 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 and classical fluids. This similarity in the geometric and topological evolution suggests there are universal aspects in the behaviour of knots in dissipative fields.

]]>Authors: R. Toskovic, R. van den Berg, A. Spinelli, I. S. Eliens, B. van den Toorn, B. Bryant, J.-S. Caux & A. F. Otte

The ability to manipulate single atoms has opened up the door to constructing interesting and useful quantum structures from the ground up. On the one hand, nanoscale arrangements of magnetic atoms are at the heart of future quantum computing and spintronic devices; on the other hand, they can be used as fundamental building blocks for the realization of textbook many-body quantum models, illustrating key concepts such as quantum phase transitions, topological order or frustration as a function of system size. Here, we use low-temperature scanning tunnelling microscopy to construct arrays of magnetic atoms on a surface, designed to behave like spin-1/2 XXZ Heisenberg chains in a transverse field, for which a quantum phase transition from an antiferromagnetic to a paramagnetic phase is predicted in the thermodynamic limit. Site-resolved measurements on these finite-size realizations reveal a number of sudden ground state changes when the field approaches the critical value, each corresponding to a new domain wall entering the chains. We observe that these state crossings become closer for longer chains, suggesting the onset of critical behaviour. Our results present opportunities for further studies on quantum behaviour of many-body systems, as a function of their size and structural complexity.

]]>Authors: C. Paulsen, S. R. Giblin, E. Lhotel, D. Prabhakaran, G. Balakrishnan, K. Matsuhira & S. T. Bramwell

A non-Ohmic current that grows exponentially with the square root of applied electric field is well known from thermionic field emission (the Schottky effect), electrolytes (the second Wien effect) and semiconductors (the Poole–Frenkel effect). It is a universal signature of the attractive Coulomb force between positive and negative electrical charges, which is revealed as the charges are driven in opposite directions by the force of an applied electric field. Here we apply thermal quenches to spin ice to prepare metastable populations of bound pairs of positive and negative emergent magnetic monopoles at millikelvin temperatures. We find that the application of a magnetic field results in a universal exponential-root field growth of magnetic current, thus confirming the microscopic Coulomb force between the magnetic monopole quasiparticles and establishing a magnetic analogue of the Poole–Frenkel effect. At temperatures above 300 mK, gradual restoration of kinetic monopole equilibria causes the non-Ohmic current to smoothly evolve into the high-field Wien effect for magnetic monopoles, as confirmed by comparison to a recent and rigorous theory of the Wien effect in spin ice. Our results extend the universality of the exponential-root field form into magnetism and illustrate the power of emergent particle kinetics to describe far-from-equilibrium response in complex systems.

]]>Authors: Yun Wu, Lin-Lin Wang, Eundeok Mun, D. D. Johnson, Daixiang Mou, Lunan Huang, Yongbin Lee, S. L. Bud’ko, P. C. Canfield & Adam Kaminski

In topological quantum materials the conduction and valence bands are connected at points or along lines in the momentum space. A number of studies have demonstrated that several materials are indeed Dirac/Weyl semimetals. However, there is still no experimental confirmation of materials with line nodes, in which the Dirac nodes form closed loops in the momentum space. Here we report the discovery of a novel topological structure—Dirac node arcs—in the ultrahigh magnetoresistive material PtSn4 using laser-based angle-resolved photoemission spectroscopy data and density functional theory calculations. Unlike the closed loops of line nodes, the Dirac node arc structure arises owing to the surface states and resembles the Dirac dispersion in graphene that is extended along a short line in the momentum space. We propose that this reported Dirac node arc structure is a novel topological state that provides an exciting platform for studying the exotic properties of Dirac fermions.

]]>Authors: Leonid Levitov & Gregory Falkovich

Quantum-critical strongly correlated electron systems are predicted to feature universal collision-dominated transport resembling that of viscous fluids. However, investigation of these phenomena has been hampered by the lack of known macroscopic signatures of electron viscosity. Here we identify vorticity as such a signature and link it with a readily verifiable striking macroscopic d.c. transport behaviour. Produced by the viscous flow, vorticity can drive electric current against an applied field, resulting in a negative nonlocal voltage. We argue that the latter may play the same role for the viscous regime as zero electrical resistance does for superconductivity. Besides offering a diagnostic that distinguishes viscous transport from ohmic currents, the sign-changing electrical response affords a robust tool for directly measuring the viscosity-to-resistivity ratio. A strongly interacting electron–hole plasma in high-mobility graphene affords a unique link between quantum-critical electron transport and the wealth of fluid mechanics phenomena.

]]>Authors: Kai Hao, Galan Moody, Fengcheng Wu, Chandriker Kavir Dass, Lixiang Xu, Chang-Hsiao Chen, Liuyang Sun, Ming-Yang Li, Lain-Jong Li, Allan H. MacDonald & Xiaoqin Li

In crystals, energy band extrema in momentum space can be identified by a valley index. The internal quantum degree of freedom associated with valley pseudospin indices can act as a useful information carrier, analogous to electronic charge or spin. Interest in valleytronics has been revived in recent years following the discovery of atomically thin materials such as graphene and transition metal dichalcogenides. However, the valley coherence time—a crucial quantity for valley pseudospin manipulation—is difficult to directly probe. In this work, we use two-dimensional coherent spectroscopy to resonantly generate and detect valley coherence of excitons (Coulomb-bound electron–hole pairs) in monolayer WSe2 (refs ,). The imposed valley coherence persists for approximately one hundred femtoseconds. We propose that the electron–hole exchange interaction provides an important decoherence mechanism in addition to exciton population recombination. This work provides critical insight into the requirements and strategies for optical manipulation of the valley pseudospin for future valleytronics applications.

]]>Authors: Jeremy B. Clark, Florent Lecocq, Raymond W. Simmonds, José Aumentado & John D. Teufel

In quantum-enhanced sensing, non-classical states are used to improve the sensitivity of a measurement. Squeezed light, in particular, has proved a useful resource in enhanced mechanical displacement sensing, although the fundamental limit to this enhancement due to the Heisenberg uncertainty principle has not been encountered experimentally. Here we use a microwave cavity optomechanical system to observe the squeezing-dependent radiation pressure noise that necessarily accompanies any quantum enhancement of the measurement precision and ultimately limits the measurement noise performance. By increasing the measurement strength so that radiation pressure forces dominate the thermal motion of the mechanical oscillator, we exploit the optomechanical interaction to implement an efficient quantum nondemolition measurement of the squeezed light. Thus, our results show how the mechanical oscillator improves the measurement of non-classical light, just as non-classical light enhances the measurement of the motion.

]]>Authors: A. M. Waeber, M. Hopkinson, I. Farrer, D. A. Ritchie, J. Nilsson, R. M. Stevenson, A. J. Bennett, A. J. Shields, G. Burkard, A. I. Tartakovskii, M. S. Skolnick & E. A. Chekhovich

One of the key challenges in spectroscopy is the inhomogeneous broadening that masks the homogeneous spectral lineshape and the underlying coherent dynamics. Techniques such as four-wave mixing and spectral hole-burning are used in optical spectroscopy, and spin-echo in nuclear magnetic resonance (NMR). However, the high-power pulses used in spin-echo and other sequences often create spurious dynamics obscuring the subtle spin correlations important for quantum technologies. Here we develop NMR techniques to probe the correlation times of the fluctuations in a nuclear spin bath of individual quantum dots, using frequency-comb excitation, allowing for the homogeneous NMR lineshapes to be measured without high-power pulses. We find nuclear spin correlation times exceeding one second in self-assembled InGaAs quantum dots—four orders of magnitude longer than in strain-free III–V semiconductors. This observed freezing of the nuclear spin fluctuations suggests ways of designing quantum dot spin qubits with a well-understood, highly stable nuclear spin bath.

]]>Authors: Michael Coey, Karl Ackland, Munuswamy Venkatesan & Siddhartha Sen

The magnetism of nanoparticles and thin films of wide-bandgap oxides that include no magnetic cations is an unsolved puzzle. Progress has been hampered by both the irreproducibility of much of the experimental data, and the lack of any generally accepted theoretical explanation. The characteristic signature is a virtually anhysteretic, temperature-independent magnetization curve that saturates in an applied field that is several orders of magnitude greater than the magnetization. It would seem as if a tiny volume fraction, ≲0.1%, of the samples is magnetic and that the energy scale is unusually high for spin magnetism. Here we investigate the effect of dispersing 4 nm CeO2 nanoparticles with powders of γAl2O3, sugar or latex microspheres. The saturation magnetization, Ms ≍ 60 A m−1 for compact samples, is maximized by 1 wt% lanthanum doping. Dispersing the CeO2 nanopowder reduces its magnetic moment by up to an order of magnitude, and there is a characteristic length scale of order 100 nm for the magnetism to appear in CeO2 nanoparticle clusters. The phenomenon is explained in terms of a giant orbital paramagnetism that appears in coherent mesoscopic domains due to resonant interaction with zero-point fluctuations of the vacuum electromagnetic field. The theory explains the observed temperature-independent magnetization curve and its doping and dispersion dependence, based on a length scale of 300 nm that corresponds to the wavelength of a maximum in the ultraviolet absorption spectrum of the magnetic CeO2 nanoparticles. The coherent domains occupy roughly 10% of the sample volume.

]]>Authors: Krishna Neupane, Ajay P. Manuel & Michael T. Woodside

Protein folding features a diffusive search over a multidimensional energy landscape in conformational space for the minimum-energy structure. Experiments, however, are usually interpreted in terms of a one-dimensional (1D) projection of the full landscape onto a practical reaction coordinate. Although simulations have shown that folding kinetics can be described well by diffusion over a 1D projection, 1D approximations have not yet been fully validated experimentally. We used folding trajectories of single molecules held under tension in optical tweezers to compare the conditional probability of being on a transition path, calculated from the trajectory, with the prediction for ideal 1D diffusion over the measured 1D landscape, calculated from committor statistics. We found good agreement for the protein PrP (refs ,) and for one of the structural transitions in a leucine-zipper coiled-coil, but not for a second transition in the coiled-coil, owing to poor reaction-coordinate quality. These results show that 1D descriptions of folding can indeed be good, even for complex tertiary structures. More fundamentally, they also provide a fully experimental validation of the basic physical picture of folding as diffusion over a landscape.

]]>Authors: Eva M. Schmid, Matthew H. Bakalar, Kaushik Choudhuri, Julian Weichsel, Hyoung Sook Ann, Phillip L. Geissler, Michael L. Dustin & Daniel A. Fletcher

]]>Authors: Sebastian Golde, Thomas Palberg & Hans Joachim Schöpe

]]>Author: R. Betti & O. A. Hurricane

]]>Author: J. Ongena, R. Koch, R. Wolf & H. Zohm

]]>Author: Philip Ball

Some concepts are useful but difficult to quantify, as Philip Ball illustrates with the property of hydrophobicity.

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