We demonstrate the coupling of bright and dark surface lattice resonances (SLRs), which are collective Fano resonances in 2D plasmonic crystals. As a result of this coupling, a frequency stop gap in the dispersion relation of SLRs is observed. The different field symmetries of the low- and high-frequency SLR bands lead to pronounced differences in their coupling to free-space radiation. Standing waves of very narrow spectral width compared to localized surface-plasmon resonances are formed at the high-frequency band edge, while subradiant damping onsets at the low-frequency band edge, leading the resonance into darkness. We introduce a coupled-oscillator analog to the plasmonic crystal, which serves to elucidate the physics of the coupled plasmonic resonances and which is used to estimate very high quality factors for SLRs.

We design a quantum simulator for the Majorana equation, a non-Hamiltonian relativistic wave equation that might describe neutrinos and other exotic particles beyond the standard model. Driven by the need of the simulation, we devise a general method for implementing a number of mathematical operations that are unphysical, including charge conjugation, complex conjugation, and time reversal. Furthermore, we describe how to realize the general method in a system of trapped ions. The work opens a new front in quantum simulations.

We describe the hyperboloidal compactification for Teukolsky equations in Kerr spacetime. We include null infinity on the numerical grid by attaching a hyperboloidal layer to a compact domain surrounding the rotating black hole and the orbit of an inspiralling point particle. This technique allows us to study, for the first time, gravitational waveforms from large- and extreme-mass-ratio inspirals in Kerr spacetime extracted at null infinity. Tests and comparisons of our results with previous calculations establish the accuracy and efficiency of the hyperboloidal layer method.

We computationally and experimentally investigate the use of metamaterial resonators as bandpass filters and other components that enable control of guided surface electromagnetic waves. The guided surface electromagnetic wave propagates on a planar Goubau line, launched via a coplanar waveguide coupler with $50\Omega$ impedance. Experimental samples targeted for either microwave or terahertz frequencies are measured and shown to be in excellent agreement with simulations. Metamaterial elements are designed to absorb energy only of the planar Goubau line and yield narrow-band resonances with relatively high quality factors. Two independent configurations of coupled metamaterial elements are demonstrated that modify the otherwise flat transmission spectrum of the planar Goubau line. By physically shunting the capacitive gaps of the coupled metamaterial elements, we demonstrate the potential for a large dynamic range in transmissivity, suggesting the use of this configuration for high-bandwidth terahertz communications.

We further develop an approach to identify the braiding statistics associated to a given fractional quantum Hall state through adiabatic transport of quasiparticles. This approach is based on the notion of adiabatic continuity between quantum Hall states on the torus and simple product states—or patterns—in the thin torus limit, together with a suitable coherent state ansatz for localized quasiholes that respects the modular invariance of the torus. We give a refined and unified account of the application of this method to the Laughlin and Moore-Read states, which may serve as a pedagogical introduction to the nuts and bolts of this technique. Our main result is that the approach is also applicable—without further assumptions—to more complicated non-Abelian states. We demonstrate this in great detail for the level $k=3$ Read-Rezayi state at filling factor $\nu =3/2$. These results may serve as an independent check of other techniques, where the statistics are inferred from conformal block monodromies. Our approach has the benefit of giving rise to intuitive pictures representing the transformation of topological sectors during braiding, and allows for a self-consistent derivation of non-Abelian statistics without heavy mathematical machinery.

Chern insulators are band insulators exhibiting a nonzero Hall conductance but preserving the lattice translational symmetry. We conclusively show that a partially filled Chern insulator at $1/3$ filling exhibits a fractional quantum Hall effect and rule out charge-density-wave states that have not been ruled out by previous studies. By diagonalizing the Hubbard interaction in the flat-band limit of these insulators, we show the following: The system is incompressible and has a 3-fold degenerate ground state whose momenta can be computed by postulating an generalized Pauli principle with no more than 1 particle in 3 consecutive orbitals. The ground-state density is constant, and equal to $1/3$ in momentum space. Excitations of the system are fractional-statistics particles whose total counting matches that of quasiholes in the Laughlin state based on the same generalized Pauli principle. The entanglement spectrum of the state has a clear entanglement gap which seems to remain finite in the thermodynamic limit. The levels below the gap exhibit counting identical to that of Laughlin $1/3$ quasiholes. Both the 3 ground states and excited states exhibit spectral flow upon flux insertion. All the properties above disappear in the trivial state of the insulator—both the many-body energy gap and the entanglement gap close at the phase transition when the single-particle Hamiltonian goes from topologically nontrivial to topologically trivial. These facts clearly show that fractional many-body states are possible in topological insulators.

For several atomistic models of glass formers, at conditions below their glassy-dynamics–onset temperatures, $T_{\mathrm{o}}$, we use importance sampling of trajectory space to study the structure, statistics, and dynamics of excitations responsible for structural relaxation. Excitations are detected in terms of persistent particle displacements of length $a$. At supercooled conditions, for $a$ of the order of or smaller than a particle diameter, we find that excitations are associated with correlated particle motions that are sparse and localized, occupying a volume with an average radius that is temperature-independent and no larger than a few particle diameters. We show that the statistics and dynamics of these excitations are facilitated and hierarchical. Excitation-energy scales grow logarithmically with $a$. Excitations at one point in space facilitate the birth and death of excitations at neighboring locations, and space-time excitation structures are microcosms of heterogeneous dynamics at larger scales. This nature of dynamics becomes increasingly dominant as temperature $T$ is lowered. We show that slowing of dynamics upon decreasing temperature below $T_{\mathrm{o}}$ is the result of a decreasing concentration of excitations and concomitantly growing length scales for dynamical correlations that develop in a hierarchical manner, and further that the structural-relaxation time $\tau$ follows the parabolic law, $\log (\tau /{\tau }_{\mathrm{o}})=J^2(1/T-1/T_{\mathrm{o}}{)}^2$, for $T<T_{\mathrm{o}}$, where $J$, ${\tau }_{\mathrm{o}}$ and $T_{\mathrm{o}}$ can be predicted quantitatively from dynamics at short time scales. Particle motion is facilitated and directional, and we show that this becomes more apparent with decreasing $T$. We show that stringlike motion is a natural consequence of facilitated, hierarchical dynamics.

Several thousand compounds from the Inorganic Crystal Structure Database have been considered as nanograined, sintered-powder thermoelectrics with the high-throughput ab-initio AFLOW framework. Regression analysis unveils that the power factor is positively correlated with both the electronic band gap and the carrier effective mass, and that the probability of having large thermoelectric power factors increases with the increasing number of atoms per primitive cell. Avenues for further investigation are revealed by this work. These avenues include the role of experimental and theoretical databases in the development of novel materials.

The ability to engineer both linear and nonlinear coupling with a mechanical resonator is an important goal for the preparation and investigation of macroscopic mechanical quantum behavior. In this work, a measurement based scheme is presented where linear or square mechanical-displacement coupling can be achieved using the optomechanical interaction that is linearly proportional to the mechanical position. The resulting square-displacement measurement strength is compared to that attainable in the dispersive case that has a direct interaction with the mechanical-displacement squared. An experimental protocol and parameter set are discussed for the generation and observation of non-Gaussian states of motion of the mechanical element.

We demonstrate strong-field ionization from multiple orbitals of excited-state uracil molecules. The molecules are excited to the first bright state by an ultrafast laser pulse in the deep ultraviolet and then ionized with a strong-field laser pulse in the near infrared during ultrafast relaxation back down to the ground state. We measure time- and angle-dependent ion yields for multiple fragments created by strong-field ionization, and interpret the temporally and angularly resolved yields via ab initio electronic structure calculations. We find that the angular distribution for the electron removed from the lowest unoccupied molecular orbital follows the symmetry of the molecular orbital, whereas ionization of the molecule by removing electrons from deeper bound orbitals is more complicated.

We present a quantum optics formalism to study the intensity power broadening of a semiconductor quantum dot interacting with an acoustic-phonon bath and a high-$Q$ microcavity. Power broadening is investigated using a time-convolutionless master equation in the polaron frame, which allows for a nonperturbative treatment of the interaction of the quantum dot with the phonon reservoir. We calculate the full non-Lorentzian photoluminescence (PL) line shapes and numerically extract the intensity linewidths of the quantum-dot exciton and the cavity mode as a function of the pump rate and temperature. For increasing field strengths, multiphonon and multiphoton effects are found to be important, even for phonon-bath temperatures as low as 4 K. We show that the interaction of the quantum dot with the phonon reservoir introduces pronounced features in the power-broadened PL line shape, enabling one to observe clear signatures of electron-phonon scattering. The PL line shapes from cavity pumping and exciton pumping are found to be distinctly different, primarily since the latter is excited through the exciton-phonon reservoir. To help explain the underlying physics of phonon scattering on the power-broadened line shape, an effective phonon Lindblad master equation derived from the full time-convolutionless master equation is introduced; we identify and calculate distinct Lindblad scattering contributions from electron-phonon interactions, including effects such as excitation-induced dephasing, incoherent exciton excitation, and exciton-cavity feeding. Our effective phonon master equation is shown to reproduce the full PL intensity and the phonon-coupling effects very well, suggesting that its general Lindblad form may find widespread use in semiconductor cavity-QED.

We measure the bending energy of double-stranded DNA in the nonlinear (sharply bent) regime. The measurements are obtained from the melting curves of stressed DNA ring molecules. The nonlinear elastic behavior is captured by a single parameter: the critical torque ${\tau }_{\mathrm{c}}$ at which the molecule develops a kink. In this regime, the elastic energy is linear in the kink angle. This phenomenology is the same as for the previously reported case of nicked DNA. For the sequences examined, we find ${\tau }_{\mathrm{c}}=31\mathrm{pN}\times \mathrm{nm}$. This critical torque corresponds to a characteristic energy scale $(\pi /2){\tau }_{\mathrm{c}}=12k{T}_{\mathrm{room}}$ relevant for molecular biology processes associated with DNA bending.

A new paradigm of resistive pulse sensing (Coulter counting) is developed using a liquid bridge in lieu of a solid pore as the sensing aperture, whereby the flexible liquid aperture circumvents the clogging issue of conventional Coulter counters. The electrohydrodynamic bridge is formed between two opposing Taylor cones and stabilized by radial polarization stresses. Passage of a colloidal particle through the upstream conical apex triggers a current oscillation at the resonant frequency of the cone-jet bridge. The relative current change is indicative of the particle-to-jet diameter ratio.

We propose a dynamical theory of market liquidity that predicts that the average supply/demand profile is V shaped and vanishes around the current price. This result is generic, and only relies on mild assumptions about the order flow and on the fact that prices are, to a first approximation, diffusive. This naturally accounts for two striking stylized facts: First, large metaorders have to be fragmented in order to be digested by the liquidity funnel, which leads to a long memory in the sign of the order flow. Second, the anomalously small local liquidity induces a breakdown of the linear response and a diverging impact of small orders, explaining the “square-root” impact law, for which we provide additional empirical support. Finally, we test our arguments quantitatively using a numerical model of order flow based on the same minimal ingredients.

We present an analysis of the potential thermoelectric performance of hole-doped ${\mathrm{Bi}}_2{\mathrm{Se}}_3$, which is commonly considered to show inferior room temperature performance when compared to ${\mathrm{Bi}}_2{\mathrm{Te}}_3$. We find that if the lattice thermal conductivity can be reduced by nanostructuring techniques (as have been applied to ${\mathrm{Bi}}_2{\mathrm{Te}}_3$ in Refs. [W. Xie, X. Tang, Y. Yan, Q. Zhang, and T. M. Tritt, Unique Nanostructures and Enhanced Thermoelectric Performance of Melt-Spun BiSbTe Alloys, Appl. Phys. Lett. 94, 102111 (2009); B. Poudel et al., High-Thermoelectric Performance of Nanostructured Bismuth Antimony Telluride Bulk Alloys, Science 320, 634 (2008).]) the material may show optimized $ZT$ values of unity or more in the 300–500 K temperature range and thus be suitable for cooling and moderate temperature waste heat recovery and thermoelectric solar cell applications. Central to this conclusion are the larger band gap and the relatively heavier valence bands of ${\mathrm{Bi}}_2{\mathrm{Se}}_3$.

If a magnet of microscopic dimensions is brought in close proximity to a superconductor, the quantized nature of their interaction due to the creation of flux quanta in the superconducting system becomes noticeable. Herein, we directly image, via scanning Hall microscopy, the vortex-antivortex pairs in a superconducting film created by micromagnets. The number of antivortices at equilibrium conditions can be changed either by tuning the magnetic moment of the magnets or by annihilation with externally induced vortices. We demonstrate that small ac field excitations shake the antivortices sitting next to the micromagnets whereas no sizable motion is observed for the vortices sitting on top of the magnets, clearly revealing the different mobility of these two vortex species. A metastable state, which is obtained by applying a field after the system has been cooled down below the superconducting transition, shows a complex graded distribution of coexisting vortices and antivortices forming an intertwined critical state.

We propose methods to generate and manipulate vortex dipoles in an atomic Bose-Einstein condensate using Gaussian beams of red- or blue-detuned laser. Vortex dipoles with controlled velocities are shown to be created and launched by a red-detuned beam and by two blue-detuned beams. Critical beam velocities for the vortex nucleation are investigated. The launched vortex dipoles can be trapped, curved, accelerated, and decelerated by using Gaussian laser beams. Collisions between vortex dipoles are demonstrated.

Recent work has highlighted remarkable effects of classical thermal fluctuations in the dipolar spin ice compounds, such as “artificial magnetostatics,” manifesting as Coulombic power-law spin correlations and particles behaving as diffusive “magnetic monopoles.” In this paper, we address quantum spin ice, giving a unifying framework for the study of magnetism of a large class of magnetic compounds with the pyrochlore structure, and, in particular, discuss ${\mathrm{Yb}}_2{\mathrm{Ti}}_2{\mathrm{O}}_7$, and extract its full set of Hamiltonian parameters from high-field inelastic neutron scattering experiments. We show that fluctuations in ${\mathrm{Yb}}_2{\mathrm{Ti}}_2{\mathrm{O}}_7$ are strong, and that the Hamiltonian may support a Coulombic “quantum spin liquid” ground state in low magnetic fields and host an unusual quantum critical point at larger fields. This appears consistent with puzzling features seen in prior experiments on ${\mathrm{Yb}}_2{\mathrm{Ti}}_2{\mathrm{O}}_7$. Thus, ${\mathrm{Yb}}_2{\mathrm{Ti}}_2{\mathrm{O}}_7$ is the first quantum spin liquid candidate for which the Hamiltonian is quantitatively known.

The 2007 discovery of quantized conductance in HgTe quantum wells delivered the field of topological insulators (TIs) its first experimental confirmation. While many three-dimensional TIs have since been identified, HgTe remains the only known two-dimensional system in this class. Difficulty fabricating HgTe quantum wells has, moreover, hampered their widespread use. With the goal of breaking this logjam, we provide a blueprint for stabilizing a robust TI state in a more readily available two-dimensional material—graphene. Using symmetry arguments, density functional theory, and tight-binding simulations, we predict that graphene endowed with certain heavy adatoms realizes a TI with substantial band gap. For indium and thallium, our most promising adatom candidates, a modest 6% coverage produces an estimated gap near 80 K and 240 K, respectively, which should be detectable in transport or spectroscopic measurements. Engineering such a robust topological phase in graphene could pave the way for a new generation of devices for spintronics, ultra-low-dissipation electronics, and quantum information processing.

To maximize average information gain for a classical measurement, all outcomes of an observation must be equally likely. The condition of equally likely outcomes may be enforced in quantum theory by ensuring that the system’s state $\rho$ is maximally different, or complementary, to the measured observable. This requires the ability to perform unitary operations on the state, conditioned on the results of prior measurements. We consider the case of measurement of a component of angular momentum for a qudit (a $D$-dimensional system, with $D=2J+1$, where $J$ is the total angular momentum). For weak or continuous-in-time (i.e., repeated weak) measurements, we show that the complementarity condition ensures an average improvement in the rate of purification of only 2. However, we show that, by choosing the locally optimal control protocol of this type, one can attain the best possible scaling, $O(D^2)$, for the average improvement. For this protocol, the acquisition of information is nearly deterministic. Finally, we contrast these results with those for complementarity-based protocols in a register of qubits.