One-dimensional topological superconductors are known to host Majorana zero modes at domain walls terminating the topological phase. Their non-Abelian nature allows for processing quantum information by braiding operations that are insensitive to local perturbations, making Majorana zero modes a promising platform for topological quantum computation. Motivated by the ultimate goal of executing quantum-information processing on a finite time scale, we study domain walls moving at a constant velocity. We exploit an effective Lorentz invariance of the Hamiltonian to obtain an exact solution of the associated quasiparticle spectrum and wave functions for arbitrary velocities. Essential features of the solution have a natural interpretation in terms of the familiar relativistic effects of Lorentz contraction and time dilation. We find that the Majorana zero modes remain stable as long as the domain wall moves at subluminal velocities with respect to the effective speed of light of the system. However, the Majorana bound state dissolves into a continuous quasiparticle spectrum after the domain wall propagates at luminal or even superluminal velocities. This relativistic catastrophe implies that there is an upper limit for possible braiding frequencies even in a perfectly clean system with an arbitrarily large topological gap. We also exploit our exact solution to consider domain walls moving past static impurities present in the system.

Three-dimensional (3D) topological superconductors (TScs) protected by time-reversal ($\mathcal{T}$) symmetry are characterized by gapless Majorana cones on their surface. Free-fermion phases with this symmetry (class DIII) are indexed by an integer $\nu$, of which $\nu =1$ is realized by the $B$ phase of superfluid ${}^3\mathrm{He}$. Previously, it was believed that the surface must be gapless unless time-reversal symmetry is broken. Here, we argue that a fully symmetric and gapped surface is possible in the presence of strong interactions, if a special type of topological order appears on the surface. The topological order realizes $\mathcal{T}$ symmetry in an anomalous way, one that is impossible to achieve in purely two dimensions. For odd $\nu \mathrm{TScs}$, the surface topological order must be non-Abelian. We propose the simplest non-Abelian topological order that contains electronlike excitations, $\mathrm{SO}(3{)}_6$, with four quasiparticles, as a candidate surface state. Remarkably, this theory has a hidden $\mathcal{T}$ invariance that, however, is broken in any two-dimensional realization. By explicitly constructing an exactly soluble Walker-Wang model, we show that it can be realized at the surface of a short-ranged entangled 3D fermionic phase protected by $\mathcal{T}$ symmetry, with bulk electrons transforming as Kramers pairs, i.e. ${\mathcal{T}}^2=-1$ under time reversal. We also propose an Abelian theory, the semion-fermion topological order, to realize an even $\nu \mathrm{TSc}$ surface, for which an explicit model is derived using a coupled-layer construction. We argue that this is related to the $\nu =2\mathrm{TSc}$, and we use this to build candidate surface topological orders for $\nu =4$ and $\nu =8\mathrm{TScs}$. The latter is equivalent to the three-fermion state, which is the surface topological order of a ${\mathbb{Z}}_2$ bosonic topological phase protected by $\mathcal{T}$ invariance. One particular consequence of this equivalence is that a $\nu =16\mathrm{TSc}$ admits a trivially gapped $\mathcal{T}$-symmetric surface.

We report new results of Bose-Einstein condensation of polaritons in specially designed microcavities with a very high quality factor, on the order of ${10}^6$, giving polariton lifetimes of the order of 100 ps. When the polaritons are created with an incoherent pump, a dissipationless, coherent flow of the polaritons occurs over hundreds of microns, which increases as density increases. At high density, this flow is suddenly stopped, and the gas becomes trapped in a local potential minimum, with strong coherence.

Ratchets are devices that are able to rectify an otherwise oscillatory behavior by exploiting an asymmetry of the system. In rocking ratchets, the asymmetry is induced through a proper choice of external forces and modulations of nonlinear symmetric potentials. The ratchet currents thus obtained in systems as different as semiconductors, Josephson junctions, optical lattices, or ferrofluids show a set of universal features. A satisfactory explanation for them has challenged theorists for decades, and so far, we still lack a general theory of this phenomenon. Here, we provide such a theory by exploring—through functional analysis—the constraints that the simple assumption of time-shift invariance of the ratchet current imposes on its dependence on the external drivings. Because the derivation is based on so general a principle, the resulting expression is valid irrespective of the details and the nature of the physical systems to which it is applied, and of whether they are classical, quantum, or stochastic. The theory also explains deviations observed from universality under special conditions and allows us to make predictions of phenomena not yet observed in any experiment or simulation.

Adiabatic quantum computation (AQC) has been lauded for its inherent robustness to control imperfections and relaxation effects. A considerable body of previous work, however, has shown AQC to be acutely sensitive to noise that causes excitations from the adiabatically evolving ground state. In this paper, we develop techniques to mitigate such noise, and then we point out and analyze some obstacles to further progress. First, we examine two known techniques that leverage quantum error-detecting codes to suppress noise and show that they are intimately related and may be analyzed within the same formalism. Next, we analyze the effectiveness of such error-suppression techniques in AQC, identify critical constraints on their performance, and conclude that large-scale, fault-tolerant AQC will require error correction, not merely suppression. Finally, we study the consequences of encoding AQC in quantum stabilizer codes and discover that generic AQC problem Hamiltonians rapidly convert physical errors into uncorrectable logical errors. We present several techniques to remedy this problem, but all of them require unphysical resources, suggesting that the adiabatic model of quantum computation may be fundamentally incompatible with stabilizer quantum error correction.

Stromatolites can grow under the influence of microbial processes, but it is often unclear whether and how the macroscopic morphology of these rocks records biological processes. Conical stromatolites, which formed in the absence of sedimentation, provide a comparatively simple record of the interplay between microbial growth and lithification. Here, we show that the dynamics shaping conical stromatolites result from diffusive gradients within the overlying microbial mat. These gradients cause minerals to precipitate faster in regions of high curvature, resulting in measurable properties of the shapes of stromatolite laminas. This model allows us to estimate the thickness of ancient stromatolite-forming mats to be approximately $1\mathrm{mm}$, consistent with modern systems. Proceeding from the assumption that the ubiquitous process of diffusion is recorded in the translating form of a stromatolite, we derive the shape of a diffusion-driven stromatolite. The conical morphology—a distinctive feature of stromatolites growing in the absence of sedimentation—arises from these dynamics. This form is quantitatively consistent with the shape of conical stromatolites that grew for more than $2.9\times {10}^9$ yrs of Earth history.

Active electromagnetic cloaking uses an array of elementary sources to cancel the scattered fields created by an object. An active interior cloak does this by placing the sources along the boundary of the object. This process can be thought of as introducing a discontinuity in the field to cancel out the scattered field by the object. Here, an experimental version of a thin active cloak at microwave frequencies is demonstrated for an aluminum cylinder with a radius of $0.56\lambda$. The cloak consists of a 12-element magnetic-dipole array. By controlling the weights of the current on each element of the array, the scattering off of the cylinder is reduced in the backward and forward directions. The ability to disguise the aluminum cylinder as another object by varying the weights of the dipole array is also demonstrated. Finally, potential ways of overcoming the constraint of requiring a priori knowledge of the incident field leading to camouflaging-type behavior are discussed.

We present a powerful and versatile technique that enables exquisite spatial and temporal control over local solution chemistry in microfluidic devices. Using a microscope and a UV lamp, we use projection lithography to photopolymerize thin ($10–25\mu \mathrm{m}$) hydrogel membrane “microwindows” (HMMs) into standard microfluidic devices. These microwindows are permeable to solute and solvent diffusion and to electric fields, yet act as rigid walls from the standpoint of fluid flow. Reservoirs of solution may thus be rapidly imposed, switched, and maintained on one side of a HMM using standard microfluidic techniques, provoking changes in solution conditions on the other side without active mixing, stirring, or diluting. We highlight three paradigmatic experimental capabilities enabled by HMMs: (1) rapid dialysis and swapping of solute and/or solvent, (2) stable and convection-free localized concentration gradients, and (3) local electric permeability. The functional versatility of hydrogel microwindow membranes, coupled with the ease and speed of their fabrication and integration into simple microchannels or multilayer devices, will open a variety of novel applications and studies in a broad range of fields.

We investigate lasing action in aligned nitrogen molecular ions ($\mathrm{N}_2{}^{+}$) produced in an intense laser field. We find that, besides the population inversion between the ${\mathrm{B}}^2\Sigma _u{}^{+}-{\mathrm{X}}^2\Sigma _g{}^{+}$ states, which is responsible for the observed simulated amplification of a seed pulse, a rotational wave packet in the ground vibrational state ($v=0$) of the excited electronic ${\mathrm{B}}^2\Sigma _u{}^{+}$ state has been created in $\mathrm{N}_2{}^{+}$. The rotational coherence can faithfully encode its characteristics into the amplified seed pulses, enabling reconstruction of rotational wave packets of molecules in a single-shot detection manner from the frequency-resolved laser spectrum. Our results suggest that the air laser can potentially provide a promising tool for remote characterization of coherent molecular rotational wave packets.

The ability to transport energy is a fundamental property of the two-dimensional Dirac fermions in graphene. Electronic thermal transport in this system is relatively unexplored and is expected to show unique fundamental properties and to play an important role in future applications of graphene, including optoelectronics, plasmonics, and ultrasensitive bolometry. Here, we present measurements of bipolar thermal conductances due to electron diffusion and electron-phonon coupling and infer the electronic specific heat, with a minimum value of $10k_B$ (${10}^{-22}\mathrm{J}/\mathrm{K}$) per square micron. We test the validity of the Wiedemann-Franz law and find that the Lorenz number equals $1.32\times ({\pi }^2/3)(k_B/e{)}^2$. The electron-phonon thermal conductance has a temperature power law $T^2$ at high doping levels, and the coupling parameter is consistent with recent theory, indicating its enhancement by impurity scattering. We demonstrate control of the thermal conductance by electrical gating and by suppressing the diffusion channel using NbTiN superconducting electrodes, which sets the stage for future graphene-based single-microwave photon detection.

In this theoretical study, we analyze quantum walks on complex networks, which model network-based processes ranging from quantum computing to biology and even sociology. Specifically, we analytically relate the average long-time probability distribution for the location of a unitary quantum walker to that of a corresponding classical walker. The distribution of the classical walker is proportional to the distribution of degrees, which measures the connectivity of the network nodes and underlies many methods for analyzing classical networks, including website ranking. The quantum distribution becomes exactly equal to the classical distribution when the walk has zero energy, and at higher energies, the difference, the so-called quantumness, is bounded by the energy of the initial state. We give an example for which the quantumness equals a Rényi entropy of the normalized weighted degrees, guiding us to regimes for which the classical degree-dependent result is recovered and others for which quantum effects dominate.

Single quantum dots are solid-state emitters that mimic two-level atoms but with a highly enhanced spontaneous emission rate. A single quantum dot is the basis for a potentially excellent single-photon source. One outstanding problem is that there is considerable noise in the emission frequency, making it very difficult to couple the quantum dot to another quantum system. We solve this problem here with a dynamic feedback technique that locks the quantum-dot emission frequency to a reference. The incoherent scattering (resonance fluorescence) represents the single-photon output, whereas the coherent scattering (Rayleigh scattering) is used for the feedback control. The fluctuations in emission frequency are reduced to 20 MHz, just approximately $5\%$ of the quantum-dot optical linewidth, even over several hours. By eliminating the $1/f$-like noise, the relative fluctuations in quantum-dot noise power are reduced to approximately ${10}^{-5}$ at low frequency. Under these conditions, the antibunching dip in the resonance fluorescence is described extremely well by the two-level atom result. The technique represents a way of removing charge noise from a quantum device.

We discuss the global scattering response of invisibility cloaks over the entire electromagnetic spectrum, from static to very high frequencies. Based on linearity, causality, and energy conservation, we show that the total extinction and scattering, integrated over all wavelengths, of any linear, passive, causal, and nondiamagnetic cloak, necessarily increase compared to the uncloaked case. In light of this general principle, we provide a quantitative measure to compare the global performance of different cloaking techniques and we discuss solutions to minimize the global scattering signature of an object using thin, superconducting shells. Our results provide important physical insights on how invisibility cloaks operate and affect the global scattering of an object, suggesting ways to defeat countermeasures aimed at detecting cloaked objects using short impinging pulses.

We experimentally demonstrate that a thin (approximately $150\mathrm{\text{−}}\mathrm{nm}$) film of vanadium dioxide (${\mathrm{VO}}_2$) deposited on sapphire has an anomalous thermal emittance profile when heated, which arises because of the optical interaction between the film and the substrate when the ${\mathrm{VO}}_2$ is at an intermediate state of its insulator-metal transition (IMT). Within the IMT region, the ${\mathrm{VO}}_2$ film comprises nanoscale islands of the metal and dielectric phases and can thus be viewed as a natural, disordered metamaterial. This structure displays “perfect” blackbodylike thermal emissivity over a narrow wavelength range (approximately $40{\mathrm{cm}}^{-1}$), surpassing the emissivity of our black-soot reference. We observe large broadband negative differential thermal emittance over a $>10°\mathrm{C}$ range: Upon heating, the ${\mathrm{VO}}_2\mathrm{\text{−}}\mathrm{\text{sapphire}}$ structure emits less thermal radiation and appears colder on an infrared camera. Our experimental approach allows for a direct measurement and extraction of wavelength- and temperature-dependent thermal emittance. We anticipate that emissivity engineering with thin-film geometries comprising ${\mathrm{VO}}_2$ and other thermochromic materials will find applications in infrared camouflage, thermal regulation, and infrared tagging and labeling.

We obtain generalizations of the Kelvin-Planck, Clausius, and Carnot statements of the second law of thermodynamics for situations involving information processing. To this end, we consider an information reservoir (representing, e.g., a memory device) alongside the heat and work reservoirs that appear in traditional thermodynamic analyses. We derive our results within an inclusive framework in which all participating elements—the system or device of interest, together with the heat, work, and information reservoirs—are modeled explicitly by a time-independent, classical Hamiltonian. We place particular emphasis on the limits and assumptions under which cyclic motion of the device of interest emerges from its interactions with work, heat, and information reservoirs.

Droplet pinch off, which occurs when a drop of liquid detaches from a capillary, can be strongly modified in the presence of polymers, giving rise to long and slender filaments that thin slowly in time. However, little is known experimentally about the molecular conformations of the polymers in the filament itself. Since the thinning dynamics of these filaments can be used to extract macroscopic quantities of interest such as the elongational viscosity of polymer solutions, which is of importance in a variety of physical processes (electrospinning, spraying, or drag reduction), the link with the molecular scale dynamics would be an important step towards understanding the extensional properties of such solutions. We show here, experimentally, that the polymers are highly extended within this filament region and that the distribution of these extensions is stationary in time. We then determine the elongational viscosity from the full filament dynamics. Such a determination turns out to be consistent with the polymer extensions observed and also consistent with simple models of polymer elongational viscosities. The direct observation of stretched macromolecules within such suspended liquid filaments suggests that these filaments may be useful for preparing polymeric materials with specific anisotropy or for optical screening of biopolymers such as DNA.

A laser generates light through stimulated emission of radiation and requires population inversion. Quantum interference can yield lasing without inversion. However, such phase-sensitive quantum amplification still requires some atomic population in the excited state. Here, we present a new kind of quantum amplifier based on collective superradiant emission which does not need any population in the excited state. We show that parametric resonance between the driving (e.g., infrared) field and collective superradiant oscillations of the atomic polarization can yield light amplification at high (e.g., XUV) frequencies. To achieve gain, one must suppress a time-dependent Stark shift caused by the driving field. The resulting superradiant amplifier is many orders of magnitude more efficient than the usual nonlinear multiphoton excitation and holds promise for a new kind of generator of high-frequency coherent radiation. In addition to a detailed analytical analysis, confirmed by numerical simulations, we provide a physically appealing explanation of the quantum amplification by superradiant emission of radiation (QASER) operation in terms of coupled classical oscillators. We also present an experiment that demonstrates the QASER amplification mechanism in an electronic circuit, which, to the best of our knowledge, is the first experimental demonstration of the difference combination resonance.

We report a method for nanometer-scale pulsed nuclear magnetic resonance imaging and spectroscopy. Periodic radio-frequency pulses are used to create temporal correlations in the statistical polarization of a solid organic sample. The spin density is spatially encoded by applying a series of intense magnetic field gradient pulses generated by focusing electric current through a nanometer-scale metal constriction. We demonstrate this technique using a silicon nanowire mechanical oscillator as a magnetic resonance sensor to image ${}^1\mathrm{H}$ spins in a polystyrene sample. We obtain a two-dimensional projection of the sample proton density with approximately 10-nm resolution.