Necessary and sufficient conditions for the equivalence of arbitrary $n$-qubit pure quantum states under local unitary (LU) operations are derived. First, an easily computable standard form for multipartite states is introduced. Two generic states are shown to be LU equivalent iff their standard forms coincide. The LU-equivalence problem for nongeneric states is solved by presenting a systematic method to determine the LU operators (if they exist) which interconvert the two states.

By using the highly improved staggered quark formalism to handle charm, strange, and light valence quarks in full lattice QCD, and NRQCD to handle bottom valence quarks, we are able to determine accurately ratios of the $B$ meson vector-pseudoscalar mass splittings, in particular, $[m(B_c^{*})-m(B_c)]/[m(B_s^{*})-m(B_s)]$. We find this ratio to be 1.15(15), showing the “light” quark mass dependence of this splitting to be very small. Hence we predict $m(B_c^{*})=6.330(7)(2)(6)\mathrm{GeV}$, where the first two errors are from the lattice calculation and the third from existing experiment. This is the most accurate prediction of a gold-plated hadron mass from lattice QCD to date.

A solid object impacting on liquid creates a liquid jet due to the collapse of the impact cavity. Using visualization experiments with smoke particles and multiscale simulations, we show that in addition, a high-speed air jet is pushed out of the cavity. Despite an impact velocity of only $1\mathrm{m}/\mathrm{s}$, this air jet attains supersonic speeds already when the cavity is slightly larger than 1 mm in diameter. The structure of the air flow closely resembles that of compressible flow through a nozzle—with the key difference that here the “nozzle” is a liquid cavity shrinking rapidly in time.

We report on conductance measurements in carbon nanotube based double quantum dots connected to two normal electrodes and a central superconducting finger. By operating our devices as beam splitters, we provide evidence for crossed Andreev reflections tunable in situ. This opens an avenue to more sophisticated quantum opticslike experiments with spin entangled electrons.

We report the generation of entanglement between two individual ${}^{87}\mathrm{Rb}$ atoms in hyperfine ground states $|F=1,M=1⟩$ and $|F=2,M=2⟩$ which are held in two optical tweezers separated by $4\mu \mathrm{m}$. Our scheme relies on the Rydberg blockade effect which prevents the simultaneous excitation of the two atoms to a Rydberg state. The entangled state is generated in about 200 ns using pulsed two-photon excitation. We quantify the entanglement by applying global Raman rotations on both atoms. We measure that 61% of the initial pairs of atoms are still present at the end of the entangling sequence. These pairs are in the target entangled state with a fidelity of 0.75.

We present the first demonstration of a CNOT gate between two individually addressed neutral atoms. Our implementation of the CNOT uses Rydberg blockade interactions between neutral atoms held in optical traps separated by $>8\mu \mathrm{m}$. Using two different gate protocols we measure CNOT fidelities of $F=0.73$ and 0.72 based on truth table probabilities. The gate was used to generate Bell states with fidelity $F=0.48\pm 0.06$. After correcting for atom loss we obtain an a posteriori entanglement fidelity of $F=0.58$.

We present theoretical and experimental results on the mechanical damping of an atomic force microscope cantilever strongly coupled to a self-assembled InAs quantum dot. When the cantilever oscillation amplitude is large, its motion dominates the charge dynamics of the dot which in turn leads to nonlinear, amplitude-dependent damping of the cantilever. We observe highly asymmetric line shapes of Coulomb blockade peaks in the damping that reflect the degeneracy of energy levels on the dot. Furthermore, we predict that excited state spectroscopy is possible by studying the damping versus oscillation amplitude, in analogy with varying the amplitude of an ac gate voltage.

Novel simple properties of the monopole component of effective nucleon-nucleon interactions are presented, leading to the so-called monopole-based universal interaction. Shell structures are shown to change as functions of $N$ and $Z$, consistent with experiments. Some key cases of this shell evolution are discussed, clarifying the effects of central and tensor forces. The validity of the present tensor force is examined in terms of the low-momentum interaction $V_{\mathrm{lowk}}$ and the $Q_{\mathrm{box}}$ formalism.

A defect or disclination line, prepared at a designed place in a nematic liquid crystal, is used as a template for realizing a microwire directly connected to the electrodes with an accuracy of a few $\mu \mathrm{m}$. The line attracts and traps silica particles, until self-assembling a complete micronecklace. We then fix the colloids in the necklace by means of pyrrole electropolymerization. The process may be extended to connect many microwires simultaneously. This provides a new route for manufacturing automatic 3D connections, which could be important for electronic applications as Moore’s law now seems to reach some limit in 2D.

A magnetometer using spin-polarized K and ${}^3\mathrm{He}$ atoms occupying the same volume is used to search for anomalous nuclear spin-dependent forces generated by a separate ${}^3\mathrm{He}$ spin source. We measure changes in the ${}^3\mathrm{He}$ spin precession frequency with a resolution of 18 pHz and constrain anomalous spin forces between neutrons to be less than $2\times {10}^{-8}$ of their magnetic or less than $2\times {10}^{-3}$ of their gravitational interactions on a length scale of 50 cm. We present new limits on neutron coupling to light pseudoscalar and vector particles, including torsion, and constraints on recently proposed models involving unparticles and spontaneous breaking of Lorentz symmetry.

The wave-particle duality of massive objects is a cornerstone of quantum physics and a key property of many modern tools such as electron microscopy, neutron diffraction or atom interferometry. Here we report on the first experimental demonstration of quantum interference lithography with complex molecules. Molecular matter-wave interference patterns are deposited onto a reconstructed Si(111) $7\times 7$ surface and imaged using scanning tunneling microscopy. Thereby both the particle and the quantum wave character of the molecules can be visualized in one and the same image. This new approach to nanolithography therefore also represents a sensitive new detection scheme for quantum interference experiments.

Time-dependent external perturbations provide powerful probes of the function of molecular machines. Here we study biological proton pumping in an oscillating electric field. The protein cytochrome oxidase is the main energy transducer in aerobic life, converting chemical energy into an electric potential by pumping protons across a membrane. With the help of master-equation descriptions that recover the key thermodynamic and kinetic properties of this biological “fuel cell,” we show that the proton pumping efficiency and the electronic currents in steady state depend significantly on the frequency and amplitude of the applied field, allowing us to distinguish between different microscopic mechanisms of the machine. A spectral analysis reveals dominant reaction steps consistent with an electron-gated pumping mechanism.

A novel instrument allows for the first time measurements of the lateral adhesion forces at a solid-liquid interface, $f_{\parallel }$, in a way that is decoupled from the normal forces, $f_{\perp }$. We use it to measure how $f_{\parallel }$ between a drop and a surface is influenced by different $f_{\perp }$ and different histories of drop resting periods on the surface prior to sliding, $t_{\mathrm{rest}}$. The variation of $f_{\parallel }$ with $t_{\mathrm{rest}}$ is similar for different $f_{\perp }$ and always plateaus as $t_{\mathrm{rest}}\to \infty$. We show that the $f_{\parallel }$ plateau value is higher when $f_{\perp }$ is lower. This seemingly counterintuitive result is in agreement with recent theories.

A single two-dimensinoal Dirac fermion state has been recently observed on the surface of the topological insulator ${\mathrm{Bi}}_2{\mathrm{Te}}_3$ by angle-resolved photoemission spectroscopy. We study the surface band structure using $k·p$ theory and find an unconventional hexagonal warping term, which is the counterpart of cubic Dresselhaus spin-orbit coupling in rhombohedral structures. We show that this hexagonal warping term naturally explains the observed hexagonal snowflake Fermi surface. The strength of hexagonal warping is characterized by a single parameter, which is extracted from the size of the Fermi surface. We predict a number of testable signatures of hexagonal warping in spectroscopy experiments on ${\mathrm{Bi}}_2{\mathrm{Te}}_3$. We also explore the possibility of a spin-density wave due to strong nesting of the Fermi surface.

A unique feature of surface plasmon polaritons (SPPs) is that their in-plane momentum is larger than the momentum of free-propagating photons of the same energy. Therefore, it is believed that they can be excited only by evanescent fields created by total internal reflection or by local scattering. Here, we provide the first demonstration of free-space excitation of surface plasmons by means of nonlinear four-wave mixing. The process involves the vectorial addition of the momenta of three incident photons, making it possible to penetrate the light cone and directly couple to the SPP dispersion curve. Using this technique, surface plasmons can be launched on any metal surface by simply overlapping two beams of laser pulses incident from resonant directions. The excitation scheme is also applicable to other bound modes, such as waveguide modes, surface phonon polaritons, and excitations of 2D electron gases.

We report that the $(\mathrm{Ba},\mathrm{K}){\mathrm{Fe}}_2{\mathrm{As}}_2$ superconductor (transition temperature, $T_c\sim 38\mathrm{K}$) has an inverse iron isotope coefficient ${\alpha }_{\mathrm{Fe}}=-0.18(3)$ (where $T_c\sim M^{-\alpha \mathrm{Fe}}$ and $M$ is the iron isotope mass); i.e., the sample containing the large iron isotope mass depicts a higher $T_c$. Systematic inverse shifts in $T_c$ were clearly observed between the samples using three types of Fe isotopes (${}^{54}\mathrm{Fe}$, natural Fe, and ${}^{57}\mathrm{Fe}$). This indicates the first evidence of the inverse isotope effect in high-$T_c$ superconductors. This anomalous mass dependence on $T_c$ implies an exotic coupling mechanism in Fe-based superconductors.

Availability of highly reactive halogen ions at the surface of aerosols has tremendous implications for the atmospheric chemistry. Yet neither simulations, experiments, nor existing theories are able to provide a fully consistent description of the electrolyte-air interface. In this Letter a new theory is proposed which allows us to explicitly calculate the ionic density profiles, the surface tension, and the electrostatic potential difference across the solution-air interface. Predictions of the theory are compared to experiments and are found to be in excellent agreement. The theory also sheds new light on one of the oldest puzzles of physical chemistry—the Hofmeister effect.

The diffuse galactic $\gamma$-ray emission is produced by cosmic rays (CRs) interacting with the interstellar gas and radiation field. Measurements by the Energetic Gamma-Ray Experiment Telescope (EGRET) instrument on the Compton Gamma-Ray Observatory indicated excess $\gamma$-ray emission $\gtrsim 1\mathrm{GeV}$ relative to diffuse galactic $\gamma$-ray emission models consistent with directly measured CR spectra (the so-called “EGRET GeV excess”). The Large Area Telescope (LAT) instrument on the Fermi Gamma-Ray Space Telescope has measured the diffuse $\gamma$-ray emission with improved sensitivity and resolution compared to EGRET. We report on LAT measurements for energies 100 MeV to 10 GeV and galactic latitudes $10°\le |b|\le 20°$. The LAT spectrum for this region of the sky is well reproduced by a diffuse galactic $\gamma$-ray emission model that is consistent with local CR spectra and inconsistent with the EGRET GeV excess.

New physics models admit the interesting possibility of a $Z^{\prime }$ weak boson associated with an extra $U(1)$ gauge symmetry and a Higgs boson that is heavy enough to decay into a pair of $Z$ bosons. Then $Z^{\prime }$ production and decay via $Z^{\prime }\to ZH\to ZZZ$ has a distinctive LHC signal that is nearly background-free and reconstructs the $H$ and $Z^{\prime }$ masses and widths. The $Z^{\prime }$ decay to 3 pairs of leptons is especially distinctive. The $ZH$ decay mode exists even if the $Z^{\prime }$ is decoupled from leptons, which motivates an independent 6-lepton resonance search regardless of the dilepton search results.

A stable magnetic quadrupole trap for neutral atoms on a superconducting Nb thin-film disc is demonstrated. The quadrupole field is composed of the magnetic field that is generated by vortices on the disc introduced by cooling the disc across the transition temperature with a finite field and an oppositely directed uniform field applied after cooling. The trap is stable when all trapping processes are performed above the dendritic instability temperature $T_a$. When the field intensity is changed below this temperature, the quadrupole field collapses and the trap disappears. The initial vortex density decreases even when the external field is changed at a temperature $T>T_a$. However, the vortex density is stabilized at an equilibrium density, whereas at $T<T_a$, it almost completely disappears. A stable trap can be formed, even when the initial vortices are introduced through a dendritic avalanche.