In this work, we provide a detailed theoretical analysis, supported by numerical tests, of the reliability of the adaptive-resolution-simulation (AdResS) technique in sampling the grand-canonical ensemble. We demonstrate that the correct density and radial distribution functions in the hybrid region, where molecules change resolution, are two necessary conditions for considering the atomistic and coarse-grained regions in AdResS to be equivalent to subsystems of a full atomistic system with an accuracy up to the second order with respect to the probability distribution of the system. Moreover, we show that the work done by the thermostat and a thermodynamic force in the transition region is formally equivalent to balancing the chemical potential difference between the different resolutions. From these results follows the main conclusion that the atomistic region exchanges molecules with the coarse-grained region in a grand-canonical fashion with an accuracy up to (at least) second order. Numerical tests, for the relevant case of liquid water at ambient conditions, are carried out to strengthen the conclusions of the theoretical analysis. Finally, in order to show the computational convenience of AdResS as a grand-canonical setup, we compare our method to the insertion particle method in its most efficient computational implementation. This fruitful combination of theoretical principles and numerical evidence makes the adaptive-resolution technique a candidate for a natural, general, and efficient protocol for grand-canonical molecular dynamics for the case of large systems.

This paper reports an advanced study of the excited ionic states of the gas-phase nitrogen molecule in the binding-energy region of 22–34 eV, combining ultrahigh-resolution resonant photoemission (RPE) and ab initio configuration-interaction calculations. The RPE spectra are recorded for nine photon energies within the N $1s\to {\pi }^{*}$ absorption resonance of ${\mathrm{N}}_2$ by using a photon bandwidth that is considerably smaller than lifetime broadening, and the dependence on excitation energy of the decay spectra is analyzed and used for the first assignment of 12 highly overlapped molecular states. The effect on the RPE profile of avoided curve crossings between the final ${\mathrm{N}}_2^{+}$ ionic states is discussed, based on theoretical simulations that account for vibronic coupling, and compared with the experimental data. By use of synchrotron radiation with high spectral brightness, it is possible to selectively promote the molecule to highly excited vibrational sublevels of a core-excited electronic state, thereby controlling the spatial distribution of the vibrational wave packets, and to accurately image the ionic molecular potentials. In addition, the mapping of the vibrational wave functions of the core-excited states using the bound final states with far-from-equilibrium bond lengths has been achieved experimentally for the first time. Theoretical analysis has revealed the rich femtosecond nuclear dynamics underlying the mapping phenomenon.

We discuss physical properties of “integer” topological phases of bosons in $D=3+1$ dimensions, protected by internal symmetries like time reversal and/or charge conservation. These phases invoke interactions in a fundamental way but do not possess topological order; they are bosonic analogs of free-fermion topological insulators and superconductors. While a formal cohomology-based classification of such states was recently discovered, their physical properties remain mysterious. Here, we develop a field-theoretic description of several of these states and show that they possess unusual surface states, which, if gapped, must either break the underlying symmetry or develop topological order. In the latter case, symmetries are implemented in a way that is forbidden in a strictly two-dimensional theory. While these phases are the usual fate of the surface states, exotic gapless states can also be realized. For example, tuning parameters can naturally lead to a deconfined quantum critical point or, in other situations, to a fully symmetric vortex metal phase. We discuss cases where the topological phases are characterized by a quantized magnetoelectric response $\theta$, which, somewhat surprisingly, is an odd multiple of $2\pi$. Two different surface theories are shown to capture these phenomena: The first is a nonlinear sigma model with a topological term. The second invokes vortices on the surface that transform under a projective representation of the symmetry group. We identify a bulk-field theory consistent with these properties, which is a multicomponent background-field theory supplemented, crucially, with a topological term. We also provide bulk sigma-model field theories of these phases and discuss a possible topological phase characterized by the thermal analog of the magnetoelectric effect.

The adiabatic insertion of a $\pi$ flux into a quantum spin Hall insulator gives rise to localized spin and charge fluxon states. We demonstrate that $\pi$ fluxes can be used in exact quantum Monte Carlo simulations to identify a correlated $Z_2$ topological insulator using the example of the Kane-Mele-Hubbard model. In the presence of repulsive interactions, a $\pi$ flux gives rise to a Kramers doublet of spin-fluxon states with a Curie-law signature in the magnetic susceptibility. Electronic correlations also provide a bosonic mode of magnetic excitons with tunable energy that act as exchange particles and mediate a dynamical interaction of adjustable range and strength between spin fluxons. $\pi$ fluxes can therefore be used to build models of interacting spins. This idea is applied to a three-spin ring and to one-dimensional spin chains. Because of the freedom to create almost arbitrary spin lattices, correlated topological insulators with $\pi$ fluxes represent a novel kind of quantum simulator, potentially useful for numerical simulations and experiments.

At low temperatures, a spin ice enters a Coulomb phase—a state with algebraic correlations and topologically constrained spin configurations. We show how analytical and numerical approaches for model spin-ice systems reveal a crossover between two Curie laws. One of these laws characterizes the high-temperature paramagnetic regime, while the other, which we call the “spin-liquid Curie law,” characterizes the low-temperature Coulomb-phase regime, which provides implicit evidence that the topological sector fluctuates. We compare our theory with experiment for ${\mathrm{Ho}}_2{\mathrm{Ti}}_2{\mathrm{O}}_7$, where this process leads to a nonstandard temperature evolution of the bulk susceptibility and the wave-vector-dependent magnetic susceptibility, as measured by neutron scattering. Theory and experiment agree for bulk quantities and at large scattering wave vectors, but differences at small wave vectors indicate that the classical spin-ice states are not equally populated at low temperatures. More generally, the crossover appears to be a generic property of the emergent gauge field for a classical spin liquid, and it sheds light on the experimental difficulty of measuring a precise Curie-Weiss temperature in frustrated materials. The susceptibility at finite wave vectors is shown to be a local probe of fluctuations among topological sectors on varying length scales.

We implement a double-pixel compressive-sensing camera to efficiently characterize, at high resolution, the spatially entangled fields that are produced by spontaneous parametric down-conversion. This technique leverages sparsity in spatial correlations between entangled photons to improve acquisition times over raster scanning by a scaling factor up to $n^2/\log (n)$ for $n$-dimensional images. We image at resolutions up to 1024 dimensions per detector and demonstrate a channel capacity of 8.4 bits per photon. By comparing the entangled photons’ classical mutual information in conjugate bases, we violate an entropic Einstein-Podolsky-Rosen separability criterion for all measured resolutions. More broadly, our result indicates that compressive sensing can be especially effective for higher-order measurements on correlated systems.

The conflict between classical and quantum physics can be identified through a series of yes-no tests on quantum systems, without it being necessary that these systems be in special quantum states. Kochen-Specker (KS) sets of yes-no tests have this property and provide a quantum-versus-classical advantage that is free of the initialization problem that affects some quantum computers. Here, we report the first experimental implementation of a complete KS set that consists of 18 yes-no tests on four-dimensional quantum systems and show how to use the KS set to obtain a state-independent quantum advantage. We first demonstrate the unique power of this KS set for solving a task while avoiding the problem of state initialization. Such a demonstration is done by showing that, for 28 different quantum states encoded in the orbital-angular-momentum and polarization degrees of freedom of single photons, the KS set provides an impossible-to-beat solution. In a second experiment, we generate maximally contextual quantum correlations by performing compatible sequential measurements of the polarization and path of single photons. In this case, state independence is demonstrated for 15 different initial states. Maximum contextuality and state independence follow from the fact that the sequences of measurements project any initial quantum state onto one of the KS set’s eigenstates. Our results show that KS sets can be used for quantum-information processing and quantum computation and pave the way for future developments.

As an exemplary Kondo insulator, ${\mathrm{SmB}}_6$ has been studied for several decades. However, direct evidence for the development of the Kondo coherent state and for the evolution of the electronic structure in the material has not been obtained due to the compound’s rather complicated electronic and thermal transport behavior. Recently, these open questions have attracted increasing attention as the emergence of a time-reversal-invariant topological surface state in the Kondo insulator has been suggested. Here, we use point-contact spectroscopy to reveal the temperature dependence of the electronic states in ${\mathrm{SmB}}_6$. We demonstrate that ${\mathrm{SmB}}_6$ is a model Kondo insulator: Below 100 K, the conductance spectra reflect the Kondo hybridization of Sm ions, but, below about $30\mathrm{K}$, signatures of inter-ion correlation effects clearly emerge. Moreover, we find evidence that the low-temperature insulating state of this exemplary Kondo-lattice compound harbors conduction states on the surface, in support of predictions of nontrivial topology in Kondo insulators.

The voltage-gated potassium channel from Aeropyrum pernix operates by coupling the voltage-driven motion of a charged group of amino acids to the opening and closing of the pore. In this experiment, we drive this charged group with an ac field and observe the effect on the gating. The measurements for different frequencies and amplitudes of the forcing reveal an essential nonlinearity in the mechanical behavior of the molecule. Within a continuum-mechanics description, we extract the effective dissipation parameter $\gamma$ for this conformational motion and find $\gamma \approx 0.2\mathrm{g}/\mathrm{s}$, similar to recent nanorheology measurements on the conformational motion of an enzyme.

We present nanorheology measurements on the folded state of an enzyme that show directly that the (ensemble-averaged) stress-strain relations are nonlinear and frequency dependent beyond 1-Å deformation. We argue that this frequency dependence allows for opening a nonequilibrium cycle in the force-deformation plane if the forward and backward conformational changes of the enzyme during catalysis happen at different speeds. Using a heuristic model for the experimentally established viscoelastic properties of the enzyme, we examine a number of general features of enzymatic action. We find that the proposed viscoelastic cycle is consistent with the linear decrease of the speed of motor proteins with load. We find a relation between the stall force and the maximum rate for enzymes (in general) and motors (in particular). We estimate the stall force of the motor protein kinesin from thermodynamic quantities and estimate the maximum rate of enzymes from purely mechanical quantities. We propose that the viscoelastic cycle provides a framework for considering mechanochemical coupling in enzymes on the basis of possibly universal materials properties of the folded state of proteins.

We study graphene nanoribbons theoretically in the presence of spatially varying magnetic fields produced, e.g., by nanomagnets. We show, both analytically and numerically, that an exceptionally large Rashba spin-orbit interaction of the order of 10 meV can be produced by a nonuniform magnetic field. As a consequence, helical modes exist in armchair nanoribbons that exhibit nearly perfect spin polarization and are robust against boundary defects. This result paves the way for realizing spin-filter devices in graphene nanoribbons in the temperature regime of a few kelvins. If a nanoribbon in the helical regime is in proximity contact to an $s$-wave superconductor, the nanoribbon can be tuned into a topological phase that sustains Majorana fermions.

Common algorithms for computationally simulating Langevin dynamics must discretize the stochastic differential equations of motion. These resulting finite-time-step integrators necessarily have several practical issues in common: Microscopic reversibility is violated, the sampled stationary distribution differs from the desired equilibrium distribution, and the work accumulated in nonequilibrium simulations is not directly usable in estimators based on nonequilibrium work theorems. Here, we show that, even with a time-independent Hamiltonian, finite-time-step Langevin integrators can be thought of as a driven, nonequilibrium physical process. Once an appropriate worklike quantity is defined—here called the shadow work—recently developed nonequilibrium fluctuation theorems can be used to measure or correct for the errors introduced by the use of finite time steps. In particular, we demonstrate that amending estimators based on nonequilibrium work theorems to include this shadow work removes the time-step-dependent error from estimates of free energies. We also quantify, for the first time, the magnitude of deviations between the sampled stationary distribution and the desired equilibrium distribution for equilibrium Langevin simulations of solvated systems of varying sizes. While these deviations can be large, they can be eliminated altogether by Metropolization or greatly diminished by small reductions in the time step. Through this connection with driven processes, further developments in nonequilibrium fluctuation theorems can provide additional analytical tools for dealing with errors in finite-time-step integrators.

A femtosecond-laser pulse can induce ultrafast nonthermal melting of various materials along pathways that are inaccessible under thermodynamic conditions, but it is not known whether there is any structural modification at fluences just below the melting threshold. Here, we show for silicon that in this regime the room-temperature phonons become thermally squeezed, which is a process that has not been reported before in this material. We find that the origin of this effect is the sudden femtosecond-laser-induced softening of interatomic bonds, which can also be described in terms of a modification of the potential energy surface. We further find in ab initio molecular-dynamics simulations on laser-excited potential energy surfaces that the atoms move in the same directions during the first stages of nonthermal melting and thermal phonon squeezing. Our results demonstrate how femtosecond-laser-induced coherent fluctuations precurse complete atomic disordering as a function of fluence. The common underlying bond-softening mechanism indicates that this relation between thermal squeezing and nonthermal melting is not material specific.

We report an investigation with angle-resolved photoemission spectroscopy of the Fermi surface and electronic band structure of ${\mathrm{BaCo}}_2{\mathrm{As}}_2$. Although its quasinesting-free Fermi surface differs drastically from that of its Fe-pnictide cousins, we show that the ${\mathrm{BaCo}}_2{\mathrm{As}}_2$ system can be used as an approximation to the bare unoccupied band structure of the related ${\mathrm{BaFe}}_{2-x}{\mathrm{Co}}_x{\mathrm{As}}_2$ and ${\mathrm{Ba}}_{1-x}{\mathrm{K}}_x{\mathrm{Fe}}_2{\mathrm{As}}_2$ compounds. However, our experimental results, in agreement with dynamical-mean-field-theory calculations, indicate that electronic correlations are much less important in ${\mathrm{BaCo}}_2{\mathrm{As}}_2$ than in the ferropnictides. Our findings suggest that this effect is due to the increased filling of the electronic $3d$ shell in the presence of significant Hund’s exchange coupling.

In this work, we present theoretical tools suitable for quantitative modeling of large superconducting circuits that include one-dimensional Josephson-junction arrays. The large number of low-energy degrees of freedom and the peculiar interactions between them induced by flux quantization present a considerable challenge to the detailed modeling of such circuits. For the concrete example of the fluxonium device, we show how to address this challenge. Starting from the complete degrees of freedom of the circuit, we employ the relevant collective modes and circuit symmetries to obtain a systematic approximation scheme. Important circuit symmetries include approximate invariance under the symmetric group and lead to considerable simplifications of the theory. Selection rules restrict the possible coupling among different collective modes and help explain the remarkable accuracy of previous simplified models. Using this strategy, we obtain new predictions for the energy spectrum of the fluxonium device that can be tested with current experimental technology.

Ordered lipid assemblies are responsible for important physiological functions including skin barrier and axon conductivity. However, techniques commonly used to probe molecular order such as X-ray scattering and nuclear magnetic resonance are not suited for in-situ tissue studies. Here, we identify and characterize a novel contrast mechanism in nonlinear optical microscopy which is sensitive to molecular ordering in multilamellar lipid vesicles (MLVs) and in samples obtained from human skin biopsy: polarized third-harmonic generation (P-THG). We develop a multiscale theoretical framework to calculate the anisotropic, nonlinear optical response of lipid arrays as a function of molecular order. This analysis reveals that conserved carbon-carbon bond and aliphatic tail directionality are the atomic- and molecular-scale sources of the observed P-THG response, respectively. Agreement between calculations and experiments on lipid droplets and MLVs validates the use of P-THG as a probe of lipid ordering. Finally, we show that P-THG can be used to map molecular ordering in the multilamellar, intercorneocyte lipid matrix of the stratum corneum of human skin. These results provide the foundation for the use of P-THG in probing molecular order and highlight a novel biomedical application of multiphoton microscopy in an optically accessible tissue relevant to monitoring lipid-related disorder.

We present here a detailed study of the complex relationship between the electromagnetic near-field and far-field responses of “real” nanostructured metallic surfaces. The near-field and far-field responses are specified in terms of (spectra of) the surface-enhanced Raman-scattering enhancement factor (SERS EF) and optical extinction, respectively. First, it is shown that gold nanorod- and nanotube-array substrates exhibit three distinct localized surface plasmon resonances (LSPRs): a longitudinal, a transverse, and a cavity mode. The cavity mode simultaneously has the largest impact on the near-field behavior (as observed through the SERS EF) and the weakest optical interaction: It has a “near-field-type” character. The transverse and longitudinal modes have a significant impact on the far-field behavior but very little impact on SERS: They have a “far-field-type” character. We confirm the presence of the cavity mode using a combination of SERS EF spectra, electron microscopy, and electromagnetic modeling and thus clearly illustrate and explain the (lack of) correlation between the SERS EF spectra and the optical response in terms of the contrasting character of the three LSPRs. In doing so, we experimentally demonstrate that, for a surface that supports multiple LSPRs, the near-field and far-field properties can in fact be tuned almost independently. It is further demonstrated that small changes in geometrical parameters that tune the spectral location of the LPSRs can also drastically influence the character of these modes, resulting in certain unusual behavior, such as the far-field resonance redshift as the near-field resonance blueshifts.

We show that the improper ferroelectric phase transition in the multiferroic hexagonal manganites displays appropriate symmetry-breaking characteristics for testing the Kibble-Zurek mechanism originally proposed to describe early-universe phase transitions. We present an analysis of the Kibble-Zurek theory of topological defect formation applied to the hexagonal manganites, discuss the conditions determining the range of cooling rates in which Kibble-Zurek behavior is expected, and show that recent literature data are consistent with our predictions. Finally, we explore experimentally the crossover out of the Kibble-Zurek regime and find a surprising reversal of the scaling behavior.

We propose families of protocols for magic-state distillation—important components of fault-tolerance schemes—for systems of odd prime dimension. Our protocols utilize quantum Reed-Muller codes with transversal non-Clifford gates. We find that, in higher dimensions, small and effective codes can be used that have no direct analogue in qubit (two-dimensional) systems. We present several concrete protocols, including schemes for three-dimensional (qutrit) and five-dimensional (ququint) systems. The five-dimensional protocol is, by many measures, the best magic-state-distillation scheme yet discovered. It excels both in terms of error threshold with respect to depolarizing noise ($36.3\%$) and the efficiency measure known as yield, where, for a large region of parameters, it outperforms its qubit counterpart by many orders of magnitude.

The recent experimental realization of strongly imbalanced mixtures of ultracold atoms opens new possibilities for studying impurity dynamics in a controlled setting. In this paper, we discuss how the techniques of atomic physics can be used to explore new regimes and manifestations of Anderson’s orthogonality catastrophe (OC), which could not be accessed in solid-state systems. Specifically, we consider a system of impurity atoms, localized by a strong optical-lattice potential, immersed in a sea of itinerant Fermi atoms. We point out that the Ramsey-interference-type experiments with the impurity atoms allow one to study the OC in the time domain, while radio-frequency (RF) spectroscopy probes the OC in the frequency domain. The OC in such systems is universal, not only in the long-time limit, but also for all times and is determined fully by the impurity-scattering length and the Fermi wave vector of the itinerant fermions. We calculate the universal Ramsey response and RF-absorption spectra. In addition to the standard power-law contributions, which correspond to the excitation of multiple particle-hole pairs near the Fermi surface, we identify a novel, important contribution to the OC that comes from exciting one extra particle from the bottom of the itinerant band. This contribution gives rise to a nonanalytic feature in the RF-absorption spectra, which shows a nontrivial dependence on the scattering length, and evolves into a true power-law singularity with the universal exponent $1/4$ at the unitarity. We extend our discussion to spin-echo-type experiments, and show that they probe more complicated nonequilibirum dynamics of the Fermi gas in processes in which an impurity switches between states with different interaction strength several times; such processes play an important role in the Kondo problem, but remained out of reach in the solid-state systems. We show that, alternatively, the OC can be seen in the energy-counting statistics of the Fermi gas following a sudden quench of the impurity state. The energy distribution function, which can be measured in time-of-flight experiments, exhibits characteristic power-law singularities at low energies. Finally, systems in which the itinerant fermions have two or more hyperfine states provide an even richer playground for studying nonequilibrium impurity physics, allowing one to explore the nonequilibrium OC and even to simulate quantum transport through nanostructures. This provides a previously missing connection between cold atomic systems and mesoscopic quantum transport.