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.

We report the demonstration of hybrid high-$T_c$-superconductor–semiconductor tunnel junctions, enabling new interdisciplinary directions in condensed matter research. The devices are fabricated by our newly developed mechanical-bonding technique, resulting in high-$T_c$-superconductor–semiconductor tunnel diodes. Tunneling-spectra characterization of the hybrid junctions of ${\mathrm{Bi}}_2{\mathrm{Sr}}_2{\mathrm{CaCu}}_2{\mathrm{O}}_{8+\delta }$ combined with bulk GaAs, or a GaAs/AlGaAs quantum well, exhibits excess voltage and nonlinearity, similarly to spectra obtained in scanning-tunneling microscopy, and is in good agreement with theoretical predictions for a $d$-wave-superconductor–normal-material junction. Additional junctions are demonstrated using ${\mathrm{Bi}}_2{\mathrm{Sr}}_2{\mathrm{CaCu}}_2{\mathrm{O}}_{8+\delta }$ combined with graphite or ${\mathrm{Bi}}_2{\mathrm{Te}}_3$. Our results pave the way for new methods in unconventional superconductivity studies, novel materials, and quantum technology applications.

Thin membranes exhibit complex responses to external forces or geometrical constraints. A familiar example is the wrinkling, exhibited by human skin, plant leaves, and fabrics, that results from the relative ease of bending versus stretching. Here, we study the wrinkling of graphene, the thinnest and stiffest known membrane, deposited on a silica substrate decorated with silica nanoparticles. At small nanoparticle density, monolayer graphene adheres to the substrate, detached only in small regions around the nanoparticles. With increasing nanoparticle density, we observe the formation of wrinkles which connect nanoparticles. Above a critical nanoparticle density, the wrinkles form a percolating network through the sample. As the graphene membrane is made thicker, global delamination from the substrate is observed. The observations can be well understood within a continuum-elastic model and have important implications for strain-engineering the electronic properties of graphene.

The appearance of massless Dirac fermions in graphene requires two equivalent carbon sublattices of trigonal shape. While the generation of an effective mass and a band gap at the Dirac point remains an unresolved problem for freestanding extended graphene, it is well established by breaking translational symmetry by confinement and by breaking sublattice symmetry by interaction with a substrate. One of the strongest sublattice-symmetry-breaking interactions with predicted and measured band gaps ranging from 400 meV to more than 3 eV has been attributed to the interfaces of graphene with Ni and Co, which are also promising spin-filter interfaces. Here, we apply angle-resolved photoemission to epitaxial graphene on Ni(111) and Co(0001) to show the presence of intact Dirac cones 2.8 eV below the Fermi level. Our results challenge the common belief that the breaking of sublattice symmetry by a substrate and the opening of the band gap at the Dirac energy are in a straightforward relation. A simple effective model of a biased bilayer structure composed of graphene and a sublattice-symmetry-broken layer, corroborated by density-functional-theory calculations, demonstrates the general validity of our conclusions.

Sparse random networks contain structures that can be considered as diluted feed-forward networks. Modeling of cortical circuits has shown that feed-forward structures, if strongly pronounced compared to the embedding random network, enable reliable signal transmission by propagating localized (subnetwork) synchrony. This assumed prominence, however, is not experimentally observed in local cortical circuits. Here, we show that nonlinear dendritic interactions, as discovered in recent single-neuron experiments, naturally enable guided synchrony propagation already in random recurrent neural networks that exhibit mildly enhanced, biologically plausible substructures.

Heating a solid sphere at its surface induces mechanical stresses inside the sphere. If a finite amount of heat is supplied, the stresses gradually disappear as temperature becomes homogeneous throughout the sphere. We show that before this happens, there is a temporary lowering of pressure and density in the interior of the sphere, inducing a transient lowering of the temperature here. For ordinary solids this effect is small because $c_p\cong c_V$. For fluent liquids the effect is negligible because their dynamic shear modulus vanishes. For a liquid at its glass transition, however, the effect is generally considerably larger than in solids. This paper presents analytical solutions of the relevant coupled thermoviscoelastic equations. In general, there is a difference between the isobaric specific heat $c_p$ measured at constant isotropic pressure and the longitudinal specific heat $c_l$ pertaining to mechanical boundary conditions that confine the associated expansion to be longitudinal. In the exact treatment of heat propagation, the heat-diffusion constant contains $c_l$ rather than $c_p$. We show that the key parameter controlling the magnitude of the “cooling-by-heating“ effect is the relative difference between these two specific heats. For a typical glass-forming liquid, when the temperature at the surface is increased by 1 K, a lowering of the temperature at the sphere center of the order of 5 mK is expected if the experiment is performed at the glass transition. The cooling-by-heating effect is confirmed by measurements on a glucose sphere at the glass transition.

We report cooling of a single neutral atom to its three-dimensional vibrational ground state in an optical tweezer. After employing Raman sideband cooling for tens of milliseconds, we measure via sideband spectroscopy a three-dimensional ground-state occupation of about $90\%$. We further observe coherent control of the spin and motional state of the trapped atom. Our demonstration shows that an optical tweezer, formed simply by a tightly focused beam of light, creates sufficient confinement for efficient sideband cooling. This source of ground-state neutral atoms will be instrumental in numerous quantum simulation and logic applications that require a versatile platform for storing and manipulating ultracold single neutral atoms. For example, these results will improve current optical-tweezer experiments studying atom-photon coupling and Rydberg quantum logic gates, and could provide new opportunities such as rapid production of single dipolar molecules or quantum simulation in tweezer arrays.

The main characteristic of Mott insulators, as compared to band insulators, is to host low-energy spin fluctuations. In addition, Mott insulators often possess orbital degrees of freedom when crystal-field levels are partially filled. While in the majority of Mott insulators, spins and orbitals develop long-range order, the possibility for the ground state to be a quantum liquid opens new perspectives. In this paper, we provide clear evidence that the spin-orbital $\mathrm{SU}(4)$ symmetric Kugel-Khomskii model of Mott insulators on the honeycomb lattice is a quantum spin-orbital liquid. The absence of any form of symmetry breaking—lattice or $\mathrm{SU}(\mathrm{N})$—is supported by a combination of semiclassical and numerical approaches: flavor-wave theory, tensor network algorithm, and exact diagonalizations. In addition, all properties revealed by these methods are very accurately accounted for by a projected variational wave function based on the $\pi$-flux state of fermions on the honeycomb lattice at $1/4$ filling. In that state, correlations are algebraic because of the presence of a Dirac point at the Fermi level, suggesting that the symmetric Kugel-Khomskii model on the honeycomb lattice is an algebraic quantum spin-orbital liquid. This model provides an interesting starting point to understanding the recently discovered spin-orbital-liquid behavior of ${\mathrm{Ba}}_3{\mathrm{CuSb}}_2{\mathrm{O}}_9$. The present results also suggest the choice of optical lattices with honeycomb geometry in the search for quantum liquids in ultracold four-color fermionic atoms.

We use angle-resolved photoemission spectroscopy to image the emergence of substantial dispersion and spectral-weight anomalies in the electronic renormalization of the actinide compound ${\mathrm{UCoGa}}_5$ that was presumed to belong to a conventional Fermi-liquid family. Kinks or abrupt breaks in the slope of the quasiparticle dispersion are detected both at low (approximately 130 meV) and high (approximately 1 eV) binding energies below the Fermi energy, ruling out any significant contribution of phonons. We perform numerical calculations to demonstrate that the anomalies are adequately described by coupling between itinerant fermions and spin fluctuations arising from the particle-hole continuum of the spin-orbit-split $5f$ states of uranium. These anomalies resemble the “waterfall” phenomenon of the high-temperature copper-oxide superconductors, suggesting that spin fluctuations are a generic route toward multiform electronic phases in correlated materials as different as high-temperature superconductors and actinides.

We examine the propagation of the recently discovered electron vortex beams in a longitudinal magnetic field. We consider both the Aharonov-Bohm configuration with a single flux line and the Landau case of a uniform magnetic field. While stationary Aharonov-Bohm modes represent Bessel beams with flux- and vortex-dependent probability distributions, stationary Landau states manifest themselves as nondiffracting Laguerre-Gaussian beams. Furthermore, the Landau-state beams possess field- and vortex-dependent phases: (i) the Zeeman phase from coupling the quantized angular momentum to the magnetic field and (ii) the Gouy phase, known from optical Laguerre-Gaussian beams. Remarkably, together these phases determine the structure of Landau energy levels. This unified Zeeman-Landau-Gouy phase manifests itself in a nontrivial evolution of images formed by various superpositions of modes. We demonstrate that, depending on the chosen superposition, the image can rotate in a magnetic field with either (i) Larmor, (ii) cyclotron (double-Larmor), or (iii) zero frequency. At the same time, its centroid always follows the classical cyclotron trajectory, in agreement with the Ehrenfest theorem. Interestingly, the nonrotating superpositions reproduce stable multivortex configurations that appear in rotating superfluids. Our results open an avenue for the direct electron-microscopy observation of fundamental properties of free quantum-electron states in magnetic fields.

Quantum key distribution (QKD) uniquely allows the distribution of cryptographic keys with security verified by quantum mechanical limits. Both protocol execution and subsequent applications require the assistance of classical data communication channels. While using separate fibers is one option, it is economically more viable if data and quantum signals are simultaneously transmitted through a single fiber. However, noise-photon contamination arising from the intense data signal has severely restricted both the QKD distances and secure key rates. Here, we exploit a novel temporal-filtering effect for noise-photon rejection. This allows high-bit-rate QKD over fibers up to 90 km in length and populated with error-free bidirectional $\mathrm{Gb}/\mathrm{s}$ data communications. With a high-bit rate and range sufficient for important information infrastructures, such as smart cities and 10-Gbit Ethernet, QKD is a significant step closer toward wide-scale deployment in fiber networks.

An improved measurement of the electron electric dipole moment (EDM) appears feasible using ground-state alkali atoms in an atomic fountain in which a strong electric field, which couples to a conceivable EDM, is applied perpendicular to the fountain axis. In a practical fountain, the ratio of the atomic tensor Stark shift to the Zeeman shift is a factor $\mu \sim 100$. We expand the complete time-evolution operator in inverse powers of this ratio; complete results are presented for atoms of total spin $F=3$, 4, and 5. For a specific set of entangled hyperfine sublevels (coherent states), potential systematic errors enter only as even powers of $1/\mu$, making the expansion rapidly convergent. The remaining EDM-mimicking effects are further suppressed in a proposed double-differential setup, where the final state is interrogated in a differential laser configuration, and the direction of the strong electric field also is inverted. Estimates of the signal available at existing accelerator facilities indicate that the proposed apparatus offers the potential for a drastic improvement in EDM limits over existing measurements, and for constraining the parameter space of supersymmetric (SUSY) extensions of the Standard Model.

Interest in femtosecond demagnetization dynamics was sparked by Bigot’s experiment in 1996, which unveiled the elementary mechanisms that relate the electrons’ temperature to their spin order. Simultaneously, the application of fast demagnetization experiments has been demonstrated to provide key insight into technologically important systems such as high-spin-polarization metals, and consequently there is broad interest in further understanding the physics of these phenomena. To gain new and relevant insights, we performed ultrafast optical pump-probe experiments to characterize the demagnetization processes of highly spin-polarized magnetic thin films on a femtosecond time scale. Full spin polarization is obtained in half-metallic ferro- or ferrimagnets, where only one spin channel is populated at the Fermi level, whereas the other one exhibits a gap. In these materials, the spin-scattering processes is controlled via the electronic structure, and thus their ultrafast demagnetization is solely related to the spin polarization via a Fermi golden-rule model. Accordingly, a long demagnetization time correlates with a high spin polarization due to the suppression of the spin-flip scattering at around the Fermi level. Here we show that isoelectronic Heusler compounds (${\mathrm{Co}}_2\mathrm{MnSi}$, ${\mathrm{Co}}_2\mathrm{MnGe}$, and ${\mathrm{Co}}_2\mathrm{FeAl}$) exhibit a degree of spin polarization between 59% and 86%. We explain this behavior by considering the robustness of the gap against structural disorder. Moreover, we observe that CoFe-based pseudogap materials, such as partially ordered Co-Fe-Ge and Co-Fe-B alloys, can reach similar values of the spin polarization. By using the unique features of these metals we vary the number of possible spin-flip channels, which allows us to pinpoint and control the half-metals’ electronic structure and its influence on the elementary mechanisms of ultrafast demagnetization.

Neurons in cerebral cortical circuits interact by sending and receiving electrical impulses called spikes. The ongoing spiking activity of cortical circuits is fundamental to many cognitive functions including sensory processing, working memory, and decision making. London et al. [Sensitivity to Perturbations In Vivo Implies High Noise and Suggests Rate Coding in Cortex, Nature (London) 466, 123 (2010).] recently argued that even a single additional spike can cause a cascade of extra spikes that rapidly decorrelate the microstate of the network. Here, we show theoretically in a minimal model of cortical neuronal circuits that single-spike perturbations trigger only a very weak rate response. Nevertheless, single-spike perturbations are found to rapidly decorrelate the microstate of the network, although the dynamics is stable with respect to small perturbations. The coexistence of stable and unstable dynamics results from a system of exponentially separating dynamic flux tubes around stable trajectories in the network’s phase space. The radius of these flux tubes appears to decrease algebraically with neuron number $N$ and connectivity $K$, which implies that the entropy of the circuit’s repertoire of state sequences scales as $N\ln (KN)$.

A number of authors have suggested that nonlinear interactions can enhance resolution of phase shifts beyond the usual Heisenberg scaling of $1/n$, where $n$ is a measure of resources such as the number of subsystems of the probe state or the mean photon number of the probe state. These suggestions are based on calculations of “local precision” for particular nonlinear schemes. However, we show that there is no simple connection between the local precision and the average estimation error for these schemes, leading to a scaling puzzle. This puzzle is partially resolved by a careful analysis of iterative implementations of the suggested nonlinear schemes. However, it is shown that the suggested nonlinear schemes are still limited to an exponential scaling in $\sqrt{n}$. (This scaling may be compared to the exponential scaling in $n$ which is achievable if multiple passes are allowed, even for linear schemes.) The question of whether nonlinear schemes may have a scaling advantage in the presence of loss is left open. Our results are based on a new bound for average estimation error that depends on (i) an entropic measure of the degree to which the probe state can encode a reference phase value, called the $G$ asymmetry, and (ii) any prior information about the phase shift. This bound is asymptotically stronger than bounds based on the variance of the phase-shift generator. The $G$ asymmetry is also shown to directly bound the average information gained per estimate. Our results hold for any prior distribution of the shift parameter, and generalize to estimates of any shift generated by an operator with discrete eigenvalues.