Herbertsmithite, ${\mathrm{ZnCu}}_3(\mathrm{OH}{)}_6{\mathrm{Cl}}_2$, is a two-dimensional kagome lattice realization of a spin liquid, with evidence for fractionalized excitations and a gapped ground state. Such a quantum spin liquid has been proposed to underlie high-temperature superconductivity and is predicted to produce a wealth of new states, including a Dirac metal at $1/3$ electron doping. Here, we report the topochemical synthesis of electron-doped ${\mathrm{ZnLi}}_x{\mathrm{Cu}}_3(\mathrm{OH}{)}_6{\mathrm{Cl}}_2$ from $x=0$ to $x=1.8$ ($3/5$ per ${\mathrm{Cu}}^{2+}$). Contrary to expectations, no metallicity or superconductivity is induced. Instead, we find a systematic suppression of magnetic behavior across the phase diagram. Our results demonstrate that significant theoretical work is needed to understand and predict the role of doping in magnetically frustrated narrow band insulators, particularly the interplay between local structural disorder and tendency toward electron localization, and pave the way for future studies of doped spin liquids.

We introduce a method, dubbed the flux-fusion anomaly test, to detect certain anomalous symmetry fractionalization patterns in two-dimensional symmetry-enriched topological (SET) phases. We focus on bosonic systems with ${\mathbb{Z}}_2$ topological order and a symmetry group of the form $G=\mathrm{U}(1)⋊G^{\prime }$, where $G^{\prime }$ is an arbitrary group that may include spatial symmetries and/or time reversal. The anomalous fractionalization patterns we identify cannot occur in strictly $d=2$ systems but can occur at surfaces of $d=3$ symmetry-protected topological (SPT) phases. This observation leads to examples of $d=3$ bosonic topological crystalline insulators (TCIs) that, to our knowledge, have not previously been identified. In some cases, these $d=3$ bosonic TCIs can have an anomalous superfluid at the surface, which is characterized by nontrivial projective transformations of the superfluid vortices under symmetry. The basic idea of our anomaly test is to introduce fluxes of the U(1) symmetry and to show that some fractionalization patterns cannot be extended to a consistent action of $G^{\prime }$ symmetry on the fluxes. For some anomalies, this can be described in terms of dimensional reduction to $d=1$ SPT phases. We apply our method to several different symmetry groups with nontrivial anomalies, including $G=\mathrm{U}(1)\times {\mathbb{Z}}_2^T$ and $G=\mathrm{U}(1)\times {\mathbb{Z}}_2^P$, where ${\mathbb{Z}}_2^T$ and ${\mathbb{Z}}_2^P$ are time-reversal and $d=2$ reflection symmetry, respectively.

A “best-of-both-worlds” van der Waals (vdW) density functional is constructed, seamlessly supplementing the strongly constrained and appropriately normed (SCAN) meta-generalized gradient approximation for short- and intermediate-range interactions with the long-range vdW interaction from $r\mathrm{VV}10$, the revised Vydrov–van Voorhis nonlocal correlation functional. The resultant $\mathrm{SCAN}+r\mathrm{VV}10$ is the only vdW density functional to date that yields excellent interlayer binding energies and spacings, as well as intralayer lattice constants in 28 layered materials. Its versatility for various kinds of bonding is further demonstrated by its good performance for 22 interactions between molecules; the cohesive energies and lattice constants of 50 solids; the adsorption energy and distance of a benzene molecule on coinage-metal surfaces; the binding energy curves for graphene on Cu(111), Ni(111), and Co(0001) surfaces; and the rare-gas solids. We argue that a good semilocal approximation should (as SCAN does) capture the intermediate-range vdW through its exchange term. We have found an effective range of the vdW interaction between 8 and 16 Å for systems considered here, suggesting that this interaction is negligibly small at the larger distances where it reaches its asymptotic power-law decay.

Ultracold atoms, produced by laser cooling and trapping, have led to recent advances in quantum information, quantum chemistry, and quantum sensors. A lack of ultraviolet narrow-band lasers precludes laser cooling of prevalent atoms such as hydrogen, carbon, oxygen, and nitrogen. Broadband pulsed lasers can produce high power in the ultraviolet, and we demonstrate that the entire spectrum of an optical frequency comb can cool atoms when used to drive a narrow two-photon transition. This multiphoton optical force is also used to make a magneto-optical trap. These techniques may provide a route to ultracold samples of nature’s most abundant building blocks for studies of pure-state chemistry and precision measurement.

Topological phases of matter are a potential platform for the storage and processing of quantum information with intrinsic error rates that decrease exponentially with inverse temperature and with the length scales of the system, such as the distance between quasiparticles. However, it is less well understood how error rates depend on the speed with which non-Abelian quasiparticles are braided. In general, diabatic corrections to the holonomy or Berry’s matrix vanish at least inversely with the length of time for the braid, with faster decay occurring as the time dependence is made smoother. We show that such corrections will not affect quantum information encoded in topological degrees of freedom, unless they involve the creation of topologically nontrivial quasiparticles. Moreover, we show how measurements that detect unintentionally created quasiparticles can be used to control this source of error.

The accurate prediction of electronic and optical properties of molecules and solids is a persistent challenge for methods based on density functional theory. We propose a generalization of dielectric-dependent hybrid functionals to finite systems where the definition of the mixing fraction of exact and semilocal exchange is physically motivated, nonempirical, and system dependent. The proposed functional yields ionization potentials, and fundamental and optical gaps of many, diverse molecular systems in excellent agreement with experiments, including organic and inorganic molecules and semiconducting nanocrystals. We further demonstrate that this hybrid functional gives the correct alignment between energy levels of the exemplary TTF-TCNQ donor-acceptor system.

Periodic driving of a quantum system can enable new topological phases with no analog in static systems. In this paper, we systematically classify one-dimensional topological and symmetry-protected topological (SPT) phases in interacting fermionic and bosonic quantum systems subject to periodic driving, which we dub Floquet SPTs (FSPTs). For physical realizations of interacting FSPTs, many-body localization by disorder is a crucial ingredient, required to obtain a stable phase that does not catastrophically heat to infinite temperature. We demonstrate that 1D bosonic and fermionic FSPT phases are classified by the same criteria as equilibrium phases but with an enlarged symmetry group $\tilde{G}$, which now includes discrete time translation symmetry associated with the Floquet evolution. In particular, 1D bosonic FSPTs are classified by projective representations of the enlarged symmetry group $H^2\mathbf{(}\tilde{G},U(1)\mathbf{)}$. We construct explicit lattice models for a variety of systems and then formalize the classification to demonstrate the completeness of this construction. We advocate that a prototypical ${\mathbb{Z}}_2$ bosonic FSPT may be realized by very simple Hamiltonians of the type currently available in existing cold atoms and trapped ion experiments.

Experimental tools capable of monitoring both atomic and electronic structure on ultrafast (femtosecond to picosecond) time scales are needed for investigating photophysical processes fundamental to light harvesting, photocatalysis, energy and data storage, and optical display technologies. Time-resolved hard x-ray ($>3\mathrm{keV}$) spectroscopies have proven valuable for these measurements due to their elemental specificity and sensitivity to geometric and electronic structures. Here, we present the first tabletop apparatus capable of performing time-resolved x-ray emission spectroscopy. The time resolution of the apparatus is better than 6 ps. By combining a compact laser-driven plasma source with a highly efficient array of microcalorimeter x-ray detectors, we are able to observe photoinduced spin changes in an archetypal polypyridyl iron complex $[\mathrm{Fe}(2,2^{\prime }\text{−}\text{bipyridine}{)}_3{]}^{2+}$ and accurately measure the lifetime of the quintet spin state. Our results demonstrate that ultrafast hard x-ray emission spectroscopy is no longer confined to large facilities and now can be performed in conventional laboratories with 10 times better time resolution than at synchrotrons. Our results are enabled, in part, by a 100- to 1000-fold increase in x-ray collection efficiency compared to current techniques.

We study the effects of strain on the properties and dynamics of Wannier excitons in monolayer (phosphorene) and few-layer black phosphorus (BP), a promising two-dimensional material for optoelectronic applications due to its high mobility, mechanical strength, and strain-tunable direct band gap. We compare the results to the case of molybdenum disulphide (${\mathrm{MoS}}_2$) monolayers. We find that the so-called funnel effect, i.e., the possibility of controlling exciton motion by means of inhomogeneous strains, is much stronger in few-layer BP than in ${\mathrm{MoS}}_2$ monolayers and, crucially, is of opposite sign. Instead of excitons accumulating isotropically around regions of high tensile strain like in ${\mathrm{MoS}}_2$, excitons in BP are pushed away from said regions. This inverse funnel effect is moreover highly anisotropic, with much larger funnel distances along the armchair crystallographic direction, leading to a directional focusing of exciton flow. A strong inverse funnel effect could enable simpler designs of funnel solar cells and offer new possibilities for the manipulation and harvesting of light.

Recent improvements in the control of quantum systems make it seem feasible to finally build a quantum computer within a decade. While it has been shown that such a quantum computer can in principle solve certain small electronic structure problems and idealized model Hamiltonians, the highly relevant problem of directly solving a complex correlated material appears to require a prohibitive amount of resources. Here, we show that by using a hybrid quantum-classical algorithm that incorporates the power of a small quantum computer into a framework of classical embedding algorithms, the electronic structure of complex correlated materials can be efficiently tackled using a quantum computer. In our approach, the quantum computer solves a small effective quantum impurity problem that is self-consistently determined via a feedback loop between the quantum and classical computation. Use of a quantum computer enables much larger and more accurate simulations than with any known classical algorithm, and will allow many open questions in quantum materials to be resolved once a small quantum computer with around 100 logical qubits becomes available.

The art of imparting information onto a light wave by optical signal modulation is fundamental to all forms of optical communication. Among many schemes, direct modulation of laser diodes stands out as a simple, robust, and cost-effective method. However, the simultaneous changes in intensity, frequency, and phase have prevented its application in the field of secure quantum communication. Here, we propose and experimentally demonstrate a directly phase-modulated light source which overcomes the main disadvantages associated with direct modulation and is suitable for diverse applications such as coherent communications and quantum cryptography. The source separates the tasks of phase preparation and pulse generation between a pair of semiconductor lasers leading to very pure phase states. Moreover, the cavity-enhanced electro-optic effect enables the first example of subvolt half-wave phase modulation at high signal rates. The source is compact, stable, and versatile, and we show its potential to become the standard transmitter for future quantum communication networks based on attenuated laser pulses.

We show how particle-vortex duality in $d=2+1$ dimensions arises as part of an intricate web of relationships between different field theories. The starting point is “bosonization,” a conjectured duality that uses flux attachment to transmute the statistics of relativistic particles. From this seed, we derive many old and new dualities. These include particle-vortex duality for bosons as well as the recently discovered counterpart for fermions.

By performing spatially resolved Raman and photoluminescence spectroscopy with varying excitation wavelength, density, and data acquisition parameters, we achieve a unified understanding towards the spectroscopy signatures of the organic-inorganic hybrid perovskite, transforming from the pristine state (${\mathrm{CH}}_3{\mathrm{NH}}_3{\mathrm{PbI}}_3$) to the fully degraded state (i.e., ${\mathrm{PbI}}_2$) for samples with varying crystalline domain size from mesoscopic scale (approximately 100 nm) to macroscopic size (centimeters), synthesized by three different techniques. We show that the hybrid perovskite exhibits multiple stages of structure transformation occurring either spontaneously or under light illumination, with exceptionally high sensitivity to the illumination conditions (e.g., power, illumination time, and interruption pattern). We highlight four transformation stages (stages I–IV, with stage I being the pristine state) along either the spontaneous or photoinduced degradation path exhibiting distinctly different Raman spectroscopy features at each stage, and point out that previously reported Raman spectra in the literature reflect highly degraded structures of either stage III or stage IV. Additional characteristic optical features of partially degraded materials under the joint action of spontaneous and photodegradation are also given. This study offers reliable benchmark results for understanding the intrinsic material properties and structure transformation of this unique category of hybrid materials, and the findings are pertinently important to a wide range of potential applications where the hybrid material is expected to function in greatly different environment and light-matter interaction conditions.

There are two general requirements to harness the computational power of quantum mechanics: the ability to manipulate the evolution of an isolated system and the ability to faithfully extract information from it. Quantum error correction and simulation often make a more exacting demand: the ability to perform nondestructive measurements of specific correlations within that system. We realize such measurements by employing a protocol adapted from Nigg and Girvin [Phys. Rev. Lett. 110, 243604 (2013)], enabling real-time selection of arbitrary register-wide Pauli operators. Our implementation consists of a simple circuit quantum electrodynamics module of four highly coherent 3D transmon qubits, collectively coupled to a high-$Q$ superconducting microwave cavity. As a demonstration, we enact all seven nontrivial subset-parity measurements on our three-qubit register. For each, we fully characterize the realized measurement by analyzing the detector (observable operators) via quantum detector tomography and by analyzing the quantum backaction via conditioned process tomography. No single quantity completely encapsulates the performance of a measurement, and standard figures of merit have not yet emerged. Accordingly, we consider several new fidelity measures for both the detector and the complete measurement process. We measure all of these quantities and report high fidelities, indicating that we are measuring the desired quantities precisely and that the measurements are highly nondemolition. We further show that both results are improved significantly by an additional error-heralding measurement. The analyses we present here form a useful basis for the future characterization and validation of quantum measurements, anticipating the demands of emerging quantum technologies.

The loss of single-particle coherence going from the superconducting state to the normal state in underdoped cuprates is a dramatic effect that has yet to be understood. Here, we address this issue by performing angle resolved photoemission spectroscopy measurements in the presence of a transport current. We find that the loss of coherence is associated with the development of an onset in the resistance, in that well before the midpoint of the transition is reached, the sharp peaks in the angle resolved photoemission spectra are completely suppressed. Since the resistance onset is a signature of phase fluctuations, this implies that the loss of single-particle coherence is connected with the loss of long-range phase coherence.

It is an oft-cited fact that no quantum code can support a set of fault-tolerant logical gates that is both universal and transversal. This no-go theorem is generally responsible for the interest in alternative universality constructions including magic state distillation. Widely overlooked, however, is the possibility of nontransversal, yet still fault-tolerant, gates that work directly on small quantum codes. Here, we demonstrate precisely the existence of such gates. In particular, we show how the limits of nontransversality can be overcome by performing rounds of intermediate error correction to create logical gates on stabilizer codes that use no ancillas other than those required for syndrome measurement. Moreover, the logical gates we construct, the most prominent examples being Toffoli and controlled-controlled-$Z$, often complete universal gate sets on their codes. We detail such universal constructions for the smallest quantum codes, the 5-qubit and 7-qubit codes, and then proceed to generalize the approach. One remarkable result of this generalization is that any nondegenerate stabilizer code with a complete set of fault-tolerant single-qubit Clifford gates has a universal set of fault-tolerant gates. Another is the interaction of logical qubits across different stabilizer codes, which, for instance, implies a broadly applicable method of code switching.

The empirical validation of community detection methods is often based on available annotations on the nodes that serve as putative indicators of the large-scale network structure. Most often, the suitability of the annotations as topological descriptors itself is not assessed, and without this it is not possible to ultimately distinguish between actual shortcomings of the community detection algorithms, on one hand, and the incompleteness, inaccuracy, or structured nature of the data annotations themselves, on the other. In this work, we present a principled method to access both aspects simultaneously. We construct a joint generative model for the data and metadata, and a nonparametric Bayesian framework to infer its parameters from annotated data sets. We assess the quality of the metadata not according to their direct alignment with the network communities, but rather in their capacity to predict the placement of edges in the network. We also show how this feature can be used to predict the connections to missing nodes when only the metadata are available, as well as predicting missing metadata. By investigating a wide range of data sets, we show that while there are seldom exact agreements between metadata tokens and the inferred data groups, the metadata are often informative of the network structure nevertheless, and can improve the prediction of missing nodes. This shows that the method uncovers meaningful patterns in both the data and metadata, without requiring or expecting a perfect agreement between the two.

We present the first experimental evidence, supported by theory and simulation, of spatiotemporal optical vortices (STOVs). A STOV is an optical vortex with phase and energy circulation in a spatiotemporal plane. Depending on the sign of the material dispersion, the local electromagnetic energy flow is saddle or spiral about the STOV. STOVs are a fundamental element of the nonlinear collapse and subsequent propagation of short optical pulses in material media, and conserve topological charge, constraining their birth, evolution, and annihilation. We measure a self-generated STOV consisting of a ring-shaped null in the electromagnetic field about which the phase is spiral, forming a dynamic torus that is concentric with and tracks the propagating pulse. Our results, here obtained for optical pulse collapse and filamentation in air, are generalizable to a broad class of nonlinearly propagating waves.

Entangling two remote quantum systems that never interact directly is an essential primitive in quantum information science and forms the basis for the modular architecture of quantum computing. When protocols to generate these remote entangled pairs rely on using traveling single-photon states as carriers of quantum information, they can be made robust to photon losses, unlike schemes that rely on continuous variable states. However, efficiently detecting single photons is challenging in the domain of superconducting quantum circuits because of the low energy of microwave quanta. Here, we report the realization of a robust form of concurrent remote entanglement based on a novel microwave photon detector implemented in the superconducting circuit quantum electrodynamics platform of quantum information. Remote entangled pairs with a fidelity of $0.57\pm 0.01$ are generated at 200 Hz. Our experiment opens the way for the implementation of the modular architecture of quantum computation with superconducting qubits.

Using low-temperature electrical measurements, the interrelation between electron transport, magnetic properties, and ionic defect structure in complex oxide interface systems is investigated, focusing on ${\mathrm{NdGaO}}_3/{\mathrm{SrTiO}}_3$ (100) interfaces. Field-dependent Hall characteristics (2–300 K) are obtained for samples grown at various growth pressures. In addition to multiple electron transport, interfacial magnetism is tracked exploiting the anomalous Hall effect (AHE). These two properties both contribute to a nonlinearity in the field dependence of the Hall resistance, with multiple carrier conduction evident below 30 K and AHE at temperatures $\lesssim 10\mathrm{K}$. Considering these two sources of nonlinearity, we suggest a phenomenological model capturing the complex field dependence of the Hall characteristics in the low-temperature regime. Our model allows the extraction of the conventional transport parameters and a qualitative analysis of the magnetization. The electron mobility is found to decrease systematically with increasing growth pressure. This suggests dominant electron scattering by acceptor-type strontium vacancies incorporated during growth. The AHE scales with growth pressure. The most pronounced AHE is found at increased growth pressure and, thus, in the most defective, low-mobility samples, indicating a correlation between transport, magnetism, and cation defect concentration.