The interactions of the excited states of a single chromophore with static and dynamic electric fields spatially varying at the atomic scale are investigated in a joint experimental and theoretical effort. In this configuration, the spatial extension of the fields confined at the apex of a scanning tunneling microscope tip is smaller than that of the molecular exciton, a property used to generate fluorescence maps of the chromophore with intramolecular resolution. Theoretical simulations of the electrostatic and electrodynamic interactions occurring at the picocavity junction formed by the chromophore, the tip, and the substrate reveal the key role played by subtle variations of Purcell, Lamb, and Stark effects. They also demonstrate that hyper-resolved fluorescence maps of the line shift and linewidth of the excitonic emission can be understood as images of the static charge redistribution upon electronic excitation of the molecule and as the distribution of the dynamical charge oscillation associated with the molecular exciton, respectively.

Recurrent neural networks (RNNs) are powerful dynamical models, widely used in machine learning (ML) and neuroscience. Prior theoretical work has focused on RNNs with additive interactions. However, gating, i.e., multiplicative, interactions are ubiquitous in real neurons and also the central feature of the best-performing RNNs in ML. Here, we show that gating offers flexible control of two salient features of the collective dynamics: (i) timescales and (ii) dimensionality. The gate controlling timescales leads to a novel, marginally stable state, where the network functions as a flexible integrator. Unlike previous approaches, gating permits this important function without parameter fine-tuning or special symmetries. Gates also provide a flexible, context-dependent mechanism to reset the memory trace, thus complementing the memory function. The gate modulating the dimensionality can induce a novel, discontinuous chaotic transition, where inputs push a stable system to strong chaotic activity, in contrast to the typically stabilizing effect of inputs. At this transition, unlike additive RNNs, the proliferation of critical points (topological complexity) is decoupled from the appearance of chaotic dynamics (dynamical complexity). The rich dynamics are summarized in phase diagrams, thus providing a map for principled parameter initialization choices to ML practitioners.

Network inference is the process of learning the properties of complex networks from data. Besides using information about known links in the network, node attributes and other forms of network metadata can help solve network inference problems. Indeed, several approaches have been proposed to introduce metadata into probabilistic network models and to use them to make better inferences. However, we know little about the effect of such metadata in the inference process. Here, we investigate this issue. We find that, rather than affecting inference gradually, adding metadata causes a crossover in the inference process and in our ability to make accurate predictions, from a situation in which metadata do not play any role to a situation in which metadata completely dominate the inference process. When network data and metadata are partly correlated, metadata optimally contributes to the inference process at the crossover between data-dominated and metadata-dominated regimes.

We discuss several low-energy backgrounds to sub-GeV dark-matter searches, which arise from high-energy particles of cosmic or radioactive origin that interact with detector materials. We focus, in particular, on Cherenkov radiation, transition radiation, and luminescence or phonons from electron-hole pair recombination and show that these processes are an important source of backgrounds at both current and planned detectors. We perform detailed analyses of these backgrounds at several existing and proposed experiments based on a wide variety of detection strategies and levels of shielding. We find that a large fraction of the observed single-electron events in the SENSEI 2020 run originate from Cherenkov photons generated by high-energy events in the Skipper charge coupled device and from recombination photons generated in a phosphorus-doped layer of the same instrument. In a SuperCDMS HVeV 2020 run, Cherenkov photons produced in printed-circuit boards located near the sensor likely explain the origin of most of the events containing 2–6 electrons. At SuperCDMS SNOLAB, radioactive contaminants inside the Cirlex located inside or on the copper side walls of their detectors produce many Cherenkov photons, which could dominate the low-energy backgrounds. For the EDELWEISS experiment, Cherenkov or luminescence backgrounds are subdominant to their observed event rate but could still limit the sensitivity of their future searches. We also point out that Cherenkov radiation, transition radiation, and recombination could be a significant source of backgrounds at future experiments aiming to detect dark matter via scintillation or phonon signals. We also discuss the implications of our results for the development of superconducting qubits and low-threshold searches for coherent neutrino scattering. Fortunately, several design strategies to mitigate these backgrounds can be implemented, such as minimizing nonconductive materials near the target, implementing active and passive shielding, and using multiple nearby detectors.

Deterministic photon-photon gates enable the controlled generation of entanglement between mobile carriers of quantum information. Such gates have thus far been exclusively realized in the optical domain and by relying on postselection. Here, we present a nonpostselected, deterministic, photon-photon gate in the microwave frequency range realized using superconducting circuits. We emit photonic qubits from a source chip and route those qubits to a gate chip with which we realize a universal gate set by combining controlled absorption and reemission with single-qubit gates and qubit-photon controlled-phase gates. We measure quantum process fidelities of 75% for single- and of 57% for two-qubit gates, limited mainly by radiation loss and decoherence. This universal gate set has a wide range of potential applications in superconducting quantum networks.

Central to the success of adaptive systems is their ability to interpret signals from their environment and respond accordingly—they act as agents interacting with their surroundings. Such agents typically perform better when able to execute increasingly complex strategies. This comes with a cost: the more information the agent must recall from its past experiences, the more memory it will need. Here we investigate the power of agents capable of quantum information processing. We uncover the most general form a quantum agent need adopt to maximize memory compression advantages and provide a systematic means of encoding their memory states. We show these encodings can exhibit extremely favorable scaling advantages relative to memory-minimal classical agents, particularly when information must be retained about events increasingly far into the past.

The statistics of gap ratios between consecutive energy levels is a widely used tool—in particular, in the context of many-body physics—to distinguish between chaotic and integrable systems, described, respectively, by Gaussian ensembles of random matrices and Poisson statistics. In this work, we extend the study of the gap ratio distribution $P(r)$ to the case where discrete symmetries are present. This is important since in certain situations it may be very impractical, or impossible, to split the model into symmetry sectors, let alone in cases where the symmetry is not known in the first place. Starting from the known expressions for surmises in the Gaussian ensembles, we derive analytical surmises for random matrices comprised of several independent blocks. We check our formulas against simulations from large random matrices, showing excellent agreement. We then present a large set of applications in many-body physics, ranging from quantum clock models and anyonic chains to periodically driven spin systems. In all these models, the existence of a (sometimes hidden) symmetry can be diagnosed through the study of the spectral gap ratios, and our approach furnishes an efficient way to characterize the number and size of independent symmetry subspaces. We finally discuss the relevance of our analysis for existing results in the literature, as well as its practical usefulness, and point out possible future applications and extensions.

Density matrix exponentiation (DME) is a general technique for using a quantum state $\rho$ to enact the quantum operation $e^{-i\rho \theta }$ on a target system. It was first proposed in the context of quantum machine learning, but has since been shown to have broad applications in quantum metrology and computation. No experimental demonstration of DME has been performed thus far due to its demanding circuit depths and the need to efficiently generate multiple identical copies of $\rho$ during the finite lifetime of the target system. In this work, we describe the first demonstration of the DME algorithm, which we accomplish using a superconducting quantum processor. Our demonstration relies on a 99.7% fidelity controlled-phase gate implemented using two tunable superconducting transmon qubits. We achieve a fidelity surpassing 90% at circuit depths exceeding 70 when comparing the output of the circuit executed on our quantum processor to a simulation assuming perfect operations and measurements.

Network homophily, the tendency of similar nodes to be connected, and transitivity, the tendency of two nodes to be connected if they share a common neighbor, are conflated properties in network analysis since one mechanism can drive the other. Here, we present a generative model and corresponding inference procedure that are capable of distinguishing between both mechanisms. Our approach is based on a variation of the stochastic block model (SBM) with the addition of triadic closure edges, and its inference can identify the most plausible mechanism responsible for the existence of every edge in the network, in addition to the underlying community structure itself. We show how the method can evade the detection of spurious communities caused solely by the formation of triangles in the network and how it can improve the performance of edge prediction when compared to the pure version of the SBM without triadic closure.

Skyrmions are topologically protected, vortexlike formations of a field that cannot be removed by any smooth transformation and emerge in a range of fundamentally different, either quantum or classical systems, from spin textures to chiral ferromagnets and chiral complex fluids. Notably, they are generally observed in thin ordered or disordered quasi-2D layers, but little is known about their three-dimensional structuring and organization, including structural transitions from 2D to 3D. Here, we show experimentally and numerically that the blue phase (BP) III of a chiral liquid crystal is a 3D fluid of chiral skyrmion filaments of the nematic orientational field, entangled with a 3D network of topological defect lines. It is an effective 3D dynamic fluid determined by the thermal fluctuations of two distinct branches of excitations: rapid internal fluctuations of the skyrmion structure and a slow collective motion of the skyrmion filaments. When confined to less than an approximately 150-nm layer, the 3D bulk skyrmion fluid transforms into a different effectively 2D liquid of half-skyrmions, with the dynamics of the skyrmion liquid slowing down by an order of magnitude and with the individual skyrmions lingering, and even disappearing into, and reappearing from the homogeneous liquid crystal. The thickness-temperature phase diagram actually shows that both the BPIII and BPI phases are made of skyrmions, which when confined to less than approximately 150 nm cells transform equally into a 2D half-skyrmion liquid. The temperature range of this 2D half-skyrmion liquid is much broader than the temperature interval of BP phases, which makes BP materials interesting for broad-temperature-range skyrmionic applications. We envisage a soft matter skyrmionic device, in which skyrmions are created and detected by light.

A shape resonance emerges during the light absorption in many molecules with a gigantic burst amplitude and a lifetime of hundreds of attoseconds. Recent advances in attosecond metrology revealed the attosecond lifetime of the shape resonance. For a heteronuclear molecule, the asymmetric initial state and landscape of the molecular potential would lead to an asymmetric shape resonance, whose effect, however, has not been characterized yet. Here, we employ an attosecond interferometer to investigate the molecular-frame photoionization time delay in the vicinity of the shape resonance of the NO molecule. Driven by photons with energy ranging from 23.8 eV to 36.5 eV, a 150 attosecond difference in the time delay is observed between photoemission from the $\mathrm{N}/\mathrm{O}$ end. Our quantum scattering theoretical simulations reproduce well our experimental findings. It illustrates that the asymmetric time delay originates from the interference between resonant and nonresonant photoionization pathways.

Kagome metals $A{\mathrm{V}}_3{\mathrm{Sb}}_5$ ($A=\mathrm{K}$, Rb, and Cs) exhibit a unique superconducting ground state coexisting with charge-density wave (CDW), whereas how these characteristics are affected by carrier doping remains unexplored because of the lack of an efficient carrier-doping method. Here we report successful electron doping to ${\mathrm{CsV}}_3{\mathrm{Sb}}_5$ by Cs dosing, as visualized by angle-resolved photoemission spectroscopy. We found that the electron doping with Cs dosing proceeds in an orbital-selective way, as characterized by a marked increase in electron filling of the Sb $5p_z$ and V $3d_{xz/yz}$ bands as opposed to the relatively insensitive nature of the V $3d_{xy/x^2-y^2}$ bands. By monitoring the temperature evolution of the CDW gap around the $\overline{M}$ point, we found that the CDW can be completely killed by Cs dosing while keeping the saddle point with the V $3d_{xy/x^2-y^2}$ character almost pinned at the Fermi level. The present result suggests a crucial role of multiorbital effect to the occurrence of CDW and provides an important step toward manipulating the CDW and superconductivity in $A{\mathrm{V}}_3{\mathrm{Sb}}_5$.

Recent developments in higherorder topological phases have revealed the relationship between nontrivial multipole moments in the bulk and the emergence of fractionally quantized charges at the boundary. Here, we put forth a proposal of the three-dimensional octupole insulator with fractionally quantized corner charges $\pm e/8$: sodium chloride, commonly known as table salt. The fractional quantization of the corner charge is unaffected by the quantum fluctuation of the electric charge per ion, as we demonstrate explicitly with ab initio calculations. We further show that the electrostatic signature of the fractional charge is well preserved even when the ideal crystal is sprinkled with defects, and provide a systematic analysis on how the corner charge contribution could be isolated from the electric-field corrections originating from realistic surface relaxation. Our results suggest that the observation of corner charges from quantized multipole moments in solids might be imminent.

We study magic angle graphene in the presence of both strain and particle-hole symmetry breaking due to nonlocal interlayer tunneling. We perform a self-consistent Hartree-Fock study that incorporates these effects alongside realistic interaction and substrate potentials and explore a comprehensive set of competing orders including those that break translational symmetry at arbitrary wave vectors. We find that at all nonzero integer fillings very small strains, comparable to those measured in scanning tunneling experiments, stabilize a fundamentally new type of time-reversal-symmetric and spatially nonuniform order. This order, which we dub the “incommensurate Kekulé spiral” (IKS) order, spontaneously breaks both the emergent valley-charge conservation and moiré translation symmetries but preserves a modified translation symmetry ${\widehat{T}}^{\prime }$—which simultaneously shifts the spatial coordinates and rotates the $U(1)$ angle which characterizes the spontaneous intervalley coherence. We discuss the phenomenological and microscopic properties of this order. We argue that our findings are consistent with all experimental observations reported so far, suggesting a unified explanation of the global phase diagram in terms of the IKS order.

Efficient quantum state measurement is important for maximizing the extracted information from a quantum system. For multiqubit quantum processors, in particular, the development of a scalable architecture for rapid and high-fidelity readout remains a critical unresolved problem. Here we propose reservoir computing as a resource-efficient solution to quantum measurement of superconducting multiqubit systems. We consider a small network of Josephson parametric oscillators, which can be implemented with minimal device overhead and in the same platform as the measured quantum system. We theoretically analyze the operation of such a device as a reservoir computer to classify stochastic time-dependent signals subject to quantum statistical features. We apply this reservoir computer to the task of multinomial classification of measurement trajectories from joint multiqubit readout. For a 2-qubit dispersive measurement under realistic conditions we demonstrate a classification fidelity reliably exceeding that of an optimal linear filter using only 2–5 reservoir nodes, while simultaneously requiring far less calibration data—as little as a few shots per state. We understand this remarkable performance through an analysis of the network dynamics and develop an intuitive picture of reservoir processing generally. Finally, we demonstrate how to operate this device to perform 2-qubit state tomography and continuous parity monitoring with equal effectiveness and ease of calibration. This reservoir processor avoids computationally intensive training common to other machine learning frameworks and can be implemented as an integrated cryogenic superconducting device for low-latency processing of quantum signals on the computational edge.

We discuss how to use correlations between different physical observables to improve recently obtained thermodynamics bounds, notably the fluctuation-response inequality and the thermodynamic uncertainty relation (TUR). We show that increasing the number of measured observables will always produce a tighter bound. This tighter bound becomes particularly useful if one of the observables is a conserved quantity, whose expectation is invariant under a given perturbation of the system. For the case of the TUR, we show that this applies to any function of the state of the system. The resulting correlation TUR takes into account the correlations between a current and a noncurrent observable, thereby tightening the TUR. We demonstrate our finding on a model of the ${\mathrm{F}}_1$-ATPase molecular motor, a Markov jump model consisting of two rings and transport through a two-dimensional channel. We find that the correlation TUR is significantly tighter than the TUR and can be close to an equality even far from equilibrium.

Detection of the energy conversion pathways between photons, charge carriers, and the lattice is of fundamental importance to understand fundamental physics and to advance materials and devices. Yet, such insight remains incomplete due to experimental challenges in disentangling the various signatures on overlapping timescales. Here, we show that attosecond core-level x-ray absorption fine-structure spectroscopy (XANES) meets this challenge by providing an unambiguous and simultaneous view on the temporal evolution of the photon-carrier-phonon system. We provide surprising new results by applying the method to graphite, a seemingly well-studied system whose investigation is complicated by a variety of mechanisms occurring across a wide range of temporal scales. The simultaneous real-time measurement of electrons and holes reveals disparate scattering mechanisms for infrared excitation close to the Fermi energy. We find that ultrafast dephasing of the coherent carrier dynamics is governed by impact excitation (IE) for electrons, while holes exhibit a switchover from impact excitation to Auger heating (AH) already during the 11-fs duration of the infrared light field. We attribute this switchover to the limited scattering phase space in the $n$-doped material. We further elucidate the excitation mechanisms of strongly coupled optical phonons (SCOPs). The coherent excitation of both SCOPs is nondisplacive and is explained by the strong electron-phonon scattering, i.e., via a seemingly incoherent process. We identify the $A_1^{\prime }$ phonon as the dominating channel for dissipation of electronic coherence. Moreover, unobserved in graphite, we find high-frequency oscillations up to 90 THz, which arise from the modulation of the electronic density of states by the atomic displacements along the $E_{2g}$ and $A_1^{\prime }$ modes. These measurements establish the utility of core-level XANES with attosecond temporal resolution to achieve an unambiguous and simultaneous view on the temporal evolution of the photon-carrier-phonon system with surprising new results even for a seemingly well-studied system like graphite. While the graphite measurement was conducted around the $K$ edge of carbon, adapting the methodology to other materials only requires spectra coverage of the respective elemental edge of the material’s constituent. This flexibility makes our methodology widely applicable to detect and distinguish the various dynamic contributions to the flow of energy inside materials on their native timescales.

We introduce topological invariants for gapless systems and study the associated boundary phenomena. More generally, the symmetry properties of the low-energy conformal field theory (CFT) provide discrete invariants establishing the notion of symmetry-enriched quantum criticality. The charges of nonlocal scaling operators, or more generally, of symmetry defects, are topological and imply the presence of localized edge modes. We primarily focus on the $1+1d$ case where the edge has a topological degeneracy, whose finite-size splitting can be exponential or algebraic in system size depending on the involvement of additional gapped sectors. An example of the exponential case is given by tuning the spin-1 Heisenberg chain to a symmetry-breaking Ising phase. An example of the algebraic case arises between the gapped Ising and cluster phases: This symmetry-enriched Ising CFT has an edge mode with finite-size splitting scaling as $1/L^{14}$. In addition to such new cases, our formalism unifies various examples previously studied in the literature. Similar to gapped symmetry-protected topological phases, a given CFT can split into several distinct symmetry-enriched CFTs. This raises the question of classification, to which we give a partial answer—including a complete characterization of symmetry-enriched $1+1d$ Ising CFTs. Nontrivial topological invariants can also be constructed in higher dimensions, which we illustrate for a symmetry-enriched $2+1d$ CFT without gapped sectors.

Correcting errors in real time is essential for reliable large-scale quantum computations. Realizing this high-level function requires a system capable of several low-level primitives, including single-qubit and two-qubit operations, midcircuit measurements of subsets of qubits, real-time processing of measurement outcomes, and the ability to condition subsequent gate operations on those measurements. In this work, we use a 10-qubit quantum charge-coupled device trapped-ion quantum computer to encode a single logical qubit using the $[[7,1,3]]$ color code, first proposed by Steane [Phys. Rev. Lett. 77, 793 (1996)]. The logical qubit is initialized into the eigenstates of three mutually unbiased bases using an encoding circuit, and we measure an average logical state preparation and measurement (SPAM) error of $1.7(2)\times {10}^{-3}$, compared to the average physical SPAM error $2.4(4)\times {10}^{-3}$ of our qubits. We then perform multiple syndrome measurements on the encoded qubit, using a real-time decoder to determine any necessary corrections that are done either as software updates to the Pauli frame or as physically applied gates. Moreover, these procedures are done repeatedly while maintaining coherence, demonstrating a dynamically protected logical qubit memory. Additionally, we demonstrate non-Clifford qubit operations by encoding a $\overline{T}|+{⟩}_L$ magic state with an error rate below the threshold required for magic state distillation. Finally, we present system-level simulations that allow us to identify key hardware upgrades that may enable the system to reach the pseudothreshold.

A salient feature of solid-state quantum-Hall-type topological materials in two dimensions is the presence of conducting electronic edge states that are insensitive to scattering by disorder. Such unidirectional edge states have been predicted and observed in many other experimental settings, including photonics, mechanical, and acoustic structures. It is of great interest to understand how topological states behave in the presence of interparticle interactions and nonlinearity. Here, we experimentally demonstrate backscatter-immune unidirectional solitonlike nonlinear states on the edge of photonic topological insulators consisting of laser-written waveguides. As a result of the optical Kerr nonlinearity of the ambient glass, the solitonlike wave packet forms a long-lived quasilocalized coherent structure that slowly radiates power into the bulk and along the edge. The realization of solitonlike edge states paves the way to an understanding of nonlinear and interacting topological systems.