Active matter exhibits various forms of nonequilibrium states in the absence of external forcing, including macroscopic steady-state currents. Such states are often too complex to be modeled from first principles, and our understanding of their physics relies heavily on minimal models. These are mostly studied in the case of “dry” active matter, where particle dynamics are dominated by friction with their surroundings. Significantly less is known about systems with long-range hydrodynamic interactions that belong to “wet” active matter. Dilute suspensions of motile bacteria, modeled as self-propelled dipolar particles interacting solely through long-ranged hydrodynamic fields, are arguably the most studied example from this class of active systems. Their phenomenology is well established: At a sufficiently high density of bacteria, there appear large-scale vortices and jets comprising many individual organisms, forming a chaotic state commonly known as bacterial turbulence. As revealed by computer simulations, below the onset of collective motion, the suspension exhibits very strong correlations between individual microswimmers stemming from the long-ranged nature of dipolar fields. Here, we demonstrate that this phenomenology is captured by the minimal model of microswimmers. We develop a kinetic theory that goes beyond the commonly used mean-field assumption and explicitly takes into account such correlations. Notably, these can be computed exactly within our theory. We calculate the fluid velocity variance, spatial and temporal correlation functions, the fluid velocity spectrum, and the enhanced diffusivity of tracer particles. We find that correlations are suppressed by particle self-propulsion, although the mean-field behavior is not restored even in the limit of very fast swimming. Our theory is not perturbative and is valid for any value of the microswimmer density below the onset of collective motion. This work constitutes a significant methodological advance and allows us to make qualitative and quantitative predictions that can be directly compared to experiments and computer simulations of microswimmer suspensions.

Accurate and predictive computations of the quantum-mechanical behavior of many interacting electrons in realistic atomic environments are critical for the theoretical design of materials with desired properties, and they require solving the grand-challenge problem of the many-electron Schrödinger equation. An infinite chain of equispaced hydrogen atoms is perhaps the simplest realistic model for a bulk material, embodying several central themes of modern condensed-matter physics and chemistry while retaining a connection to the paradigmatic Hubbard model. Here, we report a combined application of cutting-edge computational methods to determine the properties of the hydrogen chain in its quantum-mechanical ground state. Varying the separation between the nuclei leads to a rich phase diagram, including a Mott phase with quasi-long-range antiferromagnetic order, electron density dimerization with power-law correlations, an insulator-to-metal transition, and an intricate set of intertwined magnetic orders.

Direct detection of single photons at wavelengths beyond $2\mu \mathrm{m}$ under ambient conditions remains an outstanding technological challenge. One promising approach is frequency upconversion into the visible (VIS) or near-infrared (NIR) domain, where single-photon detectors are readily available. Here, we propose a nanoscale solution based on a molecular optomechanical platform to up-convert photons from the far- and mid-infrared (covering part of the terahertz gap) into the VIS-NIR domain. We perform a detailed analysis of its outgoing noise spectral density and conversion efficiency with a full quantum model. Our platform consists in doubly resonant nanoantennas focusing both the incoming long-wavelength radiation and the short-wavelength pump laser field into the same active region. There, infrared active vibrational modes are resonantly excited and couple through their Raman polarizability to the pump field. This optomechanical interaction is enhanced by the antenna and leads to the coherent transfer of the incoming low-frequency signal onto the anti-Stokes sideband of the pump laser. Our calculations demonstrate that our scheme is realizable with current technology and that optimized platforms can reach single-photon sensitivity in a spectral region where this capability remains unavailable to date.

Experimental data are often affected by uncontrolled variables that make analysis and interpretation difficult. For spatiotemporal systems, this problem is further exacerbated by their intricate dynamics. Modern machine learning methods are particularly well suited for analyzing and modeling complex datasets, but to be effective in science, the result needs to be interpretable. We demonstrate an unsupervised learning technique for extracting interpretable physical parameters from noisy spatiotemporal data and for building a transferable model of the system. In particular, we implement a physics-informed architecture based on variational autoencoders that is designed for analyzing systems governed by partial differential equations. The architecture is trained end to end and extracts latent parameters that parametrize the dynamics of a learned predictive model for the system. To test our method, we train our model on simulated data from a variety of partial differential equations with varying dynamical parameters that act as uncontrolled variables. Numerical experiments show that our method can accurately identify relevant parameters and extract them from raw and even noisy spatiotemporal data (tested with roughly 10% added noise). These extracted parameters correlate well (linearly with $R^2>0.95$) with the ground truth physical parameters used to generate the datasets. We then apply this method to nonlinear fiber propagation data, generated by an ab initio simulation, to demonstrate its capabilities on a more realistic dataset. Our method for discovering interpretable latent parameters in spatiotemporal systems will allow us to better analyze and understand real-world phenomena and datasets, which often have unknown and uncontrolled variables that alter the system dynamics and cause varying behaviors that are difficult to disentangle.

The classification and lattice model construction of symmetry-protected topological (SPT) phases in interacting fermion systems are very interesting but challenging. In this paper, we give a systematic fixed-point wave function construction of fermionic SPT (FSPT) states for generic fermionic symmetry group $G_f={\mathbb{Z}}_2^f{\times }_{{\omega }_2}{G}_b$ which is a central extension of bosonic symmetry group $G_b$ (may contain time-reversal symmetry) by the fermion parity symmetry group ${\mathbb{Z}}_2^f=\{1,P_f\}$. Our construction is based on the concept of an equivalence class of finite-depth fermionic symmetric local unitary transformations and decorating symmetry domain wall picture, subjected to certain obstructions. We also discuss the systematical construction and classification of boundary anomalous SPT states which leads to a trivialization of the corresponding bulk FSPT states. Thus, we conjecture that the obstruction-free and trivialization-free constructions naturally lead to a classification of FSPT phases. Each fixed-point wave function admits an exactly solvable commuting-projector Hamiltonian. We believe that our classification scheme can be generalized to point and space group symmetry as well as continuum Lie group symmetry.

We present the first experimental determination of the intra-atomic exchange energy between the inner $4f$ and the outer $6s5d$ shells in rare-earth elements. Inelastic electron tunneling spectroscopy on individual rare-earth atoms adsorbed on metal-supported graphene reveals an element-dependent excitation, with energy between 30 and 170 meV, linearly increasing with the spin angular momentum of the $4f$ shell. This observation is possible owing to the strong spin polarization of the outer shells, characteristic of rare-earth adatoms on graphene. This polarization gives rise to a giant magnetoresistance of up to 75% observed for Dy on $\mathrm{graphene}/\mathrm{Ir}(111)$ single-atom magnets. Density functional theory calculations of the $6s5d$ shell spin polarizations and of their intra-atomic exchange constants with the $4f$ shell yield exchange energies in agreement with the experimental values. These results prove that the description of the spin dynamics in RE considering only the $4f-5d$ interaction is oversimplified. A more realistic treatment requires us to consider a multishell intra-atomic exchange in which both $6s$ and $5d$ shells are taken into account, with the $4f-6s$ contribution possibly prevailing over the $4f-5d$ one. Our findings are important for the general understanding of magnetism in rare earths, whether they are in bulk compounds or as surface adsorbed atoms and clusters. The results presented here also push for a revision of the description of the spin dynamics in rare-earth-based systems.

We study the effects of finite temperature on normal state properties of a metal near a quantum critical point to an antiferromagnetic or Ising-nematic state. At $T=0$, bosonic and fermionic self-energies are traditionally computed within Eliashberg theory, and they obey scaling relations with characteristic power laws. Corrections to Eliashberg theory break these power laws but only at very small frequencies. Quantum Monte Carlo (QMC) simulations have shown that, already at much larger frequencies, there are strong systematic deviations from these predictions, casting doubt on the validity of the theoretical analysis. We extend Eliashberg theory to finite $T$ and argue that in the $T$ range accessible in the QMC simulations above the superconducting transition, the scaling forms for both fermionic and bosonic self-energies are quite different from those at $T=0$. We compare finite $T$ results with QMC data and find good agreement for both systems. We argue that this agreement resolves the key apparent contradiction between the theory and the QMC simulations.

Hund metals have attracted attention in recent years due to their unconventional superconductivity, which supposedly originates from non-Fermi-liquid (NFL) properties of the normal state. When studying Hund metals using dynamical mean-field theory, one arrives at a self-consistent “Hund impurity problem” involving a multiorbital quantum impurity with nonzero Hund coupling interacting with a metallic bath. If its spin and orbital degrees of freedom are screened at different energy scales, $T_{\mathrm{sp}}<T_{\text{orb}}$, the intermediate energy window is governed by a novel NFL fixed point, whose nature had not yet been clarified. We resolve this problem by providing an analytical solution of a paradigmatic example of a Hund impurity problem, involving two spin and three orbital degrees of freedom. To this end, we combine a state-of-the-art implementation of the numerical renormalization group, capable of exploiting non-Abelian symmetries, with a generalization of Affleck and Ludwig’s conformal field theory (CFT) approach for multichannel Kondo models. We characterize the NFL fixed point of Hund metals in detail for a Kondo model with an impurity forming an $\mathrm{SU}(2)\times \mathrm{SU}(3)$ spin-orbital multiplet, tuned such that the NFL energy window is very wide. The impurity’s spin and orbital susceptibilities then exhibit striking power-law behavior, which we explain using CFT arguments. We find excellent agreement between CFT predictions and numerical renormalization group results. Our main physical conclusion is that the regime of spin-orbital separation, where orbital degrees of freedom have been screened but spin degrees of freedom have not, features anomalously strong local spin fluctuations: the impurity susceptibility increases as ${\chi }_{\mathrm{sp}}^{\text{imp}}\sim {\omega }^{-\gamma }$, with $\gamma >1$.

We report a probable observation of the dc Josephson effect in mesoscopic junctions of three and four superconductors. The devices are fabricated in a top-down fashion from a hybrid semiconductor-superconductor $\mathrm{InAs}/\mathrm{Al}$ epitaxial heterostructure. In general, the critical current of an $N$-terminal junction is an ($N-1$)-dimensional hypersurface in the space of bias currents, which can be reduced to a set of critical current contours. The geometry of critical current contours exhibits nontrivial responses to electrical gating, magnetic field, and phase bias, and it can be reproduced by the scattering formulation of the Josephson effect generalized to the case of $N>2$. Besides establishing solid ground beneath a host of recent theory proposals, our experiment accomplishes an important step toward creating trijunctions of topological superconductors, essential for braiding operations.

We construct quantum error-correcting codes that embed a finite-dimensional code space in the infinite-dimensional Hilbert space of rotational states of a rigid body. These codes, which protect against both drift in the body’s orientation and small changes in its angular momentum, may be well suited for robust storage and coherent processing of quantum information using rotational states of a polyatomic molecule. Extensions of such codes to rigid bodies with a symmetry axis are compatible with rotational states of diatomic molecules as well as nuclear states of molecules and atoms. We also describe codes associated with general non-Abelian groups and develop orthogonality relations for coset spaces, laying the groundwork for quantum information processing with exotic configuration spaces.

Degeneracies play a crucial rule in precise scientific measurements as well as in sensing applications. Spherical resonators have a high degree of degeneracy thanks to their highest symmetry; yet, fabricating perfect spheres is challenging because even a stem to hold the sphere breaks the symmetry. Here we fabricate a levitating spherical resonator that is evanescently coupled to a standard optical fiber. We characterize the resonators to exhibit an optical quality factor exceeding a billion, $10\mu \mathrm{m}$ radius, and sphericity to within less than 1 Å. Using our high quality and sphericity, we experimentally lift degeneracies of orders higher than 200, which we resolve with optical finesse exceeding 10 000 000. We then present our experimentally measured degenerate modes as well as their density of states next to our corresponding theoretical calculation. Our contactless photonic resonator is compatible with standard telecom fiber technology, exhibits the highest resonance enhancement as defined by (quality factor)/(mode volume), and the modes populating our cavity show the highest order of degeneracy reported in any system ever studied. This is in comparison with other settings that typically utilize the lowest-order twofold degeneracy.

Laser-dressed photoemission spectroscopy has established itself as the gold standard of attosecond temporal metrology. In this technique, the attosecond structure of an extreme-ultraviolet pulse is retrieved from the wave function of the electron wave packet released during photoionization. Here, we show that this electron wave packet should rather be described using the density matrix formalism, thus allowing one to account for all processes that can affect its coherence, from the attosecond pulse generation to the photoemission and the measurement processes. Using this approach, we reconstruct experimentally a partially coherent electron wave packet with a purity of 0.11 (1 for full coherence). Comparison with theoretical models then allows us to identify the origins of this decoherence and to overcome several limitations such as beam-line instabilities or spectrometer resolution. Furthermore, we show numerically how this method gives access to the coherence and eigencomponents of complex photoelectron wave packets. It thus goes beyond the current measurement of photoionization time delays and provides a general framework for the analysis and understanding of complex photoemission processes.

Ultrafast phase transitions induced by femtosecond light pulses present a new opportunity for manipulating the properties of materials. Understanding how these transient states are different from, or similar to, their thermal counterparts is key to determining how materials can exhibit properties that are not found in equilibrium. In this paper, we reexamine the case of the light-induced insulator-metal phase transition in the prototypical, strongly correlated material ${\mathrm{VO}}_2$, for which a nonthermal Mott-Hubbard transition has been claimed. Here, we show that heat, even on the ultrafast timescale, plays a key role in the phase transition. When heating is properly accounted for, we find a single phase-transition threshold corresponding to the thermodynamic structural insulator-metal phase transition, and we find no evidence of a hidden transient Mott-Hubbard nonthermal phase. The interplay between the initial thermal state and the ultrafast transition may have implications for other transient states of matter.

We introduce the Rydberg composite, a new class of Rydberg matter where a single Rydberg atom is interfaced with a dense environment of neutral ground state atoms. The properties of the composite depend on both the Rydberg excitation, which provides the gross energetic and spatial scales, and the distribution of ground state atoms within the volume of the Rydberg wave function, which sculpt the electronic states. The latter range from the “trilobites,” for small numbers of scatterers, to delocalized and chaotic eigenstates, for disordered scatterer arrays, culminating in the dense scatterer limit in symmetry-dominated wave functions which promise good control in future experiments. We discuss one-, two-, and three-dimensional arrangements of scatterers using different theoretical methods, enabling us to obtain scaling behavior for the regular spectrum and measures of chaos and delocalization in the disordered regime. We also show that analogous quantum dot composites can elucidate in particular the dense scatterer limit. Thus, we obtain a systematic description of the composite states. The two-dimensional monolayer composite possesses the richest spectrum with an intricate band structure in the limit of homogeneous scatterers, experimentally accessible with pancake-shaped condensates.

The spherical $p$-spin model is a fundamental model in statistical mechanics of a disordered system with a random first-order transition. The dynamics of this model is interesting both for the physics of glasses and for its implications on hard optimization problems. Here, we revisit the out-of-equilibrium dynamics of the spherical mixed $p$-spin model, which differs from the pure $p$-spin model by the fact that the Hamiltonian is not a homogeneous function of its variables. We consider quenches (gradient descent dynamics) starting from initial conditions thermalized in the high-temperature ergodic phase. Unexpectedly, we find that, differently from the pure $p$-spin case, the asymptotic states of the dynamics keep memory of the initial condition. The final energy is a decreasing function of the initial temperature, and the system remains correlated with the initial state. This dependence disproves the idea of a unique “threshold” energy level attracting dynamics starting from high-temperature initial conditions. Thermalization, which could be achieved, e.g., by an algorithm like simulated annealing, provides an advantage in gradient descent dynamics and, last but not least, brings mean-field models closer to real glass phenomenology, where such a dependence is observed in numerical simulations. We investigate the nature of the asymptotic dynamics, finding an aging state that relaxes towards deep, marginally stable minima. However, careful analysis rules out simple generalizations of the aging solution of the pure model. We compute the constrained complexity with the aim of connecting the asymptotic solution to the energy landscape.

Most materials are changed by their history and show memory of things past. However, it is not clear when a system can continually learn new memories in sequence, without interfering with or entirely overwriting earlier memories. Here, we study the learning of multiple stable states in sequence by an elastic material that undergoes plastic changes as it is held in different configurations. We show that an elastic network with linear or nearly linear springs cannot learn continually without overwriting earlier states for a broad class of plasticity rules. On the other hand, networks of sufficiently nonlinear springs can learn continually, without erasing older states, using even simple plasticity rules. We trace this ability to cusped energy contours caused by strong nonlinearities and thus show that elastic nonlinearities play the role of Bayesian priors used in sparse statistical regression. Our model shows how specific material properties allow continual learning of new functions through deployment of the material itself.

The Jahn-Teller effect is one of the most fundamental phenomena important not only for physics but also for chemistry and material science. Solving the Jahn-Teller problem and taking into account strong electron correlations we show that quantum entanglement of the spin and orbital degrees of freedom via spin-orbit coupling strongly affects this effect. Depending on the number of $d$ electrons, it may quench (electronic configurations $t_{2g}^2$, $t_{2g}^4$, and $t_{2g}^5$), partially suppress ($t_{2g}^1$), or, in contrast, induce ($t_{2g}^3$) Jahn-Teller distortions. Moreover, in certain situations, interplay between the Jahn-Teller effect and spin-orbit coupling promotes formation of the “Mexican hat” energy surface facilitating various quantum phenomena.

In practically all branches of physics, different types of solitons, with a number of them enjoying topological protection, are found. Here we explore how one- and two-dimensional topological solitons formed by spatially localized continuous orientational patterns of optical axis in uniaxial birefringent media interact with light. These solitons, in the forms of one-dimensional twist walls and two-dimensional skyrmions, are controllably generated in thin films of cholesteric liquid crystals to introduce spatially localized patterns of effective refractive index. Laser light interacts with these solitons as quasiparticles or extended interfaces of different effective refractive indices seen by ordinary and extraordinary waves propagating within the liquid-crystal medium. Despite our system’s complex nature, our findings can be paralleled with the familiar phenomena of total reflection and refraction at interfaces of optically distinct media, albeit these behaviors arise in a medium with homogeneous density and chemical composition but with spatial variations of molecular and optical-axis orientations. By exploiting the facile response of liquid crystals to external stimuli, we show that the twist walls and skyrmions can be used to steer laser beams and to act as lenses and other optical elements, which can be reconfigured by low-voltage fields and other means. Analytical and numerical modeling, with the latter based on free-energy-minimizing configurations of the topological solitons, closely reproduce our experimental findings. The fundamental insights provided by this work potentially can be extended also to three-dimensional solitons, such as Hopfions, and may lead to technological applications of optical-axis topological solitons in telecommunications, nanophotonics, electro-optics, and so on.

A self-correcting quantum memory can store and protect quantum information for a time that increases without bound with the system size and without the need for active error correction. We demonstrate that symmetry can lead to self-correction in 3D spin-lattice models. In particular, we investigate codes given by 2D symmetry-enriched topological (SET) phases that appear naturally on the boundary of 3D symmetry-protected topological (SPT) phases. We find that while conventional on-site symmetries are not sufficient to allow for self-correction in commuting Hamiltonian models of this form, a generalized type of symmetry known as a 1-form symmetry is enough to guarantee self-correction. We illustrate this fact with the 3D “cluster-state” model from the theory of quantum computing. This model is a self-correcting memory, where information is encoded in a 2D SET-ordered phase on the boundary that is protected by the thermally stable SPT ordering of the bulk. We also investigate the gauge color code in this context. Finally, noting that a 1-form symmetry is a very strong constraint, we argue that topologically ordered systems can possess emergent 1-form symmetries, i.e., models where the symmetry appears naturally, without needing to be enforced externally.