In self-assembling systems, geometric frustration leads to complex states characterized by internal gradients of shape misfit. Frustrated assemblies have drawn recent interest due to the unique possibility that their thermodynamics can sense and select the finite size of assembly at length scales much larger than constituent building blocks or their interactions. At present, self-limitation is chiefly understood to derive from zero-temperature considerations, specifically the competition between cohesion and scale-dependent elastic costs of frustration. While effects of entropy and finite-temperature fluctuations are necessarily significant for self-assembling systems, their impact on the self-limiting states of frustrated assemblies is not known. We introduce a generic, minimal model of frustrated assembly and establish its finite-temperature and concentration-dependent thermodynamics by way of simulation and continuum theory. The phase diagram is marked by three distinct states of translation order: a dispersed vapor, a defect-riddled condensate, and the self-limiting aggregate state. We show that, at finite temperature, the self-limiting state is stable at intermediate frustration. Furthermore, in contrast to the prevailing picture, its thermodynamic boundaries with the macroscopic disperse and bulk states are temperature controlled, pointing to the essential importance of translational and conformational entropy in their formation.

First-principles calculations of phonons are often based on the adiabatic approximation and on Brillouin-zone samplings that might not always be sufficient to capture the subtleties of Kohn anomalies. These shortcomings can be addressed through corrections to the phonon self-energy arising from the low-energy electrons. The exact self-energy involves a product of a bare and a screened electron-phonon vertex [Rev. Mod. Phys. 89, 015003 (2017)]; still, calculations often employ two adiabatically screened vertices, which have been proposed as a reliable approximation for self-energy differences [Phys. Rev. B 82, 165111 (2010)]. We assess the accuracy of both approaches in estimating the phonon spectral functions of model Hamiltonians and the adiabatic low-temperature phonon dispersions of monolayer ${\mathrm{TaS}}_2$ and doped ${\mathrm{MoS}}_2$. We find that the approximate method yields excellent corrections at low computational cost, due to its designed error cancellation to first order, while using a bare vertex could in principle improve these results but is challenging in practice. We offer an alternative strategy based on downfolding to partially screened phonons and interactions [Phys. Rev. B 92, 245108 (2015)]. This is a natural scheme to include electron-electron interactions and tackle phonons in strongly correlated materials and the frequency dependence of the electron-phonon vertex.

The concept of space evolution (or space-time duality) has emerged as a promising approach for studying quantum dynamics. The basic idea involves exchanging the roles of space and time, evolving the system using a space transfer matrix rather than the time evolution operator. The infinite-volume limit is then described by the fixed points of the latter transfer matrix, also known as influence matrices. To establish the potential of this method as a bona fide computational scheme, it is important to understand whether the influence matrices can be efficiently encoded in a classical computer. Here we begin this quest by presenting a systematic characterization of their entanglement—dubbed temporal entanglement—in chaotic quantum systems. We consider the most general form of space evolution, i.e., evolution in a generic spacelike direction, and present two fundamental results. First, we show that temporal entanglement always follows a volume law in time. Second, we identify two marginal cases—(i) pure space evolution in generic chaotic systems and (ii) any spacelike evolution in dual-unitary circuits—where Rényi entropies with index larger than one are sublinear in time while the von Neumann entanglement entropy grows linearly. We attribute this behavior to the existence of a product state with large overlap with the influence matrices. This unexpected structure in the temporal entanglement spectrum might be the key to an efficient computational implementation of the space evolution.

We present comprehensive theoretical studies on the lattice relaxation and the electronic structures in general nonsymmetric twisted trilayer graphenes. By using an effective continuum model, we show that the relaxed lattice structure forms a patchwork of moiré-of-moiré domains, where a moiré pattern given by layer 1 and 2 and another pattern given by layer 2 and 3 become locally commensurate. The atomic configuration inside the domain exhibits a distinct contrast between chiral and alternating stacks, which are determined by the relative signs of the two twist angles. In the chiral case, the electronic band calculation reveals a wide energy window ($>50\mathrm{meV}$) with low density of states, featuring sparsely distributed highly one-dimensional electron bands. These one-dimensional states exhibit a sharp localization at the boundaries between supermoiré domains, and they are identified as a topological boundary state between distinct Chern insulators. The alternating trilayer exhibits a coexistence of the flat bands and a monolayerlike Dirac cone, and it is attributed to the formation of moiré-of-moiré domains equivalent to the mirror-symmetric twisted trilayer graphene.

The interplay between stochastic chemical reactions and diffusion can generate rich spatiotemporal patterns. While the timescale for individual reaction or diffusion events may be very fast, the timescales for organization can be much longer. That separation of timescales makes it particularly challenging to anticipate how the rapid microscopic dynamics gives rise to macroscopic rates in the nonequilibrium dynamics of many reacting and diffusing chemical species. Within the regime of stochastic fluctuations, the standard approach is to employ Monte Carlo sampling to simulate realizations of random trajectories. Here, we present an alternative numerically tractable approach to extract macroscopic rates from the full ensemble evolution of many-body reaction-diffusion problems. The approach leverages the Doi-Peliti second-quantized representation of reaction-diffusion master equations along with compression and evolution algorithms from tensor networks. By focusing on a Schlögl model with one-dimensional diffusion between $L$ otherwise well-mixed sites, we illustrate the potential of the tensor network approach to compute rates from many-body systems, here with approximately $3\times {10}^{15}$ microstates. Specifically, we compute the rate for switching between metastable macrostates, with the expense for computing those rates growing subexponentially in $L$. Because we directly work with ensemble evolutions, we crucially bypass many of the difficulties encountered by rare event sampling techniques—detailed balance and reaction coordinates are not needed.

Superconducting qubits are a leading system for realizing large-scale quantum processors, but overall gate fidelities suffer from coherence times limited by microwave dielectric loss. Recently discovered tantalum-based qubits exhibit record lifetimes exceeding 0.3 ms. Here, we perform systematic, detailed measurements of superconducting tantalum resonators in order to disentangle sources of loss that limit state-of-the-art tantalum devices. By studying the dependence of loss on temperature, microwave photon number, and device geometry, we quantify materials-related losses and observe that the losses are dominated by several types of saturable two-level systems (TLSs), with evidence that both surface and bulk related TLSs contribute to loss. Moreover, we show that surface TLSs can be altered with chemical processing. With four different surface conditions, we quantitatively extract the linear absorption associated with different surface TLS sources. Finally, we quantify the impact of the chemical processing at single-photon powers, the relevant conditions for qubit device performance. In this regime, we measure resonators with internal quality factors ranging from 5 to $15\times {10}^6$, comparable to the best qubits reported. In these devices, the surface and bulk TLS contributions to loss are comparable, showing that systematic improvements in materials on both fronts are necessary to improve qubit coherence further.

Generative adversarial networks (GANs) are a class of machine-learning models that use adversarial training to generate new samples with the same (potentially very complex) statistics as the training samples. One major form of training failure, known as mode collapse, involves the generator failing to reproduce the full diversity of modes in the target probability distribution. Here, we present an effective model of GAN training, which captures the learning dynamics by replacing the generator neural network with a collection of particles in the output space; particles are coupled by a universal kernel valid for certain wide neural networks and high-dimensional inputs. The generality of our simplified model allows us to study the conditions under which mode collapse occurs. Indeed, experiments which vary the effective kernel of the generator reveal a mode collapse transition, the shape of which can be related to the type of discriminator through the frequency principle. Further, we find that gradient regularizers of intermediate strengths can optimally yield convergence through critical damping of the generator dynamics. Our effective GAN model thus provides an interpretable physical framework for understanding and improving adversarial training.

We present an extensive study of resonant two-dimensional (2D) plasmon excitations in grating-gated quantum well heterostructures, which enable an electrical control of periodic charge carrier density profile. Our study combines theoretical and experimental investigations of nanometer-scale $\mathrm{AlGaN}/\mathrm{GaN}$ grating-gate structures and reveals that all terahertz (THz) plasmonic resonances in these structures can be explained only within the framework of the plasmonic crystal model. We identify two different plasmonic crystal phases. The first is the delocalized phase, where THz radiation is absorbed with the entire grating-gate structure that is realized at a weakly modulated 2D electron gas (2DEG) regime. In the second, the localized phase, THz radiation interacts only with the ungated portions of the structure. This phase is achieved by fully depleting the gated regions, resulting in strong modulation. By gate controlling of the modulation degree, we observe a continuous transition between these phases. We also discover that, unexpectedly, the resonant plasma frequencies of ungated parts (in the localized phase) still depend on the gate voltage. We attribute this phenomenon to the specific depletion of the conductive profile in the ungated region of the 2DEG, the so-called edge gating effect. Although we study a specific case of plasmons in $\mathrm{AlGaN}/\mathrm{GaN}$ grating-gate structures, our results have a general character and are applicable to any other semiconductor-based plasmonic crystal structures. Our work represents the first demonstration of an electrically tunable transition between different phases of THz plasmonic crystals, which is a crucial step toward a deeper understanding of THz plasma physics and the development of all-electrically tunable devices for THz optoelectronics.

Thermodynamically induced length fluctuations of high-reflectivity mirror coatings put a fundamental limit on sensitivity and stability of precision optical interferometers like gravitational-wave detectors and ultrastable lasers. The main contribution—Brownian thermal noise—is related to the mechanical loss of the coating material. ${\mathrm{Al}}_{0.92}{\mathrm{Ga}}_{0.08}\mathrm{As}/\mathrm{GaAs}$ crystalline mirror coatings are expected to reduce this limit. The first measurements of cryogenic silicon cavities revealed the existence of additional noise contributions exceeding the expected Brownian thermal noise. We describe a novel, nonthermal, photoinduced effect in birefringence that is most likely related to the recently discovered birefringence noise. Our studies of the dynamics and power dependence are an important step toward uncovering the underlying mechanisms. Averaging the anticorrelated birefringent noise results in a residual noise that is shown to be substantially different from Brownian thermal noise. To this end, we develop a new method for analyzing the coating noise in higher-order transverse-cavity modes, which makes it possible for the first time to determine the contribution of Brownian thermal noise to the total cavity noise. The new noise contributions must be considered carefully in precision interferometry experiments using similar coatings based on semiconductor materials.

It is a fundamental prediction of quantum theory that states of physical systems are described by complex vectors or density operators on a Hilbert space. However, many experiments admit effective descriptions in terms of other state spaces, such as classical probability distributions or quantum systems with superselection rules. Which kind of effective statistics would allow us to experimentally falsify quantum theory as a fundamental description of nature? Here, we address this question by introducing a methodological principle that generalizes Spekkens’s notion of noncontextuality: Processes that are statistically indistinguishable in an effective theory should not require explanation by multiple distinguishable processes in a more fundamental theory. We formulate this principle in terms of linear embeddings and simulations of one probabilistic theory by another, show how this concept subsumes standard notions of contextuality, and prove a multitude of fundamental results on the exact and approximate embedding of theories (in particular, into quantum theory). We prove that only Jordan-algebraic state spaces are exactly embeddable into quantum theory, and show how results on Bell inequalities can be used for the certification of nonapproximate embeddability. From this, we propose an experimental test of quantum theory by probing single physical systems without assuming access to a tomographically complete set of procedures or calibration of the devices, arguably avoiding a significant loophole of earlier approaches.

Imaging is of great importance in everyday life and various fields of science and technology. Conventional imaging is achieved by bending light rays originating from an object with a lens. Such ray bending requires space-variant structures, inevitably introducing a geometric center to the lens. To overcome the limitations arising from the conventional imaging mechanism, we consider imaging elements that employ a different mechanism, which we call reciprocal lenses. This type of imaging element relies on lateral ray shifting, enabled by momentum-space-variant phase modulations in periodic structures. As such, it has the distinct advantage of not requiring alignment with a geometric center. Moreover, upright real images can be produced directly with a single reciprocal lens as the directions of rays are not changed. We realize an ultrathin reciprocal lens based on a photonic crystal slab. We characterize the lateral ray shifting behavior of the reciprocal lens and demonstrate imaging. Our work gives an alternative mechanism for imaging and provides a new way to modulate electromagnetic waves.

We present a method for deriving bulk and edge invariants for interacting, many-body localized Floquet systems in two spatial dimensions. This method is based on a general mathematical object which we call a flow. As an application of our method, we derive bulk invariants for Floquet systems without symmetry, as well as for systems with U(1) symmetry. We also derive new formulations of previously known single-particle and many-body invariants. For bosonic systems without symmetry, our invariant gives a bulk counterpart of the rational-valued Gross-Nesme-Vogts-Werner index $p/q$ quantifying transport of quantum information along the edge.

The interplay between strong correlations and topology can lead to the emergence of intriguing quantum states of matter. One well-known example is the fractional quantum Hall effect, where exotic electron fluids with fractionally charged excitations form in partially filled Landau levels. The emergence of topological moiré flat bands provides exciting opportunities to realize the lattice analogs of both the integer and fractional quantum Hall effects without the need for an external magnetic field. These effects are known as the integer and fractional quantum anomalous Hall (IQAH and FQAH) effects. Here, we present direct transport evidence of the existence of both IQAH and FQAH effects in small-angle-twisted bilayer ${\mathrm{MoTe}}_2$. At zero magnetic field, we observe well-quantized Hall resistance of $h/e^2$ around moiré filling factor $\nu =-1$ (corresponding to one hole per moiré unit cell), and nearly quantized Hall resistance of $3h/2e^2$ around $\nu =-2/3$, respectively. Concomitantly, the longitudinal resistance exhibits distinct minima around $\nu =-1$ and $-2/3$. The application of an electric field induces topological quantum phase transition from the IQAH state to a charge transfer insulator at $\nu =-1$, and from the FQAH state to a topologically trivial correlated insulator, further transitioning to a metallic state at $\nu =-2/3$. Our study paves the way for the investigation of fractionally charged excitations and anyonic statistics at zero magnetic field based on semiconductor moiré materials.

The interaction between a mobile quantum impurity and a bosonic bath leads to the formation of quasiparticles, termed Bose polarons. The elementary properties of Bose polarons, such as their mutual interactions, can differ drastically from those of the bare impurities. Here, we explore Bose polaron physics in a two-dimensional nonequilibrium setting by injecting ${\sigma }^{-}$ polarized exciton-polariton impurities into a bath of coherent ${\sigma }^{+}$ polarized polaritons generated by resonant laser excitation of monolayer ${\mathrm{MoSe}}_2$ embedded in an optical cavity. By exploiting a biexciton Feshbach resonance between the impurity and the bath polaritons, we tune the interacting system to the strong-coupling regime and demonstrate the coexistence of two new quasiparticle branches. Using time-resolved pump-probe measurements, we observe how polaron dressing modifies the interaction between impurity polaritons. Remarkably, we find that the interactions between high-energy polaron quasiparticles, which are repulsive for small bath occupancy, can become attractive in the strong impurity-bath coupling regime. Our experiments provide the first direct measurement of Bose polaron-polaron interaction strength in any physical system and pave the way for exploration and control of many-body correlations in driven-dissipative settings.

We propose and demonstrate an architecture for fluxonium-fluxonium two-qubit gates mediated by transmon couplers (FTF, for fluxonium-transmon-fluxonium). Relative to architectures that exclusively rely on a direct coupling between fluxonium qubits, FTF enables stronger couplings for gates using noncomputational states while simultaneously suppressing the static controlled-phase entangling rate ($ZZ$) down to kilohertz levels, all without requiring strict parameter matching. Here, we implement FTF with a flux-tunable transmon coupler and demonstrate a microwave-activated controlled-$Z$ (CZ) gate whose operation frequency can be tuned over a 2-GHz range, adding frequency allocation freedom for FTFs in larger systems. Across this range, state-of-the-art CZ gate fidelities are observed over many bias points and reproduced across the two devices characterized in this work. After optimizing both the operation frequency and the gate duration, we achieve peak CZ fidelities in the 99.85%–99.9% range. Finally, we implement model-free reinforcement learning of the pulse parameters to boost the mean gate fidelity up to $99.922\%\pm 0.009\%$, averaged over roughly an hour between scheduled training runs. Beyond the microwave-activated CZ gate we present here, FTF can be applied to a variety of other fluxonium gate schemes to improve gate fidelities and passively reduce unwanted $ZZ$ interactions.

We provide a theoretical description of dynamical heterogeneities in glass-forming liquids, based on the premise that relaxation occurs via local rearrangements coupled by elasticity. In our framework, the growth of the dynamical correlation length $\xi$ and of the correlation volume ${\chi }_4$ are controlled by a zero-temperature fixed point. We connect this critical behavior to the properties of the distribution of local energy barriers at zero temperature. Our description makes a direct connection between dynamical heterogeneities and avalanche-type relaxation associated to dynamic facilitation, allowing us to relate the size distribution of heterogeneities to their time evolution. Within an avalanche, a local region relaxes multiple times; the more, the larger the avalanche. This property, related to the nature of the zero-temperature fixed point, directly leads to decoupling of particle diffusion and relaxation time (the so-called Stokes-Einstein violation). Our most salient predictions are tested and confirmed by numerical simulations of scalar and tensorial thermal elastoplastic models. Our most salient predictions are tested and confirmed by numerical simulations of scalar and tensorial thermal elasto-plastic models, and in agreement with molecular dynamic simulations.

We develop a class of matrix models that implement and formalize the eigenstate thermalization hypothesis (ETH) and point out that, in general, these models must contain non-Gaussian corrections in order to correctly capture thermal mean-field theory or to capture nontrivial out-of-time-order correlation functions (OTOCs) as well as their higher-order generalizations. We develop the framework of these ETH matrix models and put it in the context of recent studies in statistical physics incorporating higher statistical moments into the ETH ansatz. We then use the ETH matrix model in order to develop a matrix-integral description of Jackiw-Teitelboim (JT) gravity coupled to a single scalar field in the bulk. This particular example takes the form of a double-scaled ETH matrix model with non-Gaussian couplings matching disk correlators and the density of states of the gravitational theory. Having defined the model from the disk data, we present evidence that the model correctly captures the $\mathrm{JT}+\mathrm{matter}$ theory with multiple boundaries and, conjecturally, at higher genus. This is a shorter companion paper to the work [D. L. Jafferis et al., companion paper, Jackiw-Teitelboim gravity with matter, generalized eigenstate thermalization hypothesis, and random matrices, Phys. Rev. D 108, 066015 (2023).], serving as a guide to the much more extensive material presented there, as well as developing its underpinning in statistical physics.

Recent years have witnessed tremendous progress in creating and manipulating ground-state ultracold polar molecules. However, the two-body loss regardless of the chemical reactivities is still a hurdle for many future explorations. Here, we investigate the loss suppression of nonreactive bosonic ${}^{23}\mathrm{Na}{}^{87}\mathrm{Rb}$ molecules with a circularly polarized microwave blue detuned to the rotational transition. We achieve suppression of the loss by 2 orders of magnitude with the lowest two-body loss rate coefficient reduced to $3\times {10}^{-12}{\mathrm{cm}}^3/\mathrm{s}$. Meanwhile, the elastic collision rate coefficient is increased to the ${10}^{-8}{\mathrm{cm}}^3/\mathrm{s}$ level. The large good-to-bad collision ratio has allowed us to carry out evaporative cooling of ${}^{23}\mathrm{Na}{}^{87}\mathrm{Rb}$ with an efficiency of 1.7(2), increasing the phase-space density by a factor of 10. With further improvements, this technique holds great promises for creating a Bose-Einstein condensate of ultracold polar molecules.

A short superconducting segment can couple attached quantum dots via elastic cotunneling (ECT) and crossed Andreev reflection (CAR). Such coupled quantum dots can host Majorana bound states provided that the ratio between CAR and ECT can be controlled. Metallic superconductors have so far been shown to mediate such tunneling phenomena, albeit with limited tunability. Here, we show that Andreev bound states formed in semiconductor-superconductor heterostructures can mediate CAR and ECT over mesoscopic length scales. Andreev bound states possess both an electron and a hole component, giving rise to an intricate interference phenomenon that allows us to tune the ratio between CAR and ECT deterministically. We further show that the combination of intrinsic spin-orbit coupling in InSb nanowires and an applied magnetic field provides another efficient knob to tune the ratio between ECT and CAR and optimize the amount of coupling between neighboring quantum dots.