The extremely low superfluid density and unprecedented tunability of oxide interface superconductors provide an ideal platform for studying fluctuations in two-dimensional superconductors. In this work, we fabricate an ${\mathrm{LaAlO}}_3/{\mathrm{KTaO}}_3$ interface superconductor patterned with a nanohoneycomb array of insulating islands. Little-Parks-like magnetoresistance oscillations are observed, which are dictated by the superconducting flux quantum $h/2e$. Moreover, an anomalous negative magnetoresistance (ANMR) appears under a weak magnetic field, suggesting magnetic-field-enhanced superconductivity. By examining their dependences on temperature, measurement current, and electrical gating, we conclude that both phenomena are associated with superconducting order parameter: The $h/2e$ oscillations provide direct evidence of Cooper-pair transport, and the ANMR is interpreted as a consequence of multiple connected narrow superconducting paths with strong fluctuations.

Unmeasured causal forces influence diverse experimental time series, such as the transcription factors that regulate genes or the descending neurons that steer motor circuits. Combining the theory of skew-product dynamical systems with topological data analysis, we show that simultaneous recurrence events across multiple time series reveal the structure of their shared unobserved driving signal. We introduce a physics-based unsupervised learning algorithm that reconstructs causal drivers by iteratively building a recurrence graph with glasslike structure. As the amount of data increases, a percolation transition on this graph leads to weak ergodicity breaking for random walks—revealing the shared driver’s dynamics, even from strongly corrupted measurements. We relate reconstruction accuracy to the rate of information transfer from a chaotic driver to the response systems, and we find that effective reconstruction proceeds through gradual approximation of the driver’s dynamical attractor. Through extensive benchmarks against classical signal processing and machine learning techniques, we demonstrate our method’s ability to extract causal drivers from diverse experimental datasets spanning ecology, genomics, fluid dynamics, and physiology.

Two-dimensional materials subject to long-wavelength modulations have emerged as novel platforms to study topological and correlated quantum phases. In this article, we develop a versatile and computationally inexpensive method to predict the topological properties of materials subjected to a superlattice potential by combining degenerate perturbation theory with the method of symmetry indicators. In the absence of electronic interactions, our analysis provides a systematic rule to find the Chern number of the superlattice-induced miniband starting from the harmonics of the applied potential and a few material-specific coefficients. Our method also applies to anomalous (interaction-generated) bands, for which we derive an efficient algorithm to determine all Chern numbers compatible with a self-consistent solution to the Hartree-Fock equations. Our approach gives a microscopic understanding of the quantum anomalous Hall insulators recently observed in rhombohedral graphene multilayers.

Natural communities display a rich variety of dynamics, including global stability, multistability, periodic oscillations, and chaotic fluctuations in species abundances. While phenomenological models (e.g., generalized Lotka-Volterra dynamics) can replicate these dynamic behaviors, understanding biological reasons behind the phenomena requires modeling mechanistic interactions. In this study, we employ a simple mechanistic framework wherein numerous species compete for various resources. We discover that a broad spectrum of dynamics emerges when species consume resources that minimally contribute to their own growth—a scenario absent in the traditional MacArthur resource-consumer model. As the discrepancy between growth-promoting resources and those predominantly consumed increases, the traditional regime of global stability transitions into a dynamic regime characterized by fluctuating species abundances and the presence of alternative stable states. We pinpoint the onset of instability through random matrix analysis, finding that the critical discrepancy between growth and consumption depends on the ratio of the number of species to the number of resources. By defining growth-promoting resources as the niches of species, we find a clear mechanistic interpretation: Communities lose stability when resource consumption overlaps more with the niche of species with similar resource preferences, indicating consumption outside one’s own niche. Furthermore, we reveal fundamental symmetries of stability in such systems and extend the stability criterion beyond the scope of random matrix analysis. The overlap between consumption and niche effectively captures the diversity and sizes of attraction basins across different attractor types beyond the instability transition. Thus, our framework offers predictive insights and mechanistic explanations for the complex dynamics arising from resource competition.

Networks of interconnected materials permeate throughout nature, biology, and technology due to exceptional mechanical performance. Despite the importance of failure resistance in network design and utility, no existing physical model effectively links strand mechanics and connectivity to predict bulk fracture. Here, we reveal a scaling law that bridges these levels to predict the intrinsic fracture energy of diverse stretchable networks. Simulations and experiments demonstrate its remarkable applicability to a breadth of strand constitutive behaviors, topologies, dimensionalities, and length scales. We show that local strand rupture and nonlocal energy release contribute synergistically to the measured intrinsic fracture energy in networks. These effects coordinate such that the intrinsic fracture energy scales independent of the energy to rupture a strand; it instead depends on the strand rupture force, breaking length, and connectivity. Our scaling law establishes a physical basis for fracture of homogeneous networks with uniform strand mechanics and lattice connectivity throughout. The scaling also extends generally for fabricating tough materials from homogeneous networks across multiple length scales.

We explore the relationship between higher-form symmetries and entanglement properties in lattice gauge theories with discrete gauge groups, which can exhibit both topologically ordered phases and higher-form symmetry-protected topological (SPT) phases. Our study centers on a generalization of the Fradkin-Shenker model describing ${\mathbb{Z}}_2$ lattice gauge theory with matter, where the Gauss law constraint can be either emergent or exact. The phase diagram includes a topologically ordered deconfined phase and a nontrivial SPT phase protected by a 1-form and a 0-form symmetry, among others. We obtain the following key findings: First, the entanglement properties of the model depend on whether the 1-form symmetries and the Gauss law constraint are exact or emergent. For the emergent Gauss law, the entanglement spectrum (ES) of the nontrivial SPT phase exhibits degeneracies, which are robust at low energies against weak perturbations that explicitly break the exact 1-form symmetry. When the Gauss law and the 1-form symmetry are both exact, the ES degeneracy is extensive. This extensive degeneracy turns out to be fragile and can be removed completely by infinitesimal perturbations that explicitly break the exact 1-form symmetry while keeping the Gauss law exact. Second, we consider the ES in the topologically ordered phase where 1-form symmetries are spontaneously broken. In contrast to the ES of the nontrivial SPT phase, we find that spontaneous higher-form symmetry breaking removes “half” of the ES levels, leading to a nondegenerate ES in the topologically ordered phase, in general. Third, we derive a connection between spontaneous higher-form symmetry breaking and the topological entanglement entropy (TEE). Using this relation, we investigate the entanglement entropy that can be distilled in the deconfined phase of the original Fradkin-Shenker model using gauge-invariant measurements. We show that the TEE is robust against the measurement when the 1-form symmetry is emergent but it is fragile when the 1-form symmetry is exact. Our results demonstrate the advantage of higher-form symmetries for understanding entanglement properties of gauge theories.

The Hebel-Slichter coherence peak, observed in the spin-lattice relaxation rate $1/T_1$ just below the critical temperature $T_{\mathrm{c}}$, serves as a crucial experimental validation of the Bardeen-Cooper-Schrieffer pairing symmetry in conventional superconductors. However, no coherence peak in $1/T_1$ has been observed in unconventional superconductors like cuprates. In this study, an unconventional coherence peak is identified for the first time using nuclear quadrupole resonance on ${\mathrm{YBa}}_2{\mathrm{Cu}}_4{\mathrm{O}}_8$, pointing to a distinctive pairing symmetry. The spin-lattice relaxation rate in nuclear quadrupole resonance and nuclear magnetic resonance with nuclear spin $I>1/2$ comprises the magnetic relaxation rate $1/T_1^{\mathrm{mag}}$, which probes magnetic fluctuations, and the quadrupole relaxation rate $1/T_1^{\mathrm{quad}}$, which probes charge fluctuations. By utilizing ${}^{63}\mathrm{Cu}$ and ${}^{65}\mathrm{Cu}$ isotopes, we successfully distinguish $1/T_1^{\mathrm{mag}}$ and $1/T_1^{\mathrm{quad}}$ of ${\mathrm{YBa}}_2{\mathrm{Cu}}_4{\mathrm{O}}_8$ and reveal the presence of the coherence peak in $1/T_1^{\mathrm{quad}}$ but not in $1/T_1^{\mathrm{mag}}$, in contrast to conventional superconductors. Our finding demonstrates that unconventional superconductors do not exhibit a coherence peak in $1/T_1$ when the relaxation is due to fluctuations of the hyperfine field. Conversely, a coherence peak is expected when the relaxation is caused by electric field gradient fluctuations, due to the different coherence factors between charge and magnetic fluctuations. Our successful measurements of $1/T_1$ for the chains of ${\mathrm{YBa}}_2{\mathrm{Cu}}_4{\mathrm{O}}_8$ suggest that, should the conditions for predominant quadrupole relaxation be satisfied, this phenomenon could provide a novel approach to exploring the unconventional nature of the pairing mechanism in other superconductors.

Among the wealth of single fluorescent defects recently detected in silicon, the G center catches interest for its telecom single-photon emission that could be coupled to a metastable electron spin triplet. The G center is a unique defect where the standard Born-Oppenheimer approximation used in solid-state physics breaks down as one of its atoms, a silicon atom in interstitial position ${\mathrm{Si}}_{(\mathrm{i})}$, can move between six sites. The impact of its displacement, due either to coherent tunneling or to random jumps from one site to another, on the optical properties of G centers is still largely unknown, especially in silicon-on-insulator (SOI) samples. Here, we investigate the displacement of the center of mass of the G center in silicon. By performing photoluminescence experiments at single-defect scale, we show that individual G defects in SOI exhibit several emission dipoles and zero-phonon line fine structures with splittings up to approximately 1 meV, both indicating a motion of the defect central atom over time. Combining polarization and spectral analysis at the single-photon level, we evidence that the reconfiguration dynamics is drastically different from the one of the unperturbed G center in bulk silicon where the mobile atom is fully delocalized over all six sites through tunneling. The SOI structure freezes the ${\mathrm{Si}}_{(\mathrm{i})}$ delocalization of the G defect and, as a result, enables one to isolate linearly polarized optical lines. Under above-band-gap optical excitation, the central atom of G centers in SOI behaves as if it were in a six-slot roulette wheel, randomly alternating between localized crystal sites at each optical cycle. Comparative measurements in a bulk silicon sample and ab initio calculations highlight that strain is likely the dominant perturbation impacting the G center geometry. These results shed light on the importance of the atomic reconfiguration dynamics to understand and control the photoluminescence properties of the G center in silicon. More generally, these findings emphasize the impact of strain fluctuations inherent to SOI wafers for future quantum integrated photonics applications based on color centers in silicon.

The capacity to custom tailor the properties of quantum matter and materials is a central requirement for enlarging their range of possible functionalities. A particularly promising route is the use of driving protocols to engineer specific desired properties with a high degree of control and flexibility. Here, we present such a program for the tunable generation of sequences of symmetries on controllable timescales. Concretely, our general driving protocol for many-body systems generates a sequence of prethermal regimes, each exhibiting a lower symmetry than the preceding one. We provide an explicit construction of effective Hamiltonians exhibiting these symmetries, which imprints emergent quasiconservation laws hierarchically, enabling us to engineer the respective symmetries and concomitant orders in nonequilibrium matter. We provide explicit examples, including spatiotemporal and topological phenomena, as well as a spin chain realizing the symmetry ladder $\mathrm{SU}(2)\to \mathrm{U}(1)\to {\mathbb{Z}}_2\to E$. Our results have direct applications in experiments with quantum simulators.

We study quantum many-body scars (QMBS) in the language of commutant algebras, which are defined as symmetry algebras of families of local Hamiltonians. This framework explains the origin of dynamically disconnected subspaces seen in models with exact QMBS, i.e., the large “thermal” subspace and the small “nonthermal” subspace, which are attributed to the existence of unconventional nonlocal conserved quantities in the commutant; hence, it unifies the study of conventional symmetries and weak ergodicity-breaking phenomena into a single framework. Furthermore, this language enables us to use the von Neumann double commutant theorem to formally write down the exhaustive algebra of all Hamiltonians with a desired set of QMBS, which demonstrates that QMBS survive under large classes of local perturbations. We illustrate this using several standard examples of QMBS, including the spin-$1/2$ ferromagnetic, AKLT, spin-1 XY $\pi$-bimagnon, and the electronic $\eta$-pairing towers of states; in each of these cases, we explicitly write down a set of generators for the full algebra of Hamiltonians with these QMBS. Understanding this hidden structure in QMBS Hamiltonians also allows us to recover results of previous “brute-force” numerical searches for such Hamiltonians. In addition, this language clearly demonstrates the equivalence of several unified formalisms for QMBS proposed in the literature and also illustrates the connection between two apparently distinct classes of QMBS Hamiltonians—those that are captured by the so-called Shiraishi-Mori construction and those that lie beyond. Finally, we show that this framework motivates a precise definition for QMBS that automatically implies that they violate the conventional eigenstate thermalization hypothesis, and we discuss its implications to dynamics.

Quantum complexity is a measure of the minimal number of elementary operations required to approximately prepare a given state or unitary channel. Recently, this concept has found applications beyond quantum computing—in studying the dynamics of quantum many-body systems and the long-time properties of anti–de Sitter black holes. In this context, Brown and Susskind [Phys. Rev. D 97, 086015 (2018)] conjectured that the complexity of a chaotic quantum system grows linearly in time up to times exponential in the system size, saturating at a maximal value, and remaining maximally complex until undergoing recurrences at doubly exponential times. In this work, we prove the saturation and recurrence of complexity in two models of chaotic time evolutions based on (i) random local quantum circuits and (ii) stochastic local Hamiltonian evolution. Our results advance an understanding of the long-time behavior of chaotic quantum systems and could shed light on the physics of black-hole interiors. From a technical perspective, our results are based on establishing new quantitative connections between the Haar measure and high-degree approximate designs, as well as the fact that random quantum circuits of sufficiently high depth converge to approximate designs.

We perform extensive molecular dynamics simulations of an ensemble of realistic microgel particles in swollen conditions in a wide range of packing fractions $\zeta$. We compare neutral and charged microgels, where we consider charge distribution adherent to experimental conditions. Through a detailed analysis of single-particle behavior, we are able to identify the different regimes occurring upon increasing concentration: from shrinking to deformation and interpenetration, always connecting our findings with available experimental observations. We then link these single-particle features with the collective behavior of the suspension, finding evidence of a structural reentrance that has no counterpart in the dynamics. Hence, while the maximum of the radial distribution function displays a nonmonotonic behavior with increasing $\zeta$, the dynamics, quantified by the microgels’ mean-squared displacement, always slows down. This behavior, at odds with the simple Hertzian model, can be described by a phenomenological multi-Hertzian model, which takes into account the enhanced internal stiffness of the core. However, also this model fails when deformation enters into play, whereby more realistic many-body models are required. Thanks to our analysis, we are able to unveil the key physical mechanisms, shrinking and deformation, giving rise to the structural reentrance that holds up to very large packing fractions. We further identify key similarities and differences between neutral and charged microgels, for which we detect at high enough $\zeta$ the fusion of charged shells, previously invoked to explain key experimental findings, and responsible for the structural reentrance. Overall, our study establishes a powerful framework to uncover the physics of microgel suspensions, paving the way to tackle different regimes, e.g., high temperature, and internal architectures, such as for hollow and ultralow-cross-linked microgels, where experimental evidence is still limited.

Masers once represented the state of the art in low-noise microwave amplification technology but eventually became obsolete due to their need for cryogenic cooling. Masers based on solid-state spin systems perform most effectively as amplifiers, since they provide a large density of spins and can, therefore, operate at relatively high powers. While solid-state maser oscillators have been demonstrated at room temperature, continuous-wave amplification in these systems has only ever been realized at cryogenic temperatures. Here, we report on a continuous-wave solid-state maser amplifier operating at room temperature. We achieve this feat using a practical setup that includes an ensemble of nitrogen-vacancy center spins in a diamond crystal, a strong permanent magnet, and a simple laser diode. We describe important amplifier characteristics including gain, bandwidth, compression power, and noise temperature and discuss the prospects of realizing a room-temperature near-quantum-noise-limited amplifier with this system. Finally, we show that in a different mode of operation the spins can be used to reduce the microwave noise in an external circuit to cryogenic levels, all without the requirement for physical cooling.

Magnetoresistance (MR) oscillations serve as a hallmark of intrinsic quantum behavior, traditionally observed only in conducting systems. Here we report the discovery of MR oscillations in an insulating system, the vertical junctions of ${\mathrm{CrPS}}_4$ which is a two-dimensional $A$-type antiferromagnetic semiconductor. Systematic investigations of MR peaks under varying conditions, including electrode materials, magnetic field direction, temperature, voltage bias, and layer number, elucidate a correlation between MR oscillations and spin-canted states in ${\mathrm{CrPS}}_4$. Experimental data and analysis point out the important role of the in-gap electronic states in generating MR oscillations, and we propose that spin selected interlayer hopping of localized defect states may be responsible for it. Our findings not only illuminate the unusual electronic transport in ${\mathrm{CrPS}}_4$ but also underscore the potential of van der Waals magnets for exploring interesting phenomena.

Understanding quantum materials—solids in which interactions among constituent electrons yield a great variety of novel emergent quantum phenomena—is a forefront challenge in modern condensed matter physics. This goal has driven the invention and refinement of several experimental methods, which can spectroscopically determine the elementary excitations and correlation functions that determine material properties. Here we focus on the future experimental and theoretical trends of resonant inelastic x-ray scattering (RIXS), which is a remarkably versatile and rapidly growing technique for probing different charge, lattice, spin, and orbital excitations in quantum materials. We provide a forward-looking introduction to RIXS and outline how this technique is poised to deepen our insight into the nature of quantum materials and of their emergent electronic phenomena.

Quantum Darwinism is a paradigm to understand how classically objective reality emerges from within a fundamentally quantum universe. Despite the growing attention that this field of research has been enjoying, it is currently not known what specific properties a given Hamiltonian describing a generic quantum system must have to allow the emergence of classicality. Therefore, in the present work, we consider a broadly applicable generic model of an arbitrary finite-dimensional system interacting with an environment formed from an arbitrary collection of finite-dimensional degrees of freedom via an unspecified, potentially time-dependent Hamiltonian containing at most two-body interaction terms. We show that such models support quantum Darwinism if the set of operators acting on the system which enter the Hamiltonian satisfy a set of commutation relations with a pointer observable and with one other. We demonstrate our results by analyzing a wide range of example systems: a qutrit interacting with a qubit environment, a qubit-qubit model with interactions alternating in time, and a series of collision models including a minimal model of a quantum Maxwell demon.

Computational modeling of assembly is challenging for many systems, because their timescales can vastly exceed those accessible to simulations. This article describes the multiMSM, which is a general framework that uses Markov state models (MSMs) to enable simulating self-assembly and self-organization of finite-sized structures on timescales that are orders of magnitude longer than those accessible to brute-force dynamics simulations. As with traditional MSM approaches, the method efficiently overcomes free energy barriers and other dynamical bottlenecks. In contrast to previous MSM approaches to simulating assembly, the framework describes simultaneous assembly of many clusters and the consequent depletion of free subunits or other small oligomers. The algorithm accounts for changes in transition rates as concentrations of monomers and intermediates evolve over the course of the reaction. Using two model systems, we show that the multiMSM accurately predicts the concentrations of the full ensemble of intermediates on timescales required to reach equilibrium. Importantly, after constructing a multiMSM for one system concentration, yields at other concentrations can be approximately calculated without any further sampling. This capability allows for orders of magnitude additional speedup. In addition, the method enables highly efficient calculation of quantities such as free energy profiles, nucleation timescales, flux along the ensemble of assembly pathways, and entropy production rates. Identifying contributions of individual transitions to entropy production rates reveals sources of kinetic traps. The method is broadly applicable to systems with equilibrium or nonequilibrium dynamics and is trivially parallelizable and, thus, highly scalable.

While data qubits with a long coherence time are essential for the storage of quantum information, ancilla qubits are pivotal in quantum error correction (QEC) for fault-tolerant quantum computing. The recent development of optical tweezer arrays, such as the preparation of large-scale qubit arrays and high-fidelity gate operations, offers the potential for realizing QEC protocols, and one of the important next challenges is to control and detect ancilla qubits while minimizing atom loss and crosstalk. Here, we present the realization of a hybrid system consisting of a dual-isotope ytterbium (Yb) atom array, in which we can utilize a nuclear spin qubit of fermionic ${}^{171}\mathrm{Yb}$ as a data qubit and an optical clock qubit of bosonic ${}^{174}\mathrm{Yb}$ as an ancilla qubit with a capacity of nondestructive qubit readout. We evaluate the crosstalk between qubits regarding the impact on the coherence of the nuclear spin qubits from the imaging light for ${}^{174}\mathrm{Yb}$. For the Hahn-echo sequence with a 399 nm probe and 556 nm cooling beams for ${}^{174}\mathrm{Yb}$, we observe 99.1(1.8)% coherence retained under 20 ms exposure, yielding a discrimination fidelity of 0.9992 and a survival probability of 0.988. The Ramsey sequence with a 556 nm probe beam shows negligible influence on the coherence, suggesting the potential future improvement of low crosstalk measurements. This result highlights the potential of the hybrid-Yb atom array for midcircuit measurements for ancilla-qubit-based QEC protocols.

In living cells, proteins self-assemble into large functional structures based on specific interactions between molecularly complex patches. Because of this complexity, protein self-assembly results from a competition between a large number of distinct interaction energies, of the order of one per pair of patches. However, current self-assembly models typically ignore this aspect, and the principles by which it determines the large-scale structure of protein assemblies are largely unknown. Here, we use Monte Carlo simulations and machine learning to start to unravel these principles. We observe that despite widespread geometrical frustration, aggregates of particles with complex interactions fall within only a few categories that often display high degrees of spatial order, including crystals, fibers, and oligomers. We then successfully identify the most relevant aspect of the interaction complexity in predicting these outcomes, namely, the particles’ ability to form periodic structures. Our results provide a first extensive characterization of the rich design space associated with identical particles with complex interactions and could inspire engineered self-assembling nano-objects as well as help us to understand the emergence of robust functional protein structures.

We present a unifying framework that allows us to study the mixed crystalline-electromagnetic responses of topological semimetals in spatial dimensions up to $D=3$ through dimensional augmentation and reduction procedures. We show how this framework illuminates relations between the previously known topological semimetals and use it to identify a new class of quadrupolar nodal line semimetals for which we construct a lattice tight-binding Hamiltonian. We further utilize this framework to quantify a variety of mixed crystalline-electromagnetic responses, including several that have not previously been explored in existing literature, and show that the corresponding coefficients are universally proportional to weighted momentum-energy multipole moments of the nodal points (or lines) of the semimetal. We introduce lattice gauge fields that couple to the crystal momentum and describe how tools including the gradient expansion procedure, dimensional reduction, compactification, and the Kubo formula can be used to systematically derive these responses and their coefficients. We further substantiate these findings through analytical physical arguments, microscopic calculations, and explicit numerical simulations employing tight-binding models.