Interacting many-body systems with explicitly accessible spatiotemporal correlation functions are extremely rare, especially in the absence of Bethe-ansatz or Yang-Baxter integrability. Recently, we identified a remarkable class of such systems and termed them dual-unitary quantum circuits. These are brickwork-type local quantum circuits whose dynamics are unitary in both time and space. The spatiotemporal correlation functions of these systems turn out to be nontrivial only at the edge of the causal light cone and can be computed in terms of one-dimensional transfer matrices. Dual unitarity, however, requires fine-tuning, and the degree of generality of the observed dynamical features remains unclear. Here, we address this question by studying perturbed dual-unitary quantum circuits. Considering arbitrary perturbations of the local gates, we prove that for a particular class of unperturbed elementary dual-unitary gates the correlation functions are still expressed in terms of one-dimensional transfer matrices. These matrices, however, are now contracted over generic paths connecting the origin to a fixed end point inside the causal light cone. The correlation function is given as a sum over all such paths. Our statement is rigorous in the “dilute limit,” where only a small fraction of the gates is perturbed, and in the presence of random longitudinal fields, but we provide theoretical arguments and stringent numerical checks supporting its validity even in the clean case (no randomness) and when all gates are perturbed. As a by-product of our analysis, in the case of random longitudinal fields—which turns out to be equivalent to certain classical Markov chains—we find four types of non-dual-unitary (and nonintegrable) interacting many-body systems where the correlation functions are exactly solvable and given—without approximations—by the path-sum formula.

An anapole state that breaks inversion and time-reversal symmetries while preserving translation symmetry of an underlying lattice has aroused great interest as a new quantum state, but only a few candidate materials have been reported. Recently, in a spin-orbit coupled Mott insulator ${\mathrm{Sr}}_2({\mathrm{Ir}}_{1-x}{\mathrm{Rh}}_x){\mathrm{O}}_4$, the emergence of a possible hidden-order phase with broken inversion symmetry has been suggested at $T_{\mathrm{\Omega }}$ above the Néel temperature by optical second-harmonic-generation measurements. Moreover, polarized neutron diffraction measurements revealed broken time-reversal symmetry below $T_{\mathrm{\Omega }}$, which was supported by subsequent muon spin relaxation experiments. However, the nature of this mysterious phase remains largely elusive. Here, we investigate the hidden-order phase through the combined measurements of the in-plane magnetic anisotropy with exceptionally high-precision magnetic torque and the nematic susceptibility with elastoresistance. A distinct twofold in-plane magnetic anisotropy along the [110] Ir-O-Ir bond direction sets in below about $T_{\mathrm{\Omega }}$, providing thermodynamic evidence for a nematic phase transition with broken $C_4$ rotational symmetry. However, in contrast to the even-parity nematic transition reported in other correlated electron systems, the nematic susceptibility exhibits no divergent behavior towards $T_{\mathrm{\Omega }}$. These results provide bulk evidence for an odd-parity order parameter with broken rotational symmetry in the hidden-order state. We discuss the hidden order in terms of an anapole state, in which the polar toroidal moment is induced by two current loops in each ${\mathrm{IrO}}_6$ octahedron of opposite chirality. Contrary to the simplest loop-current pattern previously suggested, the present results are consistent with a pattern in which the intra-unit cell loop current flows along only one of the diagonal directions in the ${\mathrm{IrO}}_4$ square.

The Lie-Trotter formula, together with its higher-order generalizations, provides a direct approach to decomposing the exponential of a sum of operators. Despite significant effort, the error scaling of such product formulas remains poorly understood. We develop a theory of Trotter error that overcomes the limitations of prior approaches based on truncating the Baker-Campbell-Hausdorff expansion. Our analysis directly exploits the commutativity of operator summands, producing tighter error bounds for both real- and imaginary-time evolutions. Whereas previous work achieves similar goals for systems with geometric locality or Lie-algebraic structure, our approach holds, in general. We give a host of improved algorithms for digital quantum simulation and quantum Monte Carlo methods, including simulations of second-quantized plane-wave electronic structure, $k$-local Hamiltonians, rapidly decaying power-law interactions, clustered Hamiltonians, the transverse field Ising model, and quantum ferromagnets, nearly matching or even outperforming the best previous results. We obtain further speedups using the fact that product formulas can preserve the locality of the simulated system. Specifically, we show that local observables can be simulated with complexity independent of the system size for power-law interacting systems, which implies a Lieb-Robinson bound as a by-product. Our analysis reproduces known tight bounds for first- and second-order formulas. Our higher-order bound overestimates the complexity of simulating a one-dimensional Heisenberg model with an even-odd ordering of terms by only a factor of 5, and it is close to tight for power-law interactions and other orderings of terms. This result suggests that our theory can accurately characterize Trotter error in terms of both asymptotic scaling and constant prefactor.

We demonstrate trapping of electrons in a millimeter-sized quadrupole Paul trap driven at 1.6 GHz in a room-temperature ultrahigh vacuum setup. Cold electrons are introduced into the trap by ionization of atomic calcium via Rydberg states and stay confined by microwave and static electric fields for several tens of milliseconds. A fraction of these electrons remain trapped longer and show no measurable loss for measurement times up to a second. Electronic excitation of the motion reveals secular frequencies that can be tuned over a range of several tens to hundreds of MHz. Operating a similar electron Paul trap in a cryogenic environment may provide a platform for all-electric quantum computing with trapped electron spin qubits.

Microcavity exciton polariton systems can have a wide range of macroscopic quantum effects that may be turned into better photonic technologies. Polariton Bose-Einstein condensation and photon lasing have been widely accepted in the limits of low and high carrier densities, but identification of the expected Bardeen-Cooper-Schrieffer (BCS) state at intermediate densities remains elusive, as the optical-gain mechanism cannot be directly inferred from existing experiments. Here, using a microcavity with strong polarization selectivity, we gain direct experimental access to the reservoir absorption in the presence of polariton condensation and lasing, which reveals a fermionic gain mechanism underlying the polariton laser. A microscopic many-particle theory shows that this polariton lasing state is consistent with an open-dissipative-pumped system analog of a polaritonic BCS state.

Topological semimetals have revealed a wide array of novel transport phenomena, including electron hydrodynamics, quantum field theoretic anomalies, and extreme magnetoresistances and mobilities. However, the scattering mechanisms central to the fundamental transport properties remain largely unexplored. Here, we reveal signatures of significant phonon-electron scattering in the type-II Weyl semimetal ${\mathrm{WP}}_2$ via temperature-dependent Raman spectroscopy. Over a large temperature range, we find that the decay rates of the lowest energy $A_1$ modes are dominated by phonon-electron rather than phonon-phonon scattering. In conjunction with first-principles calculations, a combined analysis of the momentum, energy, and symmetry-allowed decay paths indicates this results from finite momentum interband and intraband scattering of the electrons. The excellent agreement with theory further suggests that such results could be true for the acoustic modes. We thus provide evidence for the importance of phonons in the transport properties of topological semimetals and identify specific properties that may contribute to such behavior in other materials.

We present a theoretical study and experimental realization of a system that is simultaneously a four-dimensional (4D) Chern insulator and a higher-order topological insulator. The system sustains the coexistence of (4-1)-dimensional chiral topological hypersurface modes (THMs) and (4-2)-dimensional chiral topological surface modes (TSMs). Our study reveals that the THMs are protected by second Chern numbers, and the TSMs are protected by a topological invariant composed of two first Chern numbers, each belonging to a Chern insulator existing in subdimensions. With the synthetic coordinates fixed, the THMs and TSMs, respectively, manifest as topological edge modes and topological corner modes (TCMs) in the real space, which are experimentally observed in a 2D acoustic lattice. These TCMs are not related to quantized polarizations, making them fundamentally distinctive from existing examples. We further show that our 4D topological system offers an effective way for the manipulation of the frequency, location, and number of TCMs, which is highly desirable for applications.

While designing the energy-momentum relation of photons is key to many linear, nonlinear, and quantum optical phenomena, a new set of light-matter properties may be realized by employing the topology of the photonic bath itself. In this work we experimentally investigate the properties of superconducting qubits coupled to a metamaterial waveguide based on a photonic analog of the Su-Schrieffer-Heeger model. We explore topologically induced properties of qubits coupled to such a waveguide, ranging from the formation of directional qubit-photon bound states to topology-dependent cooperative radiation effects. Addition of qubits to this waveguide system also enables direct quantum control over topological edge states that form in finite waveguide systems, useful for instance in constructing a topologically protected quantum communication channel. More broadly, our work demonstrates the opportunity that topological waveguide-QED systems offer in the synthesis and study of many-body states with exotic long-range quantum correlations.

Twisted bilayer graphene (TBG) provides a unique framework to elucidate the interplay between strong correlations and topological phenomena in two-dimensional systems. The existence of multiple electronic degrees of freedom—charge, spin, and valley—gives rise to a plethora of possible ordered states and instabilities. Identifying which of them are realized in the regime of strong correlations is fundamental to shed light on the nature of the superconducting and correlated insulating states observed in the TBG experiments. Here, we use unbiased, sign-problem-free quantum Monte Carlo simulations to solve an effective interacting lattice model for TBG at charge neutrality. Besides the usual cluster Hubbard-like repulsion, this model also contains an assisted-hopping interaction that emerges due to the nontrivial topological properties of TBG. Such a nonlocal interaction fundamentally alters the phase diagram at charge neutrality, gapping the Dirac cones even for infinitesimally small interactions. As the interaction strength increases, a sequence of different correlated insulating phases emerge, including a quantum valley Hall state with topological edge states, an intervalley-coherent insulator, and a valence bond solid. The charge-neutrality correlated insulating phases discovered here provide the sought-after reference states needed for a comprehensive understanding of the insulating states at integer fillings and the proximate superconducting states of TBG.

The bond-dependent Kitaev model on the honeycomb lattice with anyonic excitations has recently attracted considerable attention. However, in solid-state materials other spin interactions are present, and among such additional interactions, the off-diagonal symmetric Gamma interaction, another type of bond-dependent term, has been particularly challenging to fully understand. A minimal Kitaev-Gamma model has been investigated by various numerical techniques under a magnetic field, but definite conclusions about field-induced spin liquids remain elusive. One reason for this may lie in the limited sizes of the two-dimensional geometry it is possible to access numerically, and missed incommensurately ordered states may be interpreted as a spin liquid. Here we focus on the Kitaev-Gamma ladder model as a guide to the phase space of disordered states which could potentially become a spin liquid in the two-dimensional limit. We determine the entire phase diagram in the presence of a magnetic field along the [111] direction. Because of the competition between the interactions and the field, an extremely rich phase diagram emerges with 15 distinct phases. Focusing near the antiferromagnetic Kitaev region, we identify nine different phases solely within this region: several incommensurate magnetically ordered phases, spin-nematic, and two chiral phases with enhanced entanglement. Of particular interest is a highly entangled phase with staggered chirality with zero-net flux occurring at intermediate field, which along with its companion phases outlines a heart-shaped region of high entanglement, the heart of entanglement. We compare our results for the ladder with a $C_3$ symmetric cluster of the two-dimensional honeycomb lattice, and offer insight into possible spin liquids in the two-dimensional limit.

Opinion polarization is on the rise, causing concerns for the openness of public debates. Additionally, extreme opinions on different topics often show significant correlations. The dynamics leading to these polarized ideological opinions pose a challenge: How can such correlations emerge, without assuming them a priori in individual preferences or in a preexisting social structure? Here, we propose a simple model that qualitatively reproduces ideological opinion states found in survey data, even between rather unrelated, but sufficiently controversial, topics. Inspired by skew coordinate systems recently proposed in natural language processing models, we solidify these intuitions in a formalism of opinions unfolding in a multidimensional space where topics form a nonorthogonal basis. Opinions evolve according to the social interactions among the agents, which are ruled by homophily: Two agents sharing similar opinions are more likely to interact. The model features phase transitions between a global consensus, opinion polarization, and ideological states. Interestingly, the ideological phase emerges by relaxing the assumption of an orthogonal basis of the topic space, i.e., if topics thematically overlap. Furthermore, we analytically and numerically show that these transitions are driven by the controversialness of the topics discussed; the more controversial the topics, the more likely are opinions to be correlated. Our findings shed light upon the mechanisms driving the emergence of ideology in the formation of opinions.

Understanding the dynamics of strongly interacting disordered quantum systems is one of the most challenging problems in modern science, due to features such as the breakdown of thermalization and the emergence of glassy phases of matter. We report on the observation of anomalous relaxation dynamics in an isolated XXZ quantum spin system realized by an ultracold gas of atoms initially prepared in a superposition of two different Rydberg states. The total magnetization is found to exhibit subexponential relaxation analogous to classical glassy dynamics, but in the quantum case this relaxation originates from the buildup of nonclassical correlations. In both experiment and semiclassical simulations, we find the evolution toward a randomized state is independent of the strength of disorder up to a critical value. This hints toward a unifying description of relaxation dynamics in disordered isolated quantum systems, analogous to the generalization of statistical mechanics to out-of-equilibrium scenarios in classical spin glasses.

The heavy-fluxonium circuit is a promising building block for superconducting quantum processors due to its long relaxation and dephasing time at the flux-frustration point. However, the suppressed charge matrix elements and low transition frequency make it challenging to perform fast single-qubit gates using standard protocols. We report on new protocols for reset, fast coherent control, and readout that allow high-quality operation of the qubit with a 14 MHz transition frequency, an order of magnitude lower in energy than the ambient thermal energy scale. We utilize higher levels of the fluxonium to read out the qubit state and to initialize the qubit with 97% fidelity corresponding to cooling it to $190\mu \mathrm{K}$. Instead of using standard microwave pulses, we control the qubit only with fast-flux pulses, generating control fields much larger than the qubit frequency. We develop a universal set of gates based on nonadiabatic Landau-Zener transitions that act in 20–60 ns, less than the single-qubit Larmor period. We measure qubit coherence of $T_1,T_{2e}\sim 300\mu \mathrm{s}$ for a fluxonium in a 2D architecture and realize single-qubit gates with an average gate fidelity of 99.8% as characterized by randomized benchmarking.

The coexistence of many competing species in an ecological community is a long-standing theoretical and empirical puzzle. Classic approaches in ecology assume that species fitness and interactions in a given environment are mainly driven by a few essential species traits, and coexistence can be explained by trade-offs between these traits. The apparent diversity of species is then summarized by their positions (“ecological niches”) in a low-dimensional trait space. Yet, in a complex community, any particular set of traits and trade-offs is unlikely to encompass the full organization of the community. A diametrically opposite approach assumes that species interactions are disordered, i.e., essentially random, as might arise when many species traits combine in complex ways. This approach is appealing theoretically, and can lead to novel emergent phenomena, fundamentally different from the picture painted by low-dimensional theories. Nonetheless, fully disordered interactions are incompatible with many-species coexistence, and neither disorder nor its dynamical consequences have received direct empirical support so far. Here we ask what happens when random species interactions are minimally constrained by coexistence. We show theoretically that this leads to testable predictions. Species interactions remain highly disordered, yet with a “diffuse” statistical structure: interaction strengths are biased so that successful competitors subtly favor each other, and correlated so that competitors partition their impacts on other species. We provide strong empirical evidence for this pattern, in data from grassland biodiversity experiments that match our predictions quantitatively. This is a first-of-a-kind test of disorder on empirically measured interactions, and unique evidence that species interactions and coexistence emerge from an underlying high-dimensional space of ecological traits. Our findings provide a new null model for inferring interaction networks with minimal prior information and a set of empirical fingerprints that support a statistical physics-inspired approach of complex ecosystems.

We introduce and demonstrate a scheme for eliminating the inhomogeneous dephasing of a collective quantum state. The scheme employs off-resonant fields that continuously dress the collective state with an auxiliary sensor state, which has an enhanced and opposite sensitivity to the same source of inhomogeneity. We derive the optimal conditions under which the dressed state is fully protected from dephasing when using either one or two dressing fields. The latter provides better protection, circumvents qubit phase rotation, and suppresses the sensitivity to drive noise. We further derive expressions for all residual, higher-order sensitivities. We experimentally study the scheme by protecting a collective excitation of an atomic ensemble, where inhomogeneous dephasing originates from thermal motion. Using photon storage and retrieval, we demonstrate complete suppression of inhomogeneous dephasing and, consequently, a prolonged memory time. Our scheme may be applied to eliminate motional dephasing in other systems, improving the performance of quantum gates and memories with neutral atoms. It is also generally applicable to various gas, solid, and engineered systems, where sensitivity to variations in time, space, or other domains limits possible scale-up of the system.

One of the central issues concerning the mechanism of high-temperature superconductivity in cuprates is the nature of the ubiquitous charge order and its implications to superconductivity. Here, we use scanning tunneling microscopy to investigate the evolution of charge order from the optimally doped to strongly overdoped ${\mathrm{Bi}}_2{\mathrm{Sr}}_2{\mathrm{CuO}}_{6+\delta }$ cuprates. We find that, with increasing hole concentration, the long-range checkerboard order gradually evolves into short-range glassy patterns consisting of diluted charge puddles. Each charge puddle has a unidirectional nematic internal structure and exhibits clear pair density modulations as revealed by the spatial variations of the superconducting coherence peak and gap depth. Both the charge puddles and the nematicity vanish completely in the strongly overdoped nonsuperconducting regime, when another type of short-range order with $\sqrt{2}\times \sqrt{2}$ periodicity emerges. These results shed important new light on the intricate interplay between the intertwined orders and the superconducting phase of cuprates.

Atomic diffusion is a spontaneous process and significantly influences properties of materials, such as fracture toughness, creep-fatigue properties, thermal conductivity, thermoelectric properties, etc. Here, using extensive molecular dynamics simulations based on both ab initio and machine-learning potentials, we demonstrate that an atomic one dimensional cooperative diffusion exists in the simple cubic high-pressure finite-temperature phase of calcium in the premelting regime, where some atoms diffuse cooperatively as chains or even rings, while others remain in the solid state. This intermediate regime is triggered by anharmonicity of the system at high temperature and is stabilized by the competition between the internal energy minimization and the entropy maximization, and has close connections with the unique electronic structures of simple cubic Ca as an electride with a pseudogap. This cooperative diffusion regime explains the abnormal enhancement of the melting line of Ca under high pressure and suggests that the cooperative chain melting is a much more common high-temperature feature among metals under extreme conditions than hitherto thought. The microscopic electronic investigations of these systems combining ab initio and machine-learning data point out the direction for further understanding of other metallic systems such as the glass transition, liquid metals, etc.

Advances in high-speed imaging techniques have opened new possibilities for capturing ultrafast phenomena such as light propagation in air or through media. Capturing light in flight in three-dimensional $xyt$ space has been reported based on various types of imaging systems, whereas reconstruction of light-in-flight information in the fourth dimension $z$ has been a challenge. We demonstrate the four-dimensional light-in-flight imaging based on the observation of a superluminal motion captured by a new time-gated megapixel single-photon avalanche diode camera. A high-resolution light-in-flight video is generated without laser scanning, camera translation, interpolation, or dark noise subtraction. An unsupervised machine-learning technique is applied to analyze the measured spatiotemporal data set. A theoretical formula is introduced to perform least-square regression for numerically solving a nonlinear inverse problem, and extra-dimensional information is recovered without prior knowledge. The algorithm relies on the mathematical formulation equivalent to the superluminal motion in astrophysics, which is scaled by a factor of a quadrillionth. The reconstructed light-in-flight trajectory shows good agreement with the actual geometry of the light path. Applicability of the reconstruction approach to more complex scenes with multiple overlapped light trajectories is verified based on a data set generated by Monte Carlo simulations. Our approach could potentially provide novel functionalities to high-speed imaging applications such as non-line-of-sight imaging and time-resolved optical tomography.

In a complex and ever-changing environment, various signal transduction pathways mediate outside signals and stress to a living cell and its intracellular responses. Eukaryotic cells utilize the DNA synthesis phase (S-phase) checkpoint to respond to DNA damage and replication stress, and the activation of the S-phase checkpoint defers the routine progression in the S phase. Through the analysis of microfluidic single-cell measurements, we find that the behavior of yeast cells exhibits bimodal distribution in the activation of the S-phase checkpoint, and the nonactivated portion of cells obeys the exponential decay law over time, the rate of which is dictated by HU dosage. Mathematical modeling and further experimental evidence from different mutant strains support the idea that the activation of the yeast S-phase checkpoint is a stochastic barrier-crossing process in a double-well system, where the barrier height is determined by both DNA replication stress and autophosphorylation of the key effector kinase Rad53. Our approach, as a novel methodology, is generally applicable to quantitative analysis of the signal transduction pathways at the single-cell level.