Quantum error correction with erasure qubits promises significant advantages over standard error correction due to favorable thresholds for erasure errors. To realize this advantage in practice requires a qubit for which nearly all errors are such erasure errors, and the ability to check for erasure errors without dephasing the qubit. We demonstrate that a “dual-rail qubit” consisting of a pair of resonantly coupled transmons can form a highly coherent erasure qubit, where transmon $T_1$ errors are converted into erasure errors and residual dephasing is strongly suppressed, leading to millisecond-scale coherence within the qubit subspace. We show that single-qubit gates are limited primarily by erasure errors, with erasure probability $p_{\text{erasure}}=2.19(2)\times {10}^{-3}$ per gate while the residual errors are $\sim 40$ times lower. We further demonstrate midcircuit detection of erasure errors while introducing $<0.1\%$ dephasing error per check. Finally, we show that the suppression of transmon noise allows this dual-rail qubit to preserve high coherence over a broad tunable operating range, offering an improved capacity to avoid frequency collisions. This work establishes transmon-based dual-rail qubits as an attractive building block for hardware-efficient quantum error correction.

Natural and manmade complex systems are comprised of different elementary units, being either system components or diverse subsystems as in the case of networked systems. These units interact with each other in a possibly nonlinear way, which results in a complex dynamics that is generally dissipative and nonstationary. One of the challenges in the modeling of such systems is the identification of not only pairwise but, more importantly, higher-order interactions, together with their directions and strengths from measured multivariate time series. Here, we propose a novel data-driven approach for characterizing interactions of different orders. Our approach is based on solving a set of linear equations constructed from Kramers-Moyal coefficients derived from statistical moments of $\mathcal{N}$-dimensional multivariate time series. We demonstrate the substantial potential for applications by a data-driven reconstruction of interactions in various multidimensional and networked dynamical systems.

Quantum simulators built from ultracold atoms promise to study quantum phenomena in interacting many-body systems. However, it remains a challenge to experimentally prepare strongly correlated continuous systems such that the properties are dominated by quantum fluctuations. Here, we show how to enhance the quantum correlations in a one-dimensional multimode bosonic Josephson junction, which is a quantum simulator of the sine-Gordon field theory. Our approach is based on the ability to track the nonequilibrium dynamics of quantum properties. After creating a bosonic Josephson junction at the stable fixed point of the classical phase space, we observe squeezing oscillations in the two conjugate variables. We show that the squeezing oscillation frequency can be tuned by more than one order of magnitude, and we are able to achieve a spin squeezing close to 10 dB by utilizing these oscillatory dynamics. The impact of improved spin squeezing is directly revealed by detecting enhanced spatial phase correlations between decoupled condensates. Our work provides new ways for engineering correlations and entanglement in the external degree of freedom of interacting many-body systems.

Quantum systems with engineered Hamiltonians can be used to study many-body physics problems to provide insights beyond the capabilities of classical computers. Semiconductor gate-defined quantum dot arrays have emerged as a versatile platform for realizing generalized Fermi-Hubbard physics, one of the richest playgrounds in condensed matter physics. In this work, we employ a germanium $4\times 2$ quantum dot array and show that the naturally occurring long-range Coulomb interaction can lead to exciton formation and transport. We tune the quantum dot ladder into two capacitively coupled channels and exploit Coulomb drag to probe the binding of electrons and holes. Specifically, we shuttle an electron through one leg of the ladder and observe that a hole is dragged along in the second leg under the right conditions. This corresponds to a transition from single-electron transport in one leg to exciton transport along the ladder. Our work paves the way for the study of excitonic states of matter in quantum dot arrays.

The opening of an energy gap in the electronic structure generally indicates the presence of interactions. In materials with low carrier density and short screening length, long-range Coulomb interaction favors the spontaneous formation of electron-hole pairs, so called excitons, opening an excitonic gap at the Fermi level. Excitonic materials host unique phenomena associated with pair excitations. However, there is still no generally recognized single-crystal material with excitonic order, which is, therefore, awaited in condensed matter physics. Here, we show that excitonic states may exist in the quasi-one-dimensional material ${\mathrm{Ta}}_2{\mathrm{Pd}}_3{\mathrm{Te}}_5$, which has an almost ideal Dirac-like band structure, with the Dirac point located exactly at the Fermi level. We find that an energy gap appears at 350 K, and it grows with decreasing temperature. The spontaneous gap opening is absent in a similar material ${\mathrm{Ta}}_2{\mathrm{Ni}}_3{\mathrm{Te}}_5$. Intriguingly, the gap is destroyed by the potassium deposition on the crystal, likely due to extra-doped carriers. Furthermore, we observe a pair of in-gap flat bands, which is an analog of the impurity states in a superconducting gap. All these observations can be properly explained by an excitonic order, providing ${\mathrm{Ta}}_2{\mathrm{Pd}}_3{\mathrm{Te}}_5$ as a new and promising candidate realizing excitonic states.

The excitonic insulator (EI) is an exotic ground state of narrow-gap semiconductors and semimetals arising from spontaneous condensation of electron-hole pairs bound by attractive Coulomb interaction. Despite research on EIs dating back to half a century ago, their existence in real materials remains a subject of ongoing debate. In this study, through systematic experimental and theoretical investigations, we provide evidence for the existence of an EI ground state in a van der Waals compound ${\mathrm{Ta}}_2{\mathrm{Pd}}_3{\mathrm{Te}}_5$. Density-functional-theory calculations suggest that it is a semimetal with a small band overlap, whereas various experiments exhibit an insulating ground state with a clear band gap. Upon incorporating electron-hole Coulomb interaction into our calculations, we obtain an EI phase where the electronic symmetry breaking opens a many-body gap. Angle-resolved photoemission spectroscopy measurements exhibit that the band gap is closed with a significant change in the dispersions as the number of thermally excited charge carriers becomes sufficiently large in both equilibrium and nonequilibrium states. Structural measurements reveal a slight breaking of crystal symmetry with exceptionally small lattice distortion in the insulating state, which cannot account for the significant gap opening. Therefore, we attribute the insulating ground state with a gap opening in ${\mathrm{Ta}}_2{\mathrm{Pd}}_3{\mathrm{Te}}_5$ to exciton condensation, where the coupling to the symmetry-breaking electronic state induces a subtle change in the crystal structure.

The excitations in the Kitaev spin liquid (KSL) can be described by Majorana fermions, which have characteristic field dependence of bulk gap and topological edge modes. In the high-field state of layered honeycomb magnet $\alpha \text{−}{\mathrm{RuCl}}_3$, experimental results supporting these Majorana features have been reported recently. However, there are challenges due to sample dependence, and the impact of inevitable disorder on the KSL is poorly understood. Here, we study how low-energy excitations are modified by introducing point defects in $\alpha \text{−}{\mathrm{RuCl}}_3$ using electron irradiation, which induces site vacancies and exchange randomness. High-resolution measurements of the temperature dependence of specific heat $C(T)$ under in-plane fields $H$ reveal that, while the field-dependent Majorana gap is almost intact, additional low-energy states with $C/T=A(H)T$ are induced by introduced defects. At low temperatures, we obtain the data collapse of $C/T\sim H^{-\gamma }(T/H)$ expected for a disordered quantum spin system but with an anomalously large exponent $\gamma$. This leads us to find a power-law relationship between the coefficient $A(H)$ and the field-sensitive Majorana gap. These results are consistent with the picture that the disorder induces low-energy linear Majorana excitations, which may be considered as a weak localization effect of Majorana fermions in the KSL.

In a crystalline solid under mechanical stress, a Frank-Read source is a pinned dislocation segment that repeatedly bows and detaches, generating concentric dislocation loops. We demonstrate that, in nematic liquid crystals, an analogous Frank-Read mechanism can generate concentric disclination loops. Using experiment, simulation, and theory, we study a disclination segment pinned between surface defects on one substrate in a nematic cell. Under applied twist of the nematic director, the pinned segment bows and emits a new disclination loop which expands, leaving the original segment intact; loop emission repeats for each additional 180° of applied twist. We present experimental micrographs showing loop expansion and snap-off, numerical simulations of loop emission under both quasistatic and dynamic loading, and theoretical analysis considering both free energy minimization and the balance of competing forces. We find that the critical stress for disclination loop emission scales as the inverse of segment length and changes as a function of strain rate and temperature, in close analogy to the Frank-Read source mechanism in crystals. Lastly, we discuss how Frank-Read sources could be used to modify microstructural evolution in both passive and active nematics.

Spontaneous symmetry breaking—the phenomenon in which an infinitesimal perturbation can cause the system to break the underlying symmetry—is a cornerstone concept in the understanding of interacting solid-state systems. In a typical series of temperature-driven phase transitions, higher-temperature phases are more symmetric due to the stabilizing effect of entropy that becomes dominant as the temperature is increased. However, the opposite is rare but possible when there are multiple degrees of freedom in the system. Here, we present such an example of a symmetry-ascending phenomenon upon cooling in a magnetic kagome metal FeGe by utilizing neutron Larmor diffraction and Raman spectroscopy. FeGe has a kagome lattice structure with simple A-type antiferromagnetic order below Néel temperature $T_N\approx 400\mathrm{K}$ and a charge density wave (CDW) transition at $T_{\mathrm{CDW}}\approx 110\mathrm{K}$, followed by a spin-canting transition at around 60 K. In the paramagnetic state at 460 K, we confirm that the crystal structure is indeed a hexagonal kagome lattice. On cooling to around $T_N$, the crystal structure changes from hexagonal to monoclinic with in-plane lattice distortions on the order of ${10}^{-4}$ and the associated splitting of the double-degenerate phonon mode of the pristine kagome lattice. Upon further cooling to $T_{\mathrm{CDW}}$, the kagome lattice shows a small negative thermal expansion, and the crystal structure gradually becomes more symmetric upon further cooling. A tendency of increasing the crystalline symmetry upon cooling is unusual; it originates from an extremely weak structural instability that coexists and competes with the CDW and magnetic orders. These observations are against the expectations for a simple model with a single order parameter and hence can only be explained by a Landau free energy expansion that takes into account multiple lattice, charge, and spin degrees of freedom. Thus, the determination of the crystalline lattice symmetry as well as the unusual spin-lattice coupling is a first step towards understanding the rich electronic and magnetic properties of the system, and it sheds new light on intertwined orders where the lattice degree of freedom is no longer dominant.

One of the tenets of molecular biology is that dynamic transitions between three-dimensional structures determine the function of proteins. Therefore, it seems only natural that evolutionary analysis of proteins, presently based mainly on their primary sequence, needs to shift its focus toward their function as assessed by corresponding structural transitions. This can be facilitated by recent progress in cryogenic electron microscopy that provides atomic structures of multiple conformational states for proteins and protein assemblies isolated from evolutionarily related species. In this work, we study evolutionary conservation of multiprotein assembly function by using mechanical strain as a quantitative footprint of structural transitions. We adopt the formalism of finite strain theory, developed in condensed matter physics, and apply it, as a case study, to a classical multiprotein assembly, the ATP synthase. Protein strain analysis provides a precise characterization of rotation domains that agrees with the present biophysical knowledge. In addition, we obtain a strain distribution on the protein structure associated with functional transitions. By analyzing in detail the strain patterns of the chains responsible for ATP synthesis across distinct species, we show that they are evolutionarily conserved for the same functional transition. Such conservation is not revealed by displacement or rotation patterns. Furthermore, within each functional transition, we can identify conserved strain patterns for ATP synthases isolated from different organisms. The observed strain conservation across evolutionary distant species indicates that strain should be essential in future structure-based evolutionary studies of protein function.

In conventional ab initio methodologies, phonons are calculated by solving equations of motion involving static interatomic force constants and atomic masses. The Born-Oppenheimer approximation, where all electronic degrees of freedom are assumed to adiabatically follow the nuclear dynamics, is also adopted. This approach does not fully account for the effects of broken time-reversal symmetry in systems with magnetic order. Recent attempts to rectify this involve the inclusion of the velocity dependence of the interatomic forces in the equations of motion, which accounts for time-reversal symmetry breaking, and can result in chiral phonon modes with nonzero angular momentum even at the zone center. However, since the energy ranges of phonons and magnons typically overlap, the spins cannot be treated as adiabatically following the lattice degrees of freedom. Instead, phonon and spins must be treated on a similar footing. Focusing on zone-center modes, we propose a method involving Hessian matrices and Berry curvature tensors in terms of both phonon and spin degrees of freedom, and describe a first-principles methodology for calculating these. We then solve Lagrange’s equations of motion to determine the energies and characters of the mixed excitations, allowing us to quantify, for example, the energy splittings between chiral pairs of phonons in some cases, and the degree of magnetically induced mixing between infrared and Raman modes in others. The approach is general and can be applied to determine the adiabatic dynamics of any mixed set of slow variables.

We synthesized polycrystalline ${\mathrm{La}}_3{\mathrm{Ni}}_2{\mathrm{O}}_{7-\delta }$ ($\delta \approx 0.07$) samples by using the sol-gel method without postannealing under high oxygen pressure, and then measured temperature-dependent resistivity under various hydrostatic pressures up to 18 GPa by using the cubic anvil and two-stage multianvil apparatus. We find that the density-wave-like anomaly in resistivity is progressively suppressed with increasing pressure and the resistivity drop corresponding to the onset of superconductivity emerges at pressure as low as $\sim 6\mathrm{GPa}$. Zero resistivity is achieved at 9 GPa below $T_{\mathrm{c}}^{\mathrm{zero}}\approx 6.6\mathrm{K}$, which increases quickly with pressure to 41 K at 18 GPa. However, the diamagnetic response was not detected in the ac magnetic susceptibility measurements up to 15 GPa, indicating a filamentary nature of the observed superconductivity in the studied pressure range. The constructed $T\text{−}P$ phase diagram reveals an intimate relationship between superconductivity, density-wave-like order, and the strange-metal-like behaviors. The observation of zero-resistance state in the polycrystalline ${\mathrm{La}}_3{\mathrm{Ni}}_2{\mathrm{O}}_{7-\delta }$ samples under high pressures not only corroborates the recent report of superconductivity in the pressurized ${\mathrm{La}}_3{\mathrm{Ni}}_2{\mathrm{O}}_7$ crystals but also facilitates further studies on this emerging family of nickelate high-$T_{\mathrm{c}}$ superconductors.

Micromechanical and nanomechanical systems with exceptionally low dissipation rates are enabling the next-generation technologies of ultrasensitive detectors and quantum information systems. New techniques and methods for lowering the dissipation rate have in recent years been discovered and allowed for the engineering of mechanical oscillators with phononic modes that are extremely well isolated from the environment and thus possess quality factors close to and beyond $1\times {10}^9$. A powerful strategy for isolating and controlling a single phononic mode is based on phononic crystal engineering. Here we propose a new method for phononic crystal engineering of nanomechanical oscillators that is based on a periodic variation of the material density. To circumvent the introduction of additional bending losses resulting from the variation of material density, the added mass constitutes an array of nanopillars in which the losses will be diluted. Using this novel technique for phononic crystal engineering, we design and fabricate corrugated mechanical oscillators with quality factors approaching $1\times {10}^9$ in a room temperature environment. The flexibility space of these new phononic crystals is large and further advancement can be attained through optimized phononic crystal patterning and strain engineering via topology optimization. This will allow for the engineering of mechanical membranes with quality factors beyond $1\times {10}^9$ at room temperature. Such extremely low mechanical dissipation rates will enable the development of radically new technologies such as quantum-limited atomic force microscopy at room temperature, ultrasensitive detectors of dark matter, spontaneous waveform collapses, gravity, and high-efficiency quantum information transducers.

Polarization resolved second-harmonic generation (pSHG) microscopy is increasingly used for mapping organized arrays of noncentrosymmetric proteins such as collagen, myosin, and tubulin, and holds potential for probing their molecular structure and supramolecular organization in intact tissues. However, the contrast mechanism of pSHG is complex and the development of applications in the life sciences is hampered by the lack of models accurately relating the observed pSHG signals to the underlying molecular and macromolecular organization. In this work, we establish a general multiscale numerical framework relating the micrometer-scale SHG measurements to the atomic-scale and molecular structure of the proteins under study and their supramolecular arrangement. We first develop a new method to automatically analyze pSHG signals independently of the protein type and fiber orientation. We then characterize experimentally pSHG signals in live zebrafish larvae and show that they can be used to distinguish collagen, myosin, and tubulin structures in intact tissues. We then introduce a numerical model that considers the peptide bond (PB) as the elementary SHG source in proteins and takes into account the three-dimensional (3D) distribution of PBs to predict the second-order hyperpolarizability tensor $\beta$ of proteins, as well as the SHG efficiency and pSHG response of an arbitrary macromolecular assembly. We show that this model accurately reproduces pSHG measurements obtained from collagen, myosin, microtubule, and actin structures, revealing the precise dependence of SHG signals on the 3D distribution of PBs within protein assemblies. We then use our model to analyze pSHG from a 3D distribution of microtubule assemblies as a function of out-of-plane angles, angular disorder, and polarity. Finally, we demonstrate that our model predicts SHG from different molecular conformations of tubulin that are highly relevant from a biomedical point of view as associated with microtubules (de)polymerization. By bridging scales from the molecular bonds to the optical wavelength, our model provides an accurate interpretation of SHG signals in terms of protein structure and supramolecular organization.

Highly diverse ecosystems exhibit a broad distribution of population sizes and species turnover, where species at high and low abundances are exchanged over time. We show that these two features generically emerge in the fluctuating phase of many-variable model ecosystems with disordered species interactions, when species are supported by migration from outside the system at a small rate. We show that these and other phenomena can be understood through the existence of a scaling regime in the limit of small migration, in which large fluctuations and long timescales emerge. We construct an exact analytical theory for this asymptotic regime that provides scaling predictions on timescales and abundance distributions that are verified exactly in simulations. In this regime, a clear separation emerges between rare and abundant species at any given time, despite species moving back and forth between the rare and abundant subsets. The number of abundant species is found to lie strictly below a well-known stability bound, maintaining the system away from marginality. At the same time, other measures of diversity, which also include some of the rare species, go above this bound. In the asymptotic limit where the migration rate goes to zero, trajectories of individual species abundances are described by non-Markovian jump-diffusion processes, which proceeds as follows: A rare species remains so for some time, then experiences a jump in population sizes after which it becomes abundant (a species turnover event) and later sees its population size gradually decreasing again until rare, due to the competition with other species. The asymmetry of abundance trajectories under time reversal is maintained at a small but finite migration rate. These features may serve as fingerprints of endogenous fluctuations in highly diverse ecosystems.

The ultrafast manipulation of quantum material has led to many novel and significant discoveries. Among them, the light-induced transient superconductivity in cuprates achieved by melting competing stripe orders represents a highly appealing accomplishment. However, recent investigations have shown that the notion of photoinduced superconductivity remains a topic of controversy, and its elucidation solely through $c$-axis time-resolved terahertz spectroscopy remains an arduous task. Here, we measure the in-plane and out-of-plane transient terahertz responses simultaneously in the stripe-ordered nonsuperconducting ${\mathrm{La}}_{2-x}{\mathrm{Ba}}_x{\mathrm{CuO}}_4$ after near-infrared excitations. We find that although a pump-induced reflectivity edge appears in the $c$-axis reflectance spectrum, the reflectivity along the ${\mathrm{CuO}}_2$ planes decreases simultaneously, indicating an enhancement in the scattering rate of quasiparticles. This in-plane transient response is clearly distinct from the features associated with superconducting condensation. Therefore, we conclude the out-of-plane transient responses cannot be explained by an equivalent of Josephson tunneling. Notably, those pump-induced terahertz responses remain consistent even when we vary the near-infrared optical pump wavelengths and hole concentrations. Our results provide critical evidence that transient three-dimensional superconductivity cannot be induced by melting the competing stripe orders with pump pulses whose photon energy is much higher than the superconducting gap of cuprates.

Colloidal gels, sparse particle networks with large voids, are fundamental model systems of disordered porous materials. Unlike dense amorphous solids, they exhibit significant volumetric deformation while expelling solvents when subjected to external compression. Despite their importance in both natural and industrial settings, the relationship between their network microstructure and compressive yielding behavior has remained elusive. To address this problem, we employ confocal microscopy and a specially designed sample cell to observe the gravity-induced collapsing of colloidal gels at a single-particle level. The experimental insight gained is complemented by simulation results for gravitational collapse and homogeneous uniaxial compression. We find that, during compression, the microstructure of gels is uniquely determined solely by the local volume fraction. This relationship remains independent of the deformation strain history but is subtly influenced by the preparation history of the initial state. In contrast, compressive stress evolves as a unique function of local volume fraction, unaffected by both preparation and strain history, as long as the interparticle interaction remains identical. Moreover, we unveil that local yielding occurs in highly strained, narrow network domains, while highly stressed particles form chainlike structures to support the external stress. These findings suggest that colloidal gels undergoing compressive plastic deformation mechanically self-organize into a unique history-independent state to satisfy mechanical balance in a quasistatic condition, providing crucial microscopic insights into the compressive yielding behavior of particle network materials.

The ion-molecule reactions ${\mathrm{D}}_2^{+}+{\mathrm{NH}}_3$ and ${\mathrm{D}}_2^{+}+{\mathrm{ND}}_3$ are studied at low collision energies ($E_{\mathrm{coll}}$ from zero to approximately $k_B\times 50\mathrm{K}$), with the ${\mathrm{D}}_2^{+}$ ions in the ground rovibrational state and for different rotational temperatures of the ammonia molecules, using the Rydberg-Stark merged-beam approach. Two different rotational temperatures (approximately 15 K and approximately 40 K), measured by ($2+1$) resonance-enhanced multiphoton-ionization spectroscopy, are obtained by using a seeded supersonic expansion in He and a pure ammonia expansion, respectively. The experimental data reveal a strong enhancement of the rate coefficients at the lowest collision energies caused by the charge-dipole interaction. Calculations based on a rotationally adiabatic capture model accurately reproduce the observed kinetic-energy dependence of the rate coefficients. The rate coefficients increase with increasing rotational temperature of the ammonia molecules, which contradicts the expectation that rotational excitation should average the dipoles out. Moreover, these reactions exhibit a pronounced inverse kinetic isotope effect. The difference is caused by nuclear-spin-statistical factors and the smaller rotational constants and tunneling splittings in ${\mathrm{ND}}_3$.

Ramsey interferometry is a widely used tool for precisely measuring transition frequencies between two energy levels of a quantum system, with applications in time keeping, precision spectroscopy, quantum optics, and quantum information. Often, the coherence time of the quantum system surpasses the one of the oscillator probing the system, thereby limiting the interrogation time and associated spectral resolution. Correlation spectroscopy overcomes this limitation by probing two quantum systems with the same noisy oscillator for a measurement of their transition frequency difference; this technique has enabled very precise comparisons of atomic clocks. Here, we extend correlation spectroscopy to the case of multiple quantum systems undergoing strong correlated dephasing. We model Ramsey correlation spectroscopy with $N$ particles as a multiparameter phase estimation problem and demonstrate that multiparticle correlations can assist in reducing the measurement uncertainties even in the absence of entanglement. We derive precision limits and optimal sensing techniques for this problem and compare the performance of probe states and measurement with and without entanglement. Using one- and two-dimensional ion Coulomb crystals with up to 91 qubits, we experimentally demonstrate the advantage of measuring multiparticle correlations for reducing phase uncertainties and apply correlation spectroscopy to measure ion-ion distances, transition frequency shifts, laser-ion detunings, and path-length fluctuations. Our method can be straightforwardly implemented in experimental setups with globally coherent qubit control and qubit-resolved single-shot readout and is, thus, applicable to other physical systems such as neutral atoms in tweezer arrays.