Fluctuation-dissipation relations (FDRs) connect the internal spontaneous fluctuations of a system with its response to an external perturbation. In this work we propose a nonlinear generalized FDR (NL FDR) as a test for Markovianity of the considered nonequilibrium system; i.e., the violation of the NL FDR indicates a non-Markovian process. Previously suggested FDRs are based on linear response and require a significant number of measurements. However, the nonlinear relation holds for systems out of equilibrium and for strong perturbations. Therefore, its verification requires significantly less data than the standard linear relation. We test the NL FDR for two theoretical model systems: a particle in a tilted periodic potential and a harmonically bound particle, each driven either by white noise (leading to Markovian test cases, which should obey the NL FDR) or by colored noise (resulting in non-Markovian systems, which may not obey the relation). The degree of violation is systematically explored for the non-Markovian variants of our theoretical models. For the particle in the harmonically bound potential, all statistical measures entering the NL FDR can be calculated explicitly and can be used to elucidate why the relation is violated in the non-Markovian case. In addition, we apply our formalism and test for Markovianity in an inherently out-of-equilibrium experimental system, a tracer particle, embedded in an active bath of self-propelled agents (bristlebots) and subject to a force applied by an external air stream. An experimental violation of the NL FDR is witnessed by introducing an additional timescale to the process, when using bristlebots with two metastable speed states.

Femtosecond core-level transient absorption spectroscopy is utilized to investigate photoinduced dynamics of the charge density wave in $1T\text{−}{\mathrm{TiSe}}_2$ at the Ti $M_{2,3}$ edge (32–50 eV). Photoexcited carriers and phonons are found to primarily induce spectral redshifts of core-level excitations, and a carrier relaxation time and phonon heating time of approximately 360 fs and 1.0 ps are extracted, respectively. Pronounced oscillations in delay-dependent absorption spectra are assigned to coherent excitations of the optical $A_{1g}$ phonon (6.0 THz) and the $A_{1g}^{*}$ charge density wave amplitude mode (3.3 THz). By comparing the measured spectra with time-dependent density functional theory simulations, we determine the directions of the momentary atomic displacements of both coherent modes and estimate their amplitudes. Interestingly, the spectral fingerprint of the amplitude mode can be associated with many-body electron screening, strengthening the importance of electron-electron and simultaneous electron-phonon interaction for the stability of the charge density wave. In addition, we find that 10% and 13% of the absorbed energy is stored in the $A_{1g}$ and $A_{1g}^{*}$ coherent modes, respectively. This work presents a first look on charge density wave excitations with tabletop core-level transient absorption spectroscopy, enabling simultaneous access to electronic and lattice excitation and relaxation.

A wealth of evidence shows that real-world networks are endowed with the small-world property, i.e., that the maximal distance between any two of their nodes scales logarithmically rather than linearly with their size. In addition, most social networks are organized so that no individual is more than six connections apart from any other, an empirical regularity known as the six degrees of separation. Why social networks have this ultrasmall-world organization, whereby the graph’s diameter is independent of the network size over several orders of magnitude, is still unknown. We show that the “six degrees of separation” is the property featured by the equilibrium state of any network where individuals weigh between their aspiration to improve their centrality and the costs incurred in forming and maintaining connections. We show, moreover, that the emergence of such a regularity is compatible with all other features, such as clustering and scale-freeness, that normally characterize the structure of social networks. Thus, our results show how simple evolutionary rules of the kind traditionally associated with human cooperation and altruism can also account for the emergence of one of the most intriguing attributes of social networks.

In 1935, Einstein, Podolsky, and Rosen (EPR) conceived a gedanken experiment which became a cornerstone of quantum technology and still challenges our understanding of reality and locality today. While the experiment has been realized with small quantum systems, a demonstration of the EPR paradox with massive many-particle systems remains an important challenge, as such systems are particularly closely tied to the concept of local realism in our everyday experience and may serve as probes for new physics at the quantum-to-classical transition. In this work we report an EPR experiment with two spatially separated Bose-Einstein condensates, each containing about 700 rubidium atoms. Entanglement between the condensates results in strong correlations of their collective spins, allowing us to demonstrate the EPR paradox between them. Our results represent the first observation of the EPR paradox with spatially separated, massive many-particle systems. They show that the conflict between quantum mechanics and local realism does not disappear as the system size increases to more than a thousand massive particles. Furthermore, EPR entanglement in conjunction with individual manipulation of the two condensates on the quantum level, as we demonstrate here, constitutes an important resource for quantum metrology and information processing with many-particle systems.

The fracture of materials can take place below the critical failure condition via the slow accumulation of internal damage followed by fast crack propagation. While failure due to subcritical fracture accounts for most of the structural failures in use, it is theoretically challenging to bridge the gap between molecular damage and fracture mechanics, not to mention predicting the occurrence of sudden fracture, due to the lack of current nondestructive detection methods with suitable resolution. Here, we investigate the fracture of elastomers by using simultaneously space- and time-resolved multispeckle diffusing wave spectroscopy (MSDWS) and molecular damage mapping by mechanophore. We identify a fracture precursor that accelerates the strain-rate field over a large area (${\mathrm{cm}}^2$ scale), at considerably long times (up to thousands of seconds) before macroscopic fracture occurs. By combining deformation or damage mapping and finite-element simulations of the crack-tip strain field, we unambiguously attribute the macroscopic response in elastic deformation to highly localized molecular damage that occurs over a sample area of about $0.01{\mathrm{mm}}^2$. By unveiling this mechanism of interaction between the microscopic molecular damage and the minute but long-ranged elastic deformation field, we are able to develop MSDWS as a flexible, well-controlled tool to characterize and predict microscopic damage well before it becomes critical. Tested using ordinary imaging and simple image processing, MSDWS predictions are proven applicable for unlabeled and even opaque samples under different fracture conditions.

The detection of gravitational waves from compact binary mergers by the LIGO/Virgo Collaboration has, for the first time, allowed for tests of relativistic gravity in the strong, dynamical, and nonlinear regime. Outside Einstein’s relativity, spinning black holes may be different from their general relativistic counterparts, and their merger may then lead to a modified ringdown. We study the latter and, for the first time, derive a modified Teukolsky equation, i.e., a set of linear, decoupled differential equations that describe dynamical perturbations of non-Kerr black holes for the radiative Newman-Penrose scalars ${\mathrm{\Psi }}_0$ and ${\mathrm{\Psi }}_4$. We first focus on non-Ricci-flat, Petrov type-$D$ black hole backgrounds in modified gravity and derive the modified Teukolsky equation through direct decoupling and through a new approach, proposed by Chandrasekhar, that uses certain gauge conditions. We then extend this analysis to non-Ricci-flat, Petrov type-I black hole backgrounds in modified gravity, assuming they can be treated as a linear perturbation of Petrov type-$D$, black hole backgrounds in general relativity by generalizing Chandrasekhar’s approach, and derive the decoupled modified Teukolsky equation. We further show that our formalism can be extended beyond linear order in both modified gravity corrections and gravitational wave perturbations. Our work lays the foundation to study the gravitational waves emitted in the ringdown phase of black hole coalescence in modified gravity for black holes of any spin. Our work can also be extended to compute gravitational waves emitted by extreme mass-ratio binary inspirals in modified gravity.

Quantum-computation architecture based on $d$-level systems, or qudits, has attracted considerable attention recently due to their enlarged Hilbert space. Extensive theoretical and experimental studies have addressed aspects of algorithms and benchmarking techniques for qudit-based quantum computation and quantum-information processing. Here, we report a physical realization of a qudit with up to four embedded levels in a superconducting transmon demonstrating high-fidelity initialization, manipulation, and simultaneous multilevel readout. In addition to constructing $\mathrm{SU}(d)$ operations and benchmarking protocols for quantum-state tomography, quantum-process tomography, randomized benchmarking, etc., we experimentally carry out these operations for $d=3$ and $d=4$. Moreover, we perform prototypical quantum algorithms and observe outcomes consistent with expectations. Our work will hopefully stimulate further research interest in developing manipulation protocols and efficient applications for quantum processors with qudits.

Nonlinear wavelength conversion is a powerful control of light, especially when implemented at the nanoscale with integrated photonics. However, strict energy conservation and phase-matching requirements constrain the converted output. To overcome these constraints and enable novel functionalities, we introduce nonlinear networks—systems of nonlinear photonic elements that observe a programmable set of conservation rules. We highlight the diverse capabilities of nonlinear networks by demonstrating an optical-frequency synthesizer, which operates at nearly arbitrary output frequency exceeding the state of the art in synthesized conversion bandwidth. Using a codesigned microresonator network, our synthesizer is based on four-wave mixing (FWM) spectral translation of a tunable laser and a frequency comb. Energy conservation in FWM provides deterministic synthesis, and it allows a nearly arbitrary frequency tuning range by the dependence of resonant FWM on group-velocity dispersion, temperature, and input laser frequency. Moreover, we take advantage of efficient parametric amplification intrinsic to nonlinear networks. We operate spectral translation across output ranges up to 200 THz, and we characterize the synthesizer through precise metrology, demonstrating $<0.1\mathrm{Hz}$ absolute accuracy. Our experiments introduce nonlinear networks that perform complex functionalities, including optical synthesis with nearly limitless bandwidth.

We study theoretically how local measurements performed on critical quantum ground states affect long-distance correlations. These states are highly entangled and feature algebraic correlations between local observables. As a consequence, local measurements can have highly nonlocal effects. Our focus is on Tomonaga-Luttinger liquid ground states, a continuous family of critical states in one dimension whose structure is characterized by a Luttinger parameter $K$. We show that arbitrarily weak local measurements, performed over extended regions of space, can conspire to drive transitions in long-distance correlations. Conditioning first on a translation-invariant set of measurement outcomes, we show that there is a transition in the character of the postmeasurement quantum state for $K<1$, and highlight a formal analogy with the effect of a static defect on transport through a Tomonaga-Luttinger liquid. To investigate the full ensemble of measurement outcomes, we consider averages of physical quantities which are necessarily nonlinear in the system density matrix. We show how their behavior can be understood within a replica field theory, and for the measurements that we consider we find that the symmetry of the theory under exchange of replicas is broken for $K<1/2$. A well-known barrier to experimentally observing the collective effects of multiple measurements has been the need to postselect on random outcomes. Here we resolve this problem by introducing cross-correlations between experimental measurement results and classical simulations, which act as resource-efficient probes of the transition. The phenomena we discuss are, moreover, robust to local decoherence.

Traditionally, x-ray scattering techniques have been used to detect the breaking of the structural symmetry of the lattice, which accompanies a periodic displacement of the atoms associated with charge density wave (CDW) formation in the cuprate pseudogap states. Similarly, spectroscopic imaging scanning tunneling microscopy (STM) has visualized the short-range CDW. However, local coupling of electrons to the lattice in the form of a short-range CDW has been a challenge to visualize; thus, a link between these measurements has been missing. Here, we introduce a novel STM-based technique to visualize the local bond-length variations obtained from topographic imaging with picometer precision. Application of this technique to the high-$T_c$ cuprate superconductor ${\mathrm{Bi}}_2{\mathrm{Sr}}_2{\mathrm{CaCu}}_2{\mathrm{O}}_{8+\delta }$ reveals a high-fidelity local lattice distortion of the BiO lattice as large as 2%. In addition, analysis of local breaking of rotational symmetry associated with the bond lengths reveals modulations around four-unit-cell periodicity in both $B_1$ and $E$ representations in the $C_{4v}$ group of the lattice, which coincides with the unidirectional $d$-symmetry CDW ($d\mathrm{CDW}$) previously identified within the ${\mathrm{CuO}}_2$ planes, thus providing direct evidence of electron-lattice coupling in the pseudogap state and a link between the x-ray scattering and STM measurements. Overall, our results suggest that the periodic lattice displacements in $E$ representations correspond to a locally frozen version of the soft phonons identified by the x-ray scattering measurements, and a fluctuation of the bond length is reflected by the fluctuation of the $d\mathrm{CDW}$ formation near the quantum critical point.

In $PT$-symmetric systems, the notion of non-Abelian frame charges enables multiband topological characterization of degeneracies by examining the eigenvector-frame rotations. Interestingly, some features of these frame charges can be viewed as an analog of electric charges confined in conducting wires, only that they flow in momentum space along nodal lines. But different from electric charges, these frame charges are not integers, and non-Abelian signatures emerge when braiding between adjacent band nodal lines occurs, which flips the direction of the flow. In photonic systems, the photonic $\mathrm{\Gamma }$ point serves as the source or sink of such a frame charge flow due to a hidden braiding induced by the often-ignored electrostatic mode at zero frequency. This source naturally generates non-Abelian topological signatures in $PT$-symmetric photonic systems that can be identified even in ordinary dielectric media. We use biaxial photonic crystals as examples to show how complex nodal line configurations can be explained as the topological consequences of the frame charge flow from the $\mathrm{\Gamma }$ point to the Brillouin zone boundaries. Our results reveal that non-Abelian band topology is intrinsically manifested in general photonic systems, making them easily accessible platforms for exploring non-Abelian physics.

Feedback is a powerful and ubiquitous technique both in classical and quantum system control. Its standard implementation relies on measuring the state of a system, processing the classical signal, and feeding it back to the system. In quantum physics, however, measurements not only read out the state of the system but also modify it irreversibly. Coherent feedback is a different kind of feedback that coherently processes and feeds back quantum signals without actually measuring the system. Here, we report on the experimental realization and the theoretical analysis of an optical coherent feedback platform to control the motional state of a nanomechanical membrane in an optical cavity. The coherent feedback loop consists of a light field interacting twice with the same mechanical mode through different cavity modes, without performing any measurement. Tuning the optical phase and delay of the feedback loop allows us to control the motional state of the mechanical oscillator, its resonance frequency, and also its damping rate, which we use to cool the membrane close to the quantum ground state. Our theoretical analysis provides the optimal cooling conditions, showing that this new technique enables ground-state cooling. Experimentally, we show that we can cool the membrane to a state with ${\overline{n}}_m=4.89\pm 0.14$ phonons ($480\mathrm{\mu }\mathrm{K}$) in a 20 K environment. This lies below the theoretical limit of cavity dynamical backaction cooling in the unresolved sideband regime and is achieved with only 1% of the optical power required for cavity cooling. Our feedback scheme is very versatile, offering new opportunities for quantum control in a variety of optomechanical systems.

The adaptive immune system constantly remodels its lymphocyte repertoire for better protection against future pathogens. Its ability to improve antigen recognition on the fly relies on somatic mutation and selective expansion of B lymphocytes expressing high-affinity antigen receptors. However, this rapid evolution inside an individual appears ineffective, hitting a modest ceiling of antigen-binding affinity. Only recently, experiments began to reveal that evolving B cells physically extract antigens from presenting cells using active forces, and that the extraction level dictates clonal fitness. These observations challenge the prevailing view that the equilibrium constant of receptor-antigen binding determines selective advantage of a B cell clone. Here, we present a theoretical framework to explore ways in which tug-of-war antigen extraction impacts the quality and diversity of an evolved B cell repertoire. We propose that the apparent “ineffectiveness” of in vivo selection can be a direct consequence of nonequilibrium antigen recognition. Our theory predicts, on the one hand, that the physical limits of antigen tether strength, under tugging forces, set the affinity ceiling. On the other hand, intriguingly, cells can use force heterogeneity to diversify binding phenotype without compromising fitness, thus remaining plastic under resource constraint. These results suggest that active probing of receptor quality—via a molecular tug of war during antigen recognition—limits the potency of response to current antigens, but confer adaptive benefit against future variants. By bridging physical mechanisms and evolved functions, this work reveals a multifaceted role of active forces in immune adaptation, which rationalizes key observations on repertoire dynamics.

Many-body systems of quantum interacting particles in which time-reversal symmetry is broken give rise to a variety of rich collective behaviors and are, therefore, a major target of research in modern physics. Quantum simulators can potentially be used to explore and understand such systems, which are often beyond the computational reach of classical simulation. Of these, platforms with universal quantum control can experimentally access a wide range of physical properties. However, simultaneously achieving strong programmable interactions, strong time-reversal symmetry breaking, and high-fidelity quantum control in a scalable manner is challenging. Here, we realize quantum simulations of interacting, time-reversal-broken quantum systems in a universal trapped-ion quantum processor. Using a recently proposed, scalable scheme, we implement time-reversal-breaking synthetic gauge fields, shown for the first time in a trapped-ion chain, along with unique coupling geometries, potentially extendable to simulation of multidimensional systems. Our high-fidelity single-site resolution in control and measurement, along with highly programmable interactions, allow us to perform full state tomography of a ground state showcasing persistent current and to observe dynamics of a time-reversal-broken system with nontrivial interactions. Our results open a path toward simulation of time-reversal-broken many-body systems with a wide range of features and coupling geometries.

We present the first atlas of the continuous gravitational wave sky, produced using LIGO O3a public data. For each 0.045 Hz frequency band and every point on the sky the atlas provides gravitational wave amplitude upper limits, signal-to-noise ratios (SNRs), and frequencies where the search measures the maximum SNR. The approximately top 1.5% of the atlas results are reanalyzed with a series of more sensitive searches with the purpose of finding high SNR long coherence signals from isolated neutron stars. However, these searches do not reveal the presence of such signals. The results presented in the atlas are produced with the Falcon pipeline and cover nearly monochromatic gravitational-wave signals in the 500–1000 Hz band, with up to $\pm 5\times {10}^{-11}\mathrm{Hz}/\mathrm{s}$ frequency derivative. The Falcon pipeline computes loosely coherent power estimates to search data using a succession of coherence lengths. For this search we use six months of data, started with a 12 hour coherence length and progress to six days. Compared to the most sensitive results previously published (also produced with the Falcon pipeline), our upper limits are 50% more constraining. Neutron stars with ellipticity of ${10}^{-8}$ can be detected up to 150 pc away, while allowing for a large fraction of the stars’ energy to be lost through nongravitational channels. These results are within an order of magnitude of the minimum neutron star ellipticity of ${10}^{-9}$ suggested by Woan et al. [Astrophys. J. Lett. 863, L40 (2018)

Advanced gravitational-wave detectors that have made groundbreaking discoveries are Michelson interferometers with resonating optical cavities as their arms. As light travels at a finite speed, these cavities are optimal for enhancing signals at frequencies within the bandwidth, beyond which, however, a small amount of optical loss will significantly impact the high-frequency signals. We find an elegant interferometer configuration with an “$\mathsf{L}$ resonator” as the core, significantly surpassing the loss-limited sensitivity of dual-recycled Fabry-Perot-Michelson interferometers at high frequencies. Following this concept, we provide a broadband design of a 25-km detector with outstanding sensitivity between 2 and 4 kHz. We perform Monte Carlo population studies of binary neutron-star mergers, given the most recent merger rate from the GWTC-3 catalog and several representative neutron-star equations of state. We find that the new interferometer configuration significantly outperforms other third-generation detectors by a factor of 1.7 to 4 in the signal-to-noise ratio of the postmerger signal. Assuming a detection threshold with signal-to-noise $\text{ratio}>5$ and for the cases we explore, the new design is the only detector that robustly achieves a detection rate of the neutron-star postmerger larger than one per year, with the expected rate between $\mathcal{O}(1)$ and $\mathcal{O}(10)$ events per year.

Numerical integrations of the Solar System reveal a remarkable stability of the orbits of the inner planets over billions of years, in spite of their chaotic variations characterized by a Lyapunov time of only 5 million years and the lack of integrals of motion able to constrain their dynamics. To open a window on such long-term behavior, we compute the entire Lyapunov spectrum of a forced secular model of the inner planets. We uncover a hierarchy of characteristic exponents that spans 2 orders of magnitude, manifesting a slow-fast dynamics with a broad separation of timescales. A systematic analysis of the Fourier harmonics of the Hamiltonian, based on computer algebra, reveals three symmetries that characterize the strongest resonances responsible for the orbital chaos. These symmetries are broken only by weak resonances, leading to the existence of quasi-integrals of motion that are shown to relate to the smallest Lyapunov exponents. A principal component analysis of the orbital solutions independently confirms that the quasi-integrals are among the slowest degrees of freedom of the dynamics. Strong evidence emerges that they effectively constrain the chaotic diffusion of the orbits, playing a crucial role in the statistical stability over the Solar System lifetime.