Materials realizing the $XY$ model in two dimensions are sparse. Here we use neutron triple-axis spectroscopy to investigate the critical static and dynamical magnetic fluctuations in the square-lattice antiferromagnets ${\mathrm{Ca}}_2{\mathrm{RuO}}_4$ and ${\mathrm{Ca}}_3{\mathrm{Ru}}_2{\mathrm{O}}_7$. We probe the temperature dependence of the antiferromagnetic Bragg intensity, the $Q$ width, the amplitude, and the energy width of the magnetic diffuse scattering in the vicinity of the Néel temperature $T_{\mathrm{N}}$ to determine the critical behavior of the magnetic order parameter $M$, correlation length $\xi$, susceptibility $\chi$, and the characteristic energy $\mathrm{\Gamma }$ with the corresponding critical exponents $\beta , \nu , \gamma$, and $z$, respectively. We find that the critical behaviors of the single-layer compound ${\mathrm{Ca}}_2{\mathrm{RuO}}_4$ follow universal scaling laws that are compatible with predictions of the two-dimensional (2D) $XY$ model. The bilayer compound ${\mathrm{Ca}}_3{\mathrm{Ru}}_2{\mathrm{O}}_7$ is only partly consistent with the 2D $XY$ theory and best described by the three-dimensional (3D) Ising model, which is likely a consequence of the intrabilayer exchange interactions in combination with an orthorhombic single-ion anisotropy. Hence, our results suggest that layered ruthenates are promising solid-state platforms for research on the 2D $XY$ model and the effects of 3D interactions and additional spin-space anisotropies on the magnetic fluctuations.

High-amplitude events of the out-of-plane vorticity component ${\omega }_z$ are analyzed by stereoscopic particle image velocimetry (PIV) in the bulk region of turbulent Rayleigh-Bénard convection in air. The Rayleigh numbers $\mathrm{Ra}$ vary from $1.7\times {10}^4$ to $5.1\times {10}^5$. The experimental investigation is connected with a comprehensive statistical analysis of long-term time series of ${\omega }_z$ and individual velocity derivatives $\partial u_i/\partial x_j$. A statistical convergence for derivative moments up to an order of 6 is demonstrated. Our results are found to agree well with existing high-resolution direct numerical simulation data in the same range of parameters, including the extreme vorticity events that appear in the far exponential tails of the corresponding probability density functions. The transition from Gaussian to non-Gaussian velocity derivative statistics in the bulk of a convection flow is confirmed experimentally. The experimental data are used to train a reservoir computing model, one implementation of a recurrent neural network, to reproduce highly intermittent experimental time series of the vorticity and thus reconstruct extreme out-of-plane vorticity events. After training the model with high-resolution PIV data, the machine learning model is run with sparsely seeded, continually available, and unseen measurement data in the reconstruction phase. The dependence of the reconstruction quality on the sparsity of the partial observations is also documented. Our latter result paves the way to machine-learning-assisted experimental analyses of small-scale turbulence for which time series of missing velocity derivatives can be provided by generative algorithms.

Measurement plays a quintessential role in the control of quantum systems. Beyond initialization and readout which pertain to projective measurements, weak measurements, in particular through their back action on the system, may enable various levels of coherent control. The latter ranges from observing quantum trajectories to state dragging and steering. Furthermore, just like the adiabatic evolution of quantum states that is known to induce the Berry phase, sequential weak measurements may lead to path-dependent geometric phases. Here we measure the geometric phases induced by sequences of weak measurements and demonstrate a topological transition in the geometric phase controlled by measurement strength. This connection between weak measurement-induced quantum dynamics and topological transitions reveals subtle topological features in measurement-based manipulation of quantum systems. Our protocol could be implemented for classes of operations (e.g., braiding) that are topological in nature. Furthermore, our results open new horizons for measurement-enabled quantum control of many-body topological states.

Spoofing an electromagnetic signal involves measuring its properties and preparing a spoof signal that is a close enough copy to fool a receiver. A classic application of spoofing is in radar where an airborne target attempts to avoid being tracked by a ground-based radar by emitting pulses indicating a false range or velocity. In certain scenarios it has been shown that a sensor can exploit quantum mechanics to detect spoofing at the single-photon level. Here we analyze an idealized spoofing scenario where a transmitter-receiver pair, seeking to detect spoofing, utilizes a signal chosen randomly from a set of nonorthogonal, coherent states. We show that a spoofer optimally employing classical information on the state of the transmitted signal (i.e., the best measure-and-prepare strategy allowed by quantum mechanics) inevitably emits imperfect spoofs that can be exploited by the receiver to reveal the presence of the spoofer, or to discriminate between true reflections and spoofs. Importantly, we show that the quantum limitations on classical spoofing remain significant even in the large mean-photon-number regime.

This study demonstrates that the zeros of the diagonal components of Green functions are key quantities that can detect noninteracting topological insulators. We show that zeros of the Green functions traverse the band gap in the topological phases. The traverses induce the crosses of zeros, and the zeros' surface in the band gap, analogous to the Fermi surface of metals. By calculating the zeros of the microscopic models, we show the traverses of the zeros universally appear in all six classes of conventional noninteracting topological insulators. By utilizing the eigenvector-eigenvalue identity, which is a recently rediscovered relation in linear algebra, we prove that the traverses of the zeros in the bulk Green functions are guaranteed by the band inversions, which occur in the topological phases. The relevance of the zeros to detecting the exotic topological insulators such as the higher-order topological insulators is also discussed. For the Hamiltonians with the nearest-neighbor hoppings, we also show that the gapless edge state guarantees the zeros' surfaces in the band gap. The analysis demonstrates that the zeros can be used to detect a wide range of topological insulators and thus useful for searching new topological materials.

The $\text{U}\left(1\right)$ quantum link model on the triangular lattice has two rotation-symmetry-breaking nematic confined phases. Static external charges are connected by confining strings consisting of individual strands with fractionalized electric flux. The two phases are separated by a weak first-order phase transition with an emergent, almost exact $\text{SO}\left(2\right)$ symmetry. We construct a quantum circuit on a chip to facilitate near-term quantum computations of the nontrivial string dynamics.

In this paper we identify a previously unexplored type of topological defect in spiral spin liquids—the momentum vortex—and reveal its dominant role in shaping the low-energy physics of such systems. Spiral spin liquids are a class of classical spin liquids featuring subextensively degenerate ground states. They are distinct from spin liquids on geometrically frustrated lattices, in which the ground-state degeneracy is extensive and connected by local spin flips. Despite a handful of experimental realizations and many theoretical studies, a concrete physical picture of their spin liquidity has not been established so far. In this paper, we study a 2D spiral spin liquid model to answer this question. We find that the local momentum vector field can carry topological defects in the form of vortices, which, however, have very different properties from the commonly known spin vortices. The fluctuations of such vortices lead the system into a liquid phase at intermediate temperatures. Furthermore, the effective low-energy theory of such vortices indicates their equivalence to quadrupoles of fractons in a rank-2 U(1) gauge theory or, alternatively, to quadrupoles of disclinations in elasticity theory. At very low temperatures, the system freezes into a glassy state in which these vortices form a rigid network with straight-line domain walls. Our paper sheds light on the nature of spiral spin liquids and also paves the way toward understanding their quantum limit.

Partial differential equations (PDEs) are concise and understandable representations of domain knowledge, which are essential for deepening our understanding of physical processes and predicting future responses. However, the PDEs of many real-world problems are uncertain, which calls for PDE discovery. We propose the symbolic genetic algorithm to discover open-form PDEs (SGA-PDE) directly from data without prior knowledge about the equation structure. SGA-PDE focuses on the representation and optimization of PDEs. Firstly, SGA-PDE uses symbolic mathematics to realize the flexible representation of any given PDE, transforms a PDE into a forest, and converts each function term into a binary tree. Secondly, SGA-PDE adopts a specially designed genetic algorithm to efficiently optimize the binary trees by iteratively updating the tree topology and node attributes. The SGA-PDE is gradient free, which is a desirable characteristic in PDE discovery since it is difficult to obtain the gradient between the PDE loss and the PDE structure. In the experiment, SGA-PDE not only successfully discovered the nonlinear Burgers’ equation, the Korteweg–de Vries equation, and the Chafee-Infante equation but also handled PDEs with fractional structure and compound functions that cannot be solved by conventional PDE discovery methods.

Ultracold gases of fermionic alkaline-earth(-like) atoms are hopeful candidates for the quantum simulation of many-body physics induced by magnetic impurities (e.g., the Kondo physics), because there are spin-exchange interactions (SEIs) between two atoms in the electronic ground (${}^1\mathrm{S}_0$) and metastable (${}^3\mathrm{P}$) state, respectively. Nevertheless, this SEI cannot be tuned via magnetic Feshbach resonance. In this paper, we propose three methods to control the SEI between one atom in the ${}^1\mathrm{S}_0$ state and another atom in the ${}^3\mathrm{P}_2$ states or ${}^3\mathrm{P}_2\text{−}{}^3\mathrm{P}_0$ dressed states, with one or two laser beams. These methods are based on the spin-dependent ac-Stark shifts of the ${}^3\mathrm{P}_2$ states or the ${}^3\mathrm{P}_2\text{−}{}^3\mathrm{P}_0$ Raman coupling. We show that due to the structure of alkaline-earth (like) atoms, the heating effects induced by the laser beams of our methods are very weak. For instance, for ultracold Yb atoms, ac-Stark-shift difference of variant spin states of the ${}^3\mathrm{P}_2(F=3/2)$ level, or the strength of the ${}^3\mathrm{P}_2\text{−}{}^3\mathrm{P}_0$ Raman coupling, could be of the order of $\left(2\pi \right)\mathrm{MHz}$, while the heating rate (photon scattering rate) is only of the order of Hz. As a result, the Feshbach resonances, with which one can efficiently control the SEI by changing the laser intensity, may be induced by the laser beams with a low-enough heating rate, even if the scattering lengths of the bare interatomic interaction are so small that they are comparable with the length scale associated with the van der Waals interaction.

Successful morphogenesis on the scale of organs or organisms requires strict coordination between the constituent cells whose action on the local scale must be orchestrated accurately to achieve a functional shape on the global scale. We present a theoretical model in which morphogenetic information is encoded only through a locally preferred curvature, but with cell dynamics which simultaneously ensures that these interactions globally achieve morphogenesis and correct cell-neighbor exchanges to avoid cell stretches. This is achieved by a cell-cell interaction potential that drives correct cell intercalation to reorganize the cell sheet dynamically during the deformation processes. We demonstrate morphogenesis of simple three-dimensional shapes and study the effects of fixed cell neighbor connectivity and noisy cell division.

We use a superconducting microresonator as a cavity to sense absorption of microwaves by a superconducting quantum point contact defined by surface gates over a proximitized two-dimensional electron gas. Renormalization of the cavity frequency with phase difference across the point contact is consistent with coupling to Andreev bound states. Near π phase difference, we observe random fluctuations in absorption with gate voltage, related to quantum interference-induced modulations in the electron transmission. Close to pinch-off, we identify features consistent with the presence of a single Andreev bound state and describe the Andreev-cavity interaction using a Jaynes-Cummings model. By fitting the weak Andreev-cavity coupling, we extract ∼GHz decoherence consistent with charge noise and the transmission dispersion associated with a localized state.

We propose a continuous-variable quantum sensing scheme, in which a harmonic oscillator is employed as the probe to estimate the parameters in the spectral density of a quantum reservoir, within a non-Markovian dynamical framework. It is revealed that the sensing sensitivity can be effectively boosted by (i) optimizing the weight of the momentum-position-type coupling in the whole probe-reservoir interaction Hamiltonian, (ii) the initial quantum squeezing resource provided by the probe, (iii) the noncanonical equilibration induced by the non-Markovian effect, and (iv) applying an external driving field. Our results may have some potential applications in understanding and controlling the decoherence of dissipative continuous-variable systems.

The optical Stark effect is a tell-tale signature of coherent light–matter interaction in excitonic systems, wherein an irradiating light beam tunes exciton transition frequencies. Here we show that, when excitons are placed in a nanophotonic cavity, the excitonic Stark effect can become highly nonlinear, exhibiting multivalued and hysteretic Stark shifts that depend on the history of the irradiating light. This multistable Stark effect (MSE) arises from feedback between the cavity mode occupation and excitonic population mediated by the Stark-induced mutual tuning of the cavity and excitonic resonances. Strikingly, the MSE manifests even for very dilute exciton concentrations and can yield discontinuous Stark shift jumps of order meV. We expect that the MSE can be realized in readily available transition metal dichalcogenide excitonic systems placed in planar photonic cavities at modest pump intensities. This phenomenon can provide new means to engineer coupled states of light and matter that can persist even in the single exciton limit.

Machine learning (ML) has found widespread application over a broad range of important tasks. To enhance ML performance, researchers have investigated computational architectures whose physical implementations promise compactness, high-speed execution, physical robustness, and low-energy cost. Here, we experimentally demonstrate an approach that uses the high sensitivity of reverberant short-wavelength waves for physical realization and enhancement of computational power of a type of ML known as reservoir computing (RC). The potential computation power of RC systems increases with their effective size. We here exploit the intrinsic property of short-wavelength reverberant wave sensitivity to perturbations to expand the effective size of the RC system by means of spatial and spectral perturbations. Working in the microwave regime, this scheme is tested experimentally on different ML tasks. Our results indicate the general applicability of reverberant wave based implementations of RC and of our effective reservoir size expansion techniques.

The development of multifunctional and biocompatible microrobots for biomedical applications relies on achieving controllable locomotion. Here we describe the conditions that allow homogeneous magnetoelastic membranes composed of superparamagnetic particles to swim through viscous fluids. By solving the equations of motion, we find the dynamical modes of circular membranes in precessing magnetic fields, which are found to actuate in or out of synchronization with a magnetic field precessing above or below a critical precession frequency ${\omega }_c$, respectively. For frequencies larger than ${\omega }_c$, synchronized transverse waves propagate on the membrane along the rotational (perimeter) and radial directions. Using the lattice Boltzmann approach, we show how these waves give rise to locomotion in an incompressible fluid at low Reynolds numbers. Nonreciprocal motion resulting in swimming is achieved by breaking the morphological symmetry of the membrane, attained via truncation of a circular segment. The membrane translation can be adapted to a predetermined path by programming the external magnetic field. Our results lay the foundation for achieving directed motion in thin, homogeneous magnetoelastic membranes with a diverse array of geometries.