Across a tipping point, a stable steady state of a complex system loses its stability, shifting abruptly to an entirely different state due to tiny perturbations on the intrinsic properties or external environment. Unraveling and controlling the mechanisms that induce the occurrence of a tipping point is of paramount significance to a promotion of sustainability and resilience of a biosystem. Here, we disentangle a previously underappreciated but ubiquitous critical transition from a stable steady state directly to pulsatile (large-amplitude) oscillations in complex networks with multiple timescales. We propose a general framework to accurately uncover this kind of critical transition, even for the unknown coupling matrix. More interestingly, we provide an easy-to-use criterion for assessing how the network topology facilitates or inhibits the emergence of pulsatile oscillations through the tipping point. Three representative examples encompassing neuronal dynamics, gene regulatory networks, and ecological systems are provided to demonstrate our analytical results.

In some quantum many-body systems, the Hilbert space breaks up into a large ergodic sector and a much smaller scar subspace. It has been suggested [K. Pakrouski et al., Phys. Rev. Lett. 125, 230602 (2020)] that the two sectors may be distinguished by their transformation properties under a large group whose rank grows with the system size (it is not a symmetry of the Hamiltonian). The quantum many-body scars are invariant under this group, while all other states are not. Here we apply this idea to lattice systems containing $M$ Majorana fermions per site. The Hilbert space for $N$ sites may be decomposed under the action of the $\text{SO}\left(N\right)\times \text{SO}\left(M\right)$ group, and the scars are the $\text{SO}\left(N\right)$ singlets. For any even $M$ there are two families of scars. One of them, which we call the $\eta$ states, is symmetric under the group $\mathrm{O}\left(N\right)$. The other, the $\zeta$ states, has the $\text{SO}\left(N\right)$ invariance. For $M=4$, where our construction reduces to spin-$1/2$ fermions on a lattice with local interactions, the former family are the $N+1\eta$-pairing states, while the latter are the $N+1$ states of maximum spin. We generalize this construction to $M>4$. For $M=6$ we exhibit explicit formulas for the scar states and use them to calculate the bipartite entanglement entropy analytically. For large $N$, it grows logarithmically with the subsystem size. We present a general argument that any group-invariant scars should have the entanglement entropy that is parametrically smaller than that of typical states. The energies of the scars we find are not equidistant in general but can be made so by choosing Hamiltonian parameters. For $M>6$ we find that with local Hamiltonians the scars typically have certain degeneracies. The scar spectrum can be made ergodic by adding a nonlocal interaction term. We derive the dimension of each scar family and show the scars could have a large contribution to the density of states for small $N$.

Source radiation (radiation reaction) and vacuum field fluctuations can be seen as two inseparable contributions to processes such as spontaneous emission, the Lamb shift, or the Casimir force. Here, we propose how they can be individually probed and their space-time structure revealed in electro-optic sampling experiments. This allows us to experimentally study causality at the single-photon level and to reveal space- and timelike correlations in the quantum vacuum. A connection to the time-domain fluctuation-dissipation theorem is also made.

Quantum mechanics has paved the way for establishing shared privacy among communicating parties through a secure regime known as quantum-secured communication. Recent advancements in both theory and experimentation have unveiled the potential of quantum resources in enhancing the performance and security of estimating unknown parameters. This has led to the emergence of a novel paradigm known as quantum-secured covert sensing, wherein the sensing operation is concealed from an adversary monitoring the environment by embedding the probe signal in a bright noise background. The performance and security of such protocols are quantified using quantum measurement theory. While previous investigations into quantum-secured covert sensing primarily focused on proof-of-concept phase estimation problems, this paper presents a pioneering quantum-secured covert sensing system designed for the Doppler effect—a versatile estimation problem with broad applications. Our research uncovers an inherent trade-off among measurement precision, security, and range within the system. This work establishes a new avenue for incorporating physical-layer security into sensing systems, thereby opening up exciting possibilities for future research in this field.

Motivated by the recent synthesis of a number of Mott insulating square-kagome materials, we explore the rich phenomenology of frustrated magnetism induced by this lattice geometry, also referred to as the squagome or shuriken lattice. On the classical level, square-kagome antiferromagnets are found to exhibit extensive degeneracies, order-by-disorder, and noncoplanar ordering tendencies, which we discuss for an elementary, classical Heisenberg model with nearest-neighbor and cross-plaquette interactions. Having in mind that upon introducing quantum fluctuations noncoplanar order can melt into chiral quantum spin liquids, we provide detailed information on the multitude of noncoplanar orders, including some which break rotational symmetry (possibly leading to nematic quantum orders), as well as a number of (incommensurate) spin spiral phases. Using extensive numerical simulations, we also discuss the thermodynamic signatures of these phases, which often show multistep thermal ordering. Our comprehensive discussion of the classical square-kagome Heisenberg model, often drawing comparisons to the conventional kagome antiferromagnet, sets the stage for future explorations of quantum analogs of the various phases, either conceptually, such as in quantum spin-1/2 generalizations of our model, or experimentally, such as in the Cu-based candidate materials.

We present context-aware fidelity estimation (CAFE), a framework for benchmarking quantum operations that offers several practical advantages over existing methods such as randomized benchmarking (RB) and cross-entropy benchmarking. In CAFE, a gate or a subcircuit from some target experiment is repeated $n$ times before being measured. By using a subcircuit, we account for effects from the spatial and temporal circuit context. Since coherent errors accumulate quadratically while incoherent errors grow linearly, we can separate them by fitting the measured fidelity as a function of $n$. One can additionally interleave the subcircuit with dynamical decoupling sequences to remove certain coherent error sources from the characterization when desired. We have used CAFE to experimentally validate our single- and two-qubit unitary characterizations by measuring fidelity against estimated unitaries. In numerical simulations, we find that CAFE produces fidelity estimates at least as accurate as interleaved RB while using significantly fewer resources. We also introduce a compact formulation for preparing an arbitrary two-qubit state with a single entangling operation and use it to present a concrete example using CAFE to study controlled-$Z$ gates in parallel on a Sycamore processor.

We report laser cooling and trapping of ${}^{224}{\mathrm{Ra}}^{+}$ ions. This was realized via two-step photoionization loading of radium into an ion trap. A robust source for ${}^{224}\mathrm{Ra}$ atoms, which have a 3.6-day half-life, was realized with an effusive oven containing ${}^{228}\mathrm{Th}$, which has a 1.9-yr half-life, which continuously generates ${}^{224}\mathrm{Ra}$ via its $\alpha$-decay. We characterized the efficacy of this source and found that after depleting built-up radium the thorium decay provides a continuous source of radium atoms suitable for ion trapping. The vacuum system has been sealed for more than 6 months and continues to trap ions on demand. We also report a measurement of the ${}^{224}\mathrm{Ra} 7s^2{}^1{\mathrm{S}}_0\to 7s7p{}^1{\mathrm{P}}_1$ transition frequency: $621043830\pm 60$ MHz, which is helpful for efficient photoionization. With this measurement and previous isotope shift measurements we find that the frequency of the same transition in ${}^{226}\mathrm{Ra}$ is $621037830\pm 60$ MHz, which disagrees with the most precise measurement, $621038489\pm 15$ MHz, which is used for the recommended value in the National Institute of Standards and Technology Atomic Spectra Database.

Network reconstruction is a crucial task in understanding and controlling the collective dynamics of complex systems. Most real-world networks exhibit sparse properties, and the connection parameter is a binary signal (0 or 1). Traditional shrinkage methods, such as lasso or compressed sensing (CS), are not suitable for revealing this property. Recently, the signal lasso method was introduced to solve the network reconstruction problem, which was found to be more effective than lasso and CS methods. However, the signal lasso method has a limitation: it cannot accurately classify estimated coefficients that fall between 0 and 1. To address this issue, this paper proposes a method called adaptive signal lasso, which can accurately estimate the signal parameter and uncover the network topology in complex networks with a small number of observations. Our proposed method has at least three advantages: first, it is highly effective in uncovering the network topology and can completely shrink the signal parameter to either 0 or 1, eliminating the unclassified portion in network reconstruction; second, it performs well in both sparse and nonsparse signal scenarios and is robust to noise contamination; third, it only requires the selection of one tuning parameter, reducing computational cost and making it easy to apply. Theoretical properties of this method have been studied, and numerical simulations from linear regression, evolutionary game, and the Kuramoto model are deeply explored. Finally, two real-world examples from human behavioral experiments and the world trade web are used for illustration. It is expected that our proposed method will establish a reliable and uniform framework for estimating signal parameters in complex systems.

We present a metaheuristic conditional neural-network-based method aimed at identifying physically interesting metastable states in a potential energy surface of high rugosity. To demonstrate how this method works, we identify and analyze spin textures with topological charge $Q$ ranging from 1 to $-13$ (where antiskyrmions have $Q<0$) in the Pd/Fe/Ir(111) system, which we model using a classical atomistic spin Hamiltonian based on parameters computed from density functional theory. To facilitate the harvest of relevant spin textures, we make use of the newly developed segment anything model. Spin textures with $Q$ ranging from $-3$ to $-6$ are further analyzed using finite-temperature spin-dynamics simulations. We observe that for temperatures up to around 20 K, lifetimes longer than 200 ps are predicted, and that when these textures decay, new topological spin textures are formed. We also find that the relative stability of the spin textures depend linearly on the topological charge, but only when comparing the most stable antiskyrmions for each topological charge. In general, the number of holes (i.e., non-self-intersecting curves that define closed domain walls in the structure) in the spin texture is an important predictor of stability—the more holes, the less stable the texture. Methods for systematic identification and characterization of complex metastable skyrmionic textures—such as the one demonstrated here—are highly relevant for advancements in the field of topological spintronics.

Accurately predicting the elastic properties of crystalline solids is vital for computational materials science. However, traditional atomistic-scale ab initio approaches are computationally intensive, especially for studying complex materials with a large number of atoms in a unit cell. We introduce a data-driven approach to efficiently predict the elastic properties of crystal structures using SE(3)-equivariant graph neural networks (GNNs). This approach yields important scalar elastic moduli with an accuracy comparable to that of recent data-driven studies. Importantly, our symmetry-aware GNN model also enables the prediction of the strain energy density (SED) and the associated elastic constants, the fundamental tensorial quantities that are significantly influenced by a material's crystallographic group. The model consistently distinguishes independent elements of SED tensors, in accordance with the symmetry of the crystal structures. Finally, our deep learning model possesses meaningful latent features, offering an interpretable prediction of the elastic properties.

We show how to utilize magnetostriction to synchronize two mechanical vibration modes in a cavity magnomechanical (CMM) system. The dispersive magnetostrictive interaction provides necessary nonlinearity required for achieving synchronization. Strong phase correlation between two mechanical oscillators can be established, leading to synchronization robust against thermal noise. We develop a theoretical framework to analyze the synchronization by solving the constraint conditions of steady-state limit cycles. We determine that the strong cavity-magnon linear coupling can enhance and regulate the synchronization, which offers a path to modulate synchronization. In this paper, we reveal a mechanism for achieving and modulating synchronization and indicate that CMM systems can be an ideal platform to explore rich synchronization phenomena.

Adsorption to a surface, reversible binding, and trapping are all prevalent scenarios where particles exhibit “stickiness.” Escape and first-passage times are known to be drastically affected, but a detailed understanding of this phenomenon remains illusive. To tackle this problem, we develop an analytical approach to the escape of a diffusing particle from a domain of arbitrary shape, size, and surface reactivity. This is used to elucidate the effect of stickiness on the escape time from a slab domain, revealing how adsorption and desorption rates affect the mean and variance and providing an approach to infer these rates from measurements. Moreover, as any smooth boundary is locally flat, slab results are leveraged to devise a numerically efficient scheme for simulating sticky boundaries in arbitrary domains. Generalizing our analysis to higher dimensions reveals that the mean escape time abides a general structure that is independent of the dimensionality of the problem. This paper thus offers a starting point for analytical and numerical studies of stickiness and its role in escape, first-passage, and diffusion-controlled reactions.

We study the generation of entanglement between two qubits which communicate through a single cavity mode of quantum light but have no direct interaction. We show that such entanglement can be generated simply by exchanging quanta with a third party, which is in our case the cavity mode. Exchanging only a single quantum creates maximal entanglement. A single quantum can be provided by an external quantum light source. However, we use a classical light source to pump quanta which are used for the exchange, and investigate the degree of two-qubit entanglement. We first identify a characteristic timescale of the interaction between the cavity mode and each qubit. We investigate two regimes of the driving pulse length: one is short and the other is long compared to the characteristic timescale of the interaction. In the first regime, it is known that the pulse can pump the system by generating a displacement of the cavity mode. We show that, by using a specific pulse shape, one can make the displacement essentially vanish after the pulse finishes interaction with the cavity mode. In this case, a rotation of the qubits can be invoked. In addition, higher-order effects of the pulse including a nonlocal operation on the joint system of the cavity mode and the qubits are found, and we present a formalism to compute each term up to a given order. An explicit condition on the pulse shape for each term to be nonzero or suppressed is derived to enable an experimental design for verifying the entanglement generation using a classical light source. In the opposite regime where the driving is sufficiently long, we utilize a squeezed state which may be obtained adiabatically. We study how the squeezing and the accompanied rotation of qubits affect the generated two-qubit entanglement.

The speed of elementary quantum gates, particularly two-qubit gates, ultimately sets the limit on the speed at which quantum circuits can operate. In this work, we experimentally demonstrate commonly used two-qubit gates at nearly the fastest possible speed allowed by the physical interaction strength between two superconducting transmon qubits. We achieve this quantum speed limit by implementing experimental gates designed using a machine-learning-inspired optimal control method. Importantly, our method only requires the single-qubit drive strength to be moderately larger than the interaction strength to achieve an arbitrary two-qubit gate close to its analytical speed limit with high fidelity. Thus the method is applicable to a variety of platforms, including those with comparable single-qubit and two-qubit gate speeds, or those with always-on interactions. We expect our method to offer significant speedups for non-native two-qubit gates that are typically achieved with a long sequence of single-qubit and native two-qubit gates.

Szilárd's information engine is a canonical example in the field of thermodynamics of information. We realize experimentally a macroscopic many-particle Szilárd engine that consists of active particles and use it to lift a mass against gravity. We show that the extractable work per cycle increases when the raised weight is changed more gradually during the process. Interestingly, we find that the ideal extractable work grows with the number of particles due to giant number fluctuations. This is in contrast to the calculated behavior of a similar engine operating on thermal particles.

For open quantum systems, integration of the bath degrees of freedom using the second order cumulant expansion in the Keldysh path integral provides an alternative derivation of the effective action for systems coupled to general baths. The baths can be interacting and not necessarily Markovian. Using this method in the Markovian limit, we compute the particle-loss dynamics in various models of ultracold atomic gases, including a one-dimensional Bose-Hubbard model with two-particle losses and a multicomponent Fermi gas with interactions tuned by an optical Feshbach resonance. We explicitly demonstrate that the limit of strong two-body losses can be treated by formulating an indirect loss scheme to describe the bath-system coupling. The particle-loss dynamics thus obtained is valid at all temperatures. For the one-dimensional Bose-Hubbard model, we compare it to solutions of the phenomenological rate equations. The latter are shown to be accurate at high temperatures.

Dipolar spin ensembles with random spin positions are attracting much attention because they help us to understand decoherence as it occurs in solid-state quantum bits in contact with spin baths. Also, these ensembles are systems which may show many-body localization, at least in the sense of very slow spin dynamics. We present measurements of the autocorrelations of spins on diamond surfaces at infinite temperature in a doubly rotating frame which eliminates local disorder. Strikingly, the timescales in the longitudinal and the transversal channel differ by more than one order of magnitude, which is a factor much greater than one would have expected from simulations of spins on lattices. A previously developed dynamic mean-field theory for spins (spinDMFT) fails to explain this phenomenon. Thus, we improve it by extending it to clusters (CspinDMFT). This theory does capture the striking mismatch up to two orders of magnitude for random ensembles. Without positional disorder, however, the mismatch is only moderate with a factor below 4. The pivotal role of positional disorder suggests that the strong mismatch is linked to precursors of many-body localization.