The metal-organic-framework compound ${\mathrm{Cu}}_3{\left(\mathrm{HOTP}\right)}_2$, also known as ${\mathrm{Cu}}_3{\left(\mathrm{HHTP}\right)}_2$, is a small-gap semiconductor containing a kagome lattice of antiferromagnetically coupled $S=1/2{\mathrm{Cu}}^{\mathrm{II}}$ spins with intralayer nearest-neighbor exchange coupling $J\sim$ 2 K. The intralayer $J$ value obtained from calculations using density functional theory is shown to match with the experimental value for reasonable values of the Hubbard U parameter. Muon spin relaxation confirms no magnetic ordering down to 50 mK and sees spin fluctuations diffusing on a two-dimensional lattice. These properties are consistent with the hypothesis of a quantum spin-liquid ground state being present within highly decoupled kagome layers. Reduction of the spin-diffusion rate on cooling from the paramagnetic region to the low-temperature region reflects quantum entanglement, one of the key properties of a quantum spin liquid. It is also found that the layers become more strongly decoupled in the low-temperature region. Comparison of results for the spin diffusion, magnetic susceptibility, and specific heat in the low-temperature region suggests close proximity to a quantum critical point and a large density of low-energy spinless electronic excitations. A ${\mathrm{Z}}_2$-linear Dirac model for the low-energy spin excitations of the putative quantum spin-liquid ground state is found to provide the best match with experiment.

Reciprocal and nonreciprocal effects in dielectric and magnetic materials provide crucial information about the microscopic properties of electrons. However, experimentally distinguishing the two has proven to be challenging, especially when the associated effects are extremely small. To this end, we propose a contactless detection using a cross-cavity device where a material of interest is placed at its center. We show that the optical properties of the material, such as Kerr and Faraday rotation, or birefringence, manifest in the coupling between the cavity's electromagnetic modes and in the shift of their resonant frequencies. By calculating the dynamics of a geometrical photonic state, we formulate a measurement protocol based on the quantum metric and quantum process tomography that isolates the individual components of the material's complex refractive index and minimizes the quantum mechanical Cramér-Rao bound on the variance of the associated parameter estimation. Our approach is expected to be applicable across a broad spectrum of experimental platforms including Fock states in optical cavities, or coherent states in microwave and THz resonators.

Quantitative models that describe how biological sequences encode functional activities are ubiquitous in modern biology. One important aspect of these models is that they commonly exhibit gauge freedoms, i.e., directions in parameter space that do not affect model predictions. In physics, gauge freedoms arise when physical theories are formulated in ways that respect fundamental symmetries. However, the connections that gauge freedoms in models of sequence-function relationships have to the symmetries of sequence space have yet to be systematically studied. In this work we study the gauge freedoms of models that respect a specific symmetry of sequence space: the group of position-specific character permutations. We find that gauge freedoms arise when model parameters transform under redundant irreducible matrix representations of this group. Based on this finding, we describe an “embedding distillation” procedure that enables both analytic calculation of the number of independent gauge freedoms and efficient computation of a sparse basis for the space of gauge freedoms. We also study how parameter transformation behavior affects parameter interpretability. We find that in many (and possibly all) nontrivial models, the ability to interpret individual model parameters as quantifying intrinsic allelic effects requires that gauge freedoms be present. This finding establishes an incompatibility between two distinct notions of parameter interpretability. Our work thus advances the understanding of symmetries, gauge freedoms, and parameter interpretability in models of sequence-function relationships.

The $\mathcal{PT}$-symmetric semiclassical Rabi model explores the fundamental interaction between a two-level atom and a classical field, revealing novel phenomena in open systems through the inclusion of non-Hermitian terms. We propose a single similarity transformation that yields an effective Hamiltonian in rotating-wave approximation, enabling an analytical solution. The phase boundary of the $\mathcal{PT}$-broken phase, derived from the analytical eigenvalues, closely matches the numerically exact one over a wide range of atomic frequencies, demonstrating the effectiveness of the analytical approach, especially at the main resonance. The Floquet parity operator is also introduced, providing a deeper physical understanding of the emergence of the $\mathcal{PT}$-broken phase. Furthermore, by analyzing the dynamics of excited-state population, we observe several stable oscillations in the Fourier spectrum, demonstrating the applicability of the analytical method beyond the single-photon resonance region. The Bloch-Siegert shift is also discussed, and surprisingly, resembles its Hermitian counterpart, except for the higher-order terms in the coupling strength. The present analytical treatment provides a concise and accurate description of the main physics of this non-Hermitian atom-field interaction system.

The T cell receptor (TCR) is a key component of the adaptive immune system, recognizing foreign antigens (ligands) and triggering an immune response. To explain the high sensitivity and selectivity of the TCR in discriminating “self” from “non-self” ligands, most models evoke kinetic proofreading (KP) schemes, however it is unclear how competing models used for TCR triggering, such as the kinetic segregation (KS) model, influence KP performance. In this paper, we consider two different TCR triggering models and their influence on subsequent KP-based ligand discrimination by the TCR: a classic conformational change model (CC-KP), where ligand-TCR binding is strictly required for activation, and the kinetic segregation model (KS-KP), where only residence of the TCR within a close contact devoid of kinases is required for its activation. Building on previous work, our computational model permits a head-to-head comparison of these models in silico. While we find that both models can be used to explain the probability of TCR activation across much of the parameter space, we find biologically important regions in the parameter space where significant differences in performance can be expected. Furthermore, we show that the available experimental evidence may favor the KS-KP model over CC-KP. Our results may be used to motivate and guide future experiments to determine accurate mathematical models of TCR function.

Theoretical descriptions of the non-equilibrium dynamics of quantum many-body systems essentially employ either (i) explicit treatments, relying on the truncation of the expansion of the many-body wave function, (ii) compressed representations of the many-body wave function, or (iii) evolution of an effective (downfolded) representation through Green's functions. In this work, we select representative cases of each of the methods and address how these complementary approaches capture the dynamics driven by intense field perturbations to non-equilibrium states. Under strong driving, the systems are characterized by strong entanglement of the single-particle density matrix and natural populations approaching those of a strongly interacting equilibrium system. We generate a representative set of results that are numerically exact and form a basis for a critical comparison of the distinct families of methods. We demonstrate that the compressed formulation based on similarity-transformed Hamiltonians (coupled-cluster approach) is practically exact in weak fields and, hence, weakly or moderately correlated systems. Coupled cluster, however, struggles for strong driving fields, under which the system exhibits strongly correlated behavior, as measured by the von Neumann entropy of the single-particle density matrix. The dynamics predicted by Green's functions in the (widely popular) $GW$ approximation are less accurate, but improve significantly upon the mean-field results in the strongly driven regime.

We theoretically demonstrate x-ray second harmonic generation (SHG) with strong-field-driven high harmonic generation (HHG) from core electrons in gas-phase atoms, highlighting its potential as a powerful spectroscopic tool for studying atomic and molecular systems. Our simulations confirm the generation of HHG with x-ray SHG (HHG-XSHG) from atomic core electrons through the rescattering of electrons from x-ray two-photon excitation and subsequent tunneling ionization in an optical laser field. The resulting HHG-XSHG spectrum features a broadband multipeak structure and a distinct spectral cutoff in the x-ray regime. These findings indicate that HHG-XSHG is a valuable technique for probing core-electron dynamics, generating attosecond x-ray pulses, and exploring nonlinear interactions, effectively merging laser-driven attosecond technology with nonlinear x-ray methodologies provided by x-ray free-electron lasers.

The manipulation of quantum states through linear maps beyond quantum operations has many important applications in various areas of quantum information processing. Current methods simulate unphysical maps by sampling physical operations according to classically determined probability distributions. In this work, we show that using quantum measurement instead leads to lower simulation costs for general Hermitian-preserving maps. Remarkably, we establish the equality between the simulation cost and the well-known diamond norm, thus closing a previously known gap and assigning diamond norm a universal operational meaning for all Hermitian-preserving maps. We demonstrate our method in two applications closely related to error mitigation and quantum machine learning, where it exhibits a favorable scaling. These findings highlight the power of quantum measurement in simulating unphysical operations, in which quantum interference is believed to play a vital role. Our work paves the way for more efficient sampling techniques and has the potential to be extended to more quantum information processing scenarios.

The decoherence of a central electron spin due to the dynamics of a coupled electron-spin bath is a core problem in solid-state spin physics. Ensemble experiments have studied the central spin coherence in detail, but such experiments average out the underlying quantum dynamics of the bath. Here, we show the coherent back-action of an individual NV center on an electron-spin bath and use it to detect, prepare, and control the dynamics of a pair of bath spins. We image the NV-pair system with subnanometer resolution and reveal a long dephasing time [$T_2^{*}=44\left(9\right)$ ms] for a qubit encoded in the electron-spin pair. Our experiment reveals the microscopic quantum dynamics that underlie the central spin decoherence and provides new opportunities for controlling and sensing interacting spin systems.

In this work, a coupled theory-guided neural network (coupled-TgNN) is constructed to explore the ground states of one-dimensional binary Bose-Einstein condensates with spin-orbit coupling and a Lee-Huang-Yang term. We find that this method is markedly superior to the ordinary deep neural network due to both the theoretical guidance for the underlying problem and the coupling of neural networks. The former shows better accuracy and more strong robustness and can rapidly construct any ground state using only imaginary-time evolution data of 12 solutions as the training data, without the tedious step-by-step iterative calculation process. In addition, based on the coupled-TgNN approach, a phase transition boundary is also discovered, which clearly distinguishes the single-peak ground state phase from the striped phase. The results not only greatly reduce computational time for exploring the properties of the ground states but also provide a promising technique for discovering phase transitions in other coupled nonlinear systems.

Manipulating Hamiltonians governing physical systems has found a broad range of applications, from quantum chemistry to semiconductor design. In this work, we provide a way of manipulating Hamiltonians, by transforming their eigenvalues while keeping their eigenstates unchanged. We develop a universal algorithm that deterministically implements any desired (suitably differentiable) function on the eigenvalues of any unknown Hamiltonian, whose positive-time and negative-time dynamics are given as a black box. Our algorithm uses correlated randomness to efficiently combine two subroutines—namely controlization and Fourier series simulation—exemplifying a general compilation procedure that we develop. The time complexity of our algorithm is significantly reduced via said compilation technique compared to a naïve concatenation of the subroutines and outperforms similar methods based on the quantum singular value transformation.

Bistability and snap-through instabilities are central to various mechanisms in nature and engineering, enabling rapid movement and significant shape changes with minimal energy input. These phenomena are readily demonstrated by bending an elastic strip into an arch and rotating its edges until snapping occurs. In this article, we show that introducing a fold in such a strip significantly alters its snapping properties. In particular, folded ribbons release much more energy than the regular, unfolded case, leading to faster snapping speeds. Through numerical simulations and theory, we rationalize our experimental observations. We leverage our findings to program the snapping behavior of folded ribbons, demonstrating how our results could find practical applications, e.g., in soft robotics.

In thermal environments, information processing requires thermodynamic costs determined by the second law of thermodynamics. Information processing within finite time is particularly important, since fast information processing has practical significance but is inevitably accompanied by additional dissipation. In this paper, we reveal the fundamental thermodynamic costs and the trade-off relations between incompatible information processing such as measurement and feedback in the finite-time regime. To this end, we introduce a general framework based on the concept of the Pareto front for thermodynamic costs, revealing the existence of fundamental trade-off relations between them. Focusing on discrete Markov jump processes, we consider the trade-off relation between thermodynamic activities, which in turn determines the trade-off relation between entropy productions. To identify the Pareto fronts, we introduce a new Wasserstein distance that captures the thermodynamic costs of subsystems, providing a geometrical perspective on their structure. Our framework enables us to find the optimal entropy production of subsystems and the optimal time evolution to realize it. In an illustrative example, we find that even in situations where naive optimization of total dissipation cannot realize the function of Maxwell's demon, reduction of the dissipation in the feedback system according to the trade-off relation enables the realization of the demon. We also show that an optimal Maxwell's demon can be implemented by using double quantum dots. Furthermore, our framework is applicable to larger scale systems with multiple states, as demonstrated by a model of chemotaxis. Our results would serve as a designing principle of efficient thermodynamic machines performing information processing, from single electron devices to biochemical signal transduction.

Fluidic iontronics offer a unique capability for emulating the chemical processes found in neurons. We extract multiple distinct chemically regulated synaptic features from an experimentally accessible conical microfluidic channel carrying functionalized surface groups, using finite-element calculations of continuum transport equations. By modeling a Langmuir-type surface reaction on the channel wall, we couple fast voltage-induced volumetric salt accumulation with a long-term channel surface charge modulation by means of fast charging and slow discharging. These nonlinear charging dynamics emerge across several orders of magnitude of reaction rates and equilibria, and are understood through an analytic approximation rooted in first principles. We show how short- and long-term potentiation and depression, frequency-dependent plasticity, and chemical-electrical signal spike-timing dependence and coincidence detection (acting like a chemical-electrical AND logic gate), akin to the NMDA mechanism for Hebbian learning in biological synapses, can all be emulated.

Aging is driven by damage accumulation leading to a decline in function over time. In single-cell systems, in addition to this damage accumulation within individuals, asymmetric damage partitioning at cell division can play a crucial role in shaping demographic aging patterns. Despite experimental single-cell studies that provide quantitative data at the molecular and demographic levels, the integration of a complementary theory explaining how cellular damage production and asymmetric partitioning propagate and influence demographic patterns is still lacking. Here, we present a generic and flexible damage model using a stochastic differential equation approach that incorporates stochastic damage accumulation and asymmetric damage partitioning during cell divisions. We formulate an analytical approximation linking cellular and damage parameters to demographic aging patterns along mother cell lineages. Interestingly, the lifespan of cells follows an inverse Gaussian distribution, whose underlying properties derive from cellular and damage parameters. We demonstrate how stochasticity (noise) in damage production, asymmetry in damage partitioning, and division frequency shape lifespan distribution. Confronting the model with various empirical E. coli mother machine data reveals nonexponential scaling in mortality rates, a scaling that cannot be captured by classical Gompertz-Makeham models. Our findings provide a deeper understanding of how fundamental processes contribute to cellular damage dynamics and generate demographic patterns. Our damage model's generic nature offers a valuable framework for investigating aging in diverse biological systems.

Nonlinearity and non-Hermiticity, for example due to environmental gain-loss processes, are a common occurrence throughout numerous areas of science and lie at the root of many remarkable phenomena. For the latter, parity-time-reflection ($\mathcal{PT}$) symmetry has played an eminent role in understanding exceptional-point structures and phase transitions in these systems. Yet their interplay has remained, by and large, unexplored. We analyze models governed by the replicator equation of evolutionary game theory and related Lotka-Volterra systems of population dynamics. These are foundational nonlinear models that find widespread application and offer a broad platform for non-Hermitian theory beyond physics. In this context, we study the emergence of exceptional points in two cases: (a) when the governing symmetry properties are tied to global properties of the models and, in contrast, (b) when these symmetries emerge locally around stationary states—in which case the connection between the local linear non-Hermitian model and an underlying global nonlinear system becomes tenuous. We further outline that when the relevant symmetries are related to global properties, the location of exceptional points in the linearization around coexistence equilibria coincides with abrupt global changes in the stability of the nonlinear dynamics. Exceptional points may thus offer a new local characteristic for the understanding of these systems. Tritrophic models of population ecology serve as test cases for higher-dimensional systems.

Despite acute interest in the dynamics of non-Hermitian systems, there is a lack of consensus in the mathematical formulation of non-Hermitian quantum mechanics in the community. Different methodologies are used in the literature to study non-Hermitian dynamics. This ranges from consistent frameworks like biorthogonal quantum mechanics and metric approach characterized by modified inner products, to normalization by time-dependent norms inspired by open quantum systems. In this work, we systematically explore the similarities and differences among these various methods. Utilizing illustrative models with exact solutions, we demonstrate that these methods produce not only quantitatively different results but also distinct physical interpretations. For dissipative systems where non-Hermiticity arises as an approximation, we find that simply dividing by the norm in the $\mathcal{PT}$-broken regime closely aligns with the full master equation solutions. In contrast, for quantum systems where non-Hermiticity can be engineered exactly, incorporating metric dynamics is crucial for the probabilistic interpretation of quantum mechanics, necessitating the generalizations of similarity transformations and unitarity to non-Hermitian systems. This study lays the groundwork for further exploration of non-Hermitian Hamiltonians, potentially leveraging generalized transformations for novel physical phenomena.

Gaining a deeper understanding of the interplay between charge density wave (CDW) order and superconductivity in transition metal dichalcogenides (TMDs), particularly within the (4H/2H)-${\mathrm{Nb}X}_2 (X=\mathrm{Se}$ and S) family, remains an open and intriguing challenge. A systematic microscopic study across various compounds in this family is therefore required to unravel this complex interplay. Here, we report on muon spin rotation (µSR) and magnetotransport experiments investigating the effects of hydrostatic pressure on the superconducting transition temperature ($T_{\mathrm{c}}$), the temperature-dependent magnetic penetration depth (${\lambda }_{\mathrm{eff}}$), and the charge density wave order (CDW) in two layered chalcogenide superconductors: 4H-${\mathrm{NbSe}}_2$, which exhibits CDW order, and 2H-${\mathrm{NbS}}_2$, which lacks such order. Our observations reveal a substantial $75\%$ enhancement of the superfluid density ($n_s/m^{*}$) in 4H-${\mathrm{NbSe}}_2$ upon the maximum applied pressure of $\sim 2$ GPa, surpassing that of 2H-${\mathrm{NbSe}}_2$. Despite the absence of CDW order, a sizable $20\%$ growth in superfluid density is also observed for 2H-${\mathrm{NbS}}_2$ under an applied pressure of 1.8 GPa. Notably, the evaluated superconducting gaps in all these TMDs remain largely unaffected by changes in applied pressure, irrespective of pressure-induced partial suppression of CDW order in (4H/2H)-${\mathrm{NbSe}}_2$ or its general absence in 2H-${\mathrm{NbS}}_2$. These results underscore the complex nature of pressure-induced behaviors in these TMDs, challenging a simplistic view of competition solely between CDW order and superconductivity. Remarkably, the relationship between $n_s/m^{*}$ and $T_{\mathrm{c}}$ exhibits an unconventional correlation, indicating a noteworthy similarity with the behavior observed in cuprate, kagome, and iron-based superconductors.

Lattice softness has a significant impact on charge carrier dynamics in condensed matter systems, contributing to the emergence of various properties and functions. Examples include the remarkable carrier lifetimes and defect tolerances of hybrid organic-inorganic perovskites. Recent studies suggest the contribution of quartic anharmonicity of the lattice vibrations. The quartic anharmonicity can be discussed with a double-well potential, and the transition between the two minima can be coarse grained as a two-state jump stochastic process. Such a stochastic approach is typically employed to describe dynamic fluctuations introduced into a system by two-state transitions in the surroundings. To investigate charge transport in materials, however, it is crucial to describe not only the fluctuations but also the dynamic lattice distortions associated with charge transport. Therefore, there is a need for a theory to describe the charge carrier dynamics proceeding alongside the lattice distortion dynamics. In this study, we present a theory that describes quantum dynamics under the influence of an environment with two stable states, termed a bistable environment. The theory describes the effects of fluctuations and dissipation induced from the bistable environment in a reasonable manner, and the effects exhibit a different temperature dependence than the widely employed Gaussian environment. The physical implication of this temperature dependence is provided in terms of the environmental dynamics. The results of this study are expected to provide a step forward in describing charge carrier dynamics in materials with lattice softness and pronounced lattice anharmonicity, e.g., hybrid organic-inorganic perovskites. Moreover, these findings represent an advancement in our understanding of and capacity to predict and control the physical properties and functions of these materials.