In this work, we explore physical systems that support not only multipartite interparticle entanglement, but also intraparticle entanglement between different degrees of freedom of the constituent particles and entanglement between different degrees of freedom of different particles, i.e., algebraic entanglement. We derive a simple method for calculating the algebraic entanglement entropy between two of the particles’ degrees of freedom from collective states of the whole ensemble. Our procedure makes use of underlying symmetries in these systems, in particular, permutation symmetry of the particle indices, and shows a connection between the algebraic entanglement entropy in these systems and the irreducible representations of Lie groups which describe the particles’ degrees of freedom. Namely, we use the direct sum over irreducible representations to diagonalize the reduced density matrices in a block-by-block manner, and then utilize the multiplicity of these irreducible representations to reproduce the results from an exponentially scaled Hilbert space in only polynomial complexity. We use this to explore a variety of systems where the constituent particles support two degrees of freedom each with two levels, such as atoms with two electronic states and two momentum states. Notably, these systems may be exactly simulated in a polynomial-scaled Hilbert space, yet they support an algebraic entanglement entropy that grows linearly with the particle number, which typically requires an exponentially scaled Hilbert space.

Hierarchy is the architecture of complex systems. While Euclidean metric describes homogeneous and static systems, ultrametric geometry is for heterogeneous ensembles, hierarchic relations, and dynamic contexts. Applications spread across all fields: communication technologies, information retrieval, clusterwise regression, analysis, and synthesis of narratives and emotions. The paradigmatic model describing complex systems is the spin glass theory, according to which the topology of the many metastable energy states is intrinsically ultrametric, as a consequence of the breaking of their symmetry. Despite the importance, a real experimental observation of ultrametricity in spin glasses with a large number of spins has not yet been reported, due to the difficulty of finding a physical system in which the order parameter can be easily obtained from direct measurements. Random lasers have recently been proposed as excellent photonic counterparts of spin glasses with robust replica symmetry breaking features. Here, we report the ultrametric structure of the replica space with clustered domains in random lasers, as predicted in the Parisi ansatz. We show that the number of states forming isosceles triangles in the metric space increases through the laser threshold giving rise to the construction of a genealogical tree. Moreover, from the hierarchical topology of the states, we obtain a direct observation of the complex energy landscape with evident breaking of ergodicity in the glassy regime. These results mark a key advance in complexity science and invigorate current efforts to harness physical systems for the realization of optical computers and quantum optimization processors.

Nitrogen-rich compounds have emerged as promising candidates for high-energy-density applications owing to their superior energy content and environmental benignity, yet uncovering compounds that integrate high energy density with stability and persistence remains a significant scientific challenge. Building upon the synthesized all-single-bonded framework of Fdd2-${\mathrm{TaN}}_5$, we perform computational studies where the heaviest group-V element (Ta) was strategically substituted with its lightest congener (V), obtaining ${\mathrm{VN}}_5$—a novel compound that retains the original orthorhombic Fdd2 space group symmetry while exhibiting branched, all-single-bonded nitrogen chains. This compound exhibits a remarkable energy density ($E_d$) of 5.18 kJ/g, far exceeding that of ${\mathrm{TaN}}_5$ at 2.02 kJ/g. explo5 calculations reveal that its detonation velocity ($V_d$) and detonation pressure ($P_d$) reach 16.33 km/s and 187.4 GPa, all surpassing those of TNT. These exceptional characteristics make ${\mathrm{VN}}_5$ a highly competitive potential high-energy-density material.

Active and living matter exhibits a wide range of complex phenomena, including collective motion, pattern formation, and hierarchical structures. Collective motion in living systems is often quantified using spatial correlation functions; however, competing definitions—especially for velocity fields—yield inconsistent results across studies. Here, we clarify the distinction between “normalize-first” and “average-first” velocity correlations, and establish a robust and practical framework for computing correlation functions and extracting director and velocity correlation lengths, ${\xi }_d$ and ${\xi }_v$, respectively, from a wide range of active cell systems. Using synthetic shear and vortex fields and experimental datasets spanning epithelial monolayers, neural progenitors, and bacterial colonies, we demonstrate how noise and fitting choices affect inferred length scales, and provide recipes that yield consistent outcomes. Finally, we introduce two state diagrams—${\xi }_v$ versus ${\xi }_d$ and ${\xi }_v/{\xi }_d$ versus motility anisotropy—that locate systems within different dynamical regimes and track their trajectories during development. These tools standardize correlation analysis and link single-cell motility to emergent colony-scale flows, enabling rigorous, comparable measurements across living systems.

Optical beams with orbital angular momentum (OAM) have numerous potential applications, but the means used for their generation often lack crucial on-demand control. In this work, we present a mechanism of converting spin angular momentum (SAM) to OAM in a nonstructured beam. The conversion occurs through spin-orbit coupling in a reconfigurable photonic honeycomb lattice with staggering implemented by electromagnetically induced transparency in an atomic vapor cell. The spin-orbit coupling allows to outcouple the OAM signal from a particular band in a given valley determined by the chirality of light or the lattice staggering, providing a nonzero Berry curvature for generating OAM. The dependence of the output OAM on the chirality of the input beam is the first control knob. The staggering works as a second control knob, flipping the sign of OAM for the fixed chirality. The demonstrated conversion between SAM and OAM is important for optical communications. Our results can be extended to other implementations of paraxial photonic graphene.

Engineered dissipation provides a powerful route to controlling and stabilizing quantum states in open systems. Superconducting circuits are particularly suited to this approach due to their tunable coupling to dissipative environments. Here, we realize programmable local reservoirs for superconducting qubits through parametrically driven couplings to readout resonators, creating energy-selective incoherent pump and loss. Using coupled superconducting qubits, we autonomously stabilize entangled single-excitation states with fidelity up to 90.8%. We probe the stabilization dynamics under varying initial conditions and bath parameters, and implement robust classical shadow estimation for accurate and scalable state characterization. Finally, we numerically study a configuration where the engineered pump and loss share a common dissipative mode, leading to reservoir-mediated interference and classically correlated steady states. Our results demonstrate a scalable and hardware-efficient framework for dissipative preparation and control of correlated many-body states in superconducting circuits.

We investigate the mechanisms necessary for the stabilization of complex quantum correlations by exploring dissipative couplings to nonreciprocal reservoirs. We analyze the role of locality in the coupling between the environment and the quantum system of interest, as we consider either local couplings throughout the system or a single global coupling. We contrast the results obtained for the two scenarios in which a chain of strongly interacting hard-core bosonic atoms is coupled directly to Markovian kinetic dissipative processes or experiences effective dissipation through the mediation of the field of a lossy optical cavity. To investigate the dissipative dynamics of the many-body quantum systems considered, we perform numerical simulations employing matrix product state methods. We show that by coupling atomic tunneling terms to the global field of a dissipative cavity we can stabilize at long times both finite currents and current-current correlations throughout the atomic chain. This is in contrast to the setup in which dissipation acts directly via local tunneling processes, where currents arise in a narrow region of the system and the current-current correlations are rapidly decaying.

A broad class of correlated quantum materials features strong Hund’s coupling, yet cold-atom quantum simulators have so far focused primarily on single-orbital Fermi-Hubbard systems near a Mott insulator. Here, we show that repulsively interacting fermions loaded into the $p$ bands of a hexagonal lattice offer a unique platform to study the interplay of “Hundness” and “Mottness.” Our theory predicts that the orbital degrees of freedom, despite geometric frustration, produce a rich phase diagram featuring a competing itinerant ferromagnetic (FM) metal and a spin-1 antiferromagnetic (AFM) insulator. While FM order is known to emerge at low fillings near the flat-band limit, we show that this itinerant ferromagnetism is remarkably robust, persisting to stronger interactions and higher fillings well beyond the flat-band regime. More importantly, we identify that near half filling, FM is stabilized by a different mechanism: the double exchange with spins aligning to avoid Hund-rule penalties at the expense of the kinetic energy of Dirac fermions. The competition between the kinetic and double-exchange energies leads to, within our approximations, a first-order transition between FM and AFM orders in the chemical potential-interaction strength plane. Our analysis suggests that $p$-orbital Fermi gases—as multiorbital systems with coexisting localized and itinerant spins—reveal a rich competition between correlated “Hund metals” and other unconventional states driven by quantum fluctuations.

The cat state, as an important tool for exploring the classical-quantum boundary, not only provides important tests of macroscopic quantum effects, but also has important applications in quantum metrology and quantum computation. The three-magnon process, which originates from the magnetic dipole-dipole interaction, has been less explored in the preparation of nonclassical magnon state. Here, we develop the magnon parametric coupling process that arises from the three-magnon scattering. The magnon parametric coupling strength is analytically derived and can reach a strong coupling regime within a discretized magnon mode system. Based on this, we propose a scheme to prepare the cat state without involving external nonlinearity in a magnetic system. Through the magnon parametric coupling, the extra magnon dissipation channel provided by the magnon-photon interaction induces an effective two-magnon loss channel, thereby steering the magnon into the cat state manifold. Notably, the size of the magnon cat state is inversely proportional to the parametric coupling strength, which facilitates the preparation of large-size cat states, even under environmental decoherence. Our work opens a path for the preparation of nonclassical states in magnon spintronics systems without extra nonlinear materials and also promotes the study of fundamental nonlinear physics on the magnetic platform.

Remote synchronization (RS), in which nonadjacent nodes synchronize while directly connected nodes remain incoherent, and remote propagation (RP), in which signals are transmitted to distant nodes while intermediate nodes remain dynamically inactive, are two fundamental phenomena whose connection remains unclear. Here, we show that remote signal transmission can generate RS in a driven star network of Stuart-Landau oscillators and in empirical human brain subnetworks. In the minimal network, a periodic input propagates frequency selectively to remote nodes, as indicated by their locking to the driving frequency, while the hub remains unlocked, producing RP. When multiple remote nodes receive the same propagated signal, they form an RS state with strong mutual coherence despite weak hub coherence. Parameter-space maps show that the RS and RP regimes coincide, and empirical brain-subnetwork simulations confirm this mechanism beyond the minimal architecture. A coupling-based analysis explains the transition as network-mediated frequency-selective entrainment to a common propagated frequency. These results establish a dynamical route from remote signal transmission to long-range coherent dynamics.

We formulate stationary-density-preserving nonreversible perturbations of Fokker-Planck dynamics as gauge fields that deform relaxation spectra while leaving the invariant state fixed. When detailed balance holds, a similarity transformation maps the reversible Fokker-Planck operator to the scalar sector of a Witten-Laplacian-type supersymmetric Hamiltonian; nonreversible gauges then appear as non-Hermitian perturbations that preserve the zero mode but modify the excited spectrum. This operator viewpoint gives a common language for relaxation gaps, circulating probability currents, hypocoercive acceleration, and finite control costs. We represent admissible gauge currents by antisymmetric tensor fields and identify the detailed-balance-violating Ohzeki-Ichiki force as a constant symplectic example whose infinite-strength limit is Hamiltonian dynamics. The continuous-time spectral gap alone does not select a finite gauge strength, so we introduce a finite-time regularized objective and an actor-critic procedure for learning the gauge. An exactly solvable anisotropic Gaussian Ornstein-Uhlenbeck benchmark separates the spectral transition from the finite-time optimum and shows that the learned gauge recovers the Lyapunov-equation optimum. A double-well benchmark then illustrates the same constrained selection in a nonconvex metastable landscape. Stochastic gradient methods enter this framework as physically relevant Fokker-Planck systems: Minibatch noise acts as an effective diffusion tensor, and adaptive methods such as Adam correspond to metric choices with possible nonequilibrium currents.

We propose using even and odd Schrödinger cat states formed from coherent states of U(3) of an ensemble of qutrits with a symmetrical V configuration (a qubit-disguised qutrit) to encode a logical qubit. These carefully engineered logical qubit states are parameter-independent stationary states of the effective master equation governing the evolution of the ensemble and, consequently, constitute dark states that are invulnerable to dissipation and correlated collective dephasing. In particular, the logical qubit states are immune to single-qutrit decay (the analogous of single-photon loss process for qutrits) and simultaneous decay and driving of two qutrits (the analogous of two-photon loss and driving processes for qutrits). In addition, we show how to implement the single-qubit quantum NOT gate and the Hadamard gate followed by either the phase gate or the phase and $Z$ gates. We study analytically the case of two qutrits and conclude that the logical qubit states exhibit parity-sensitive inhomogeneous broadening and local correlated dephasing: The even logical state is completely immune to these processes, while the odd one is vulnerable. Nevertheless, in the presence of these interactions one can also define two odd states with mixed permutation symmetry (with fully distinguishable qutrits) that are immune to both inhomogeneous broadening and local correlated dephasing. We show that these results can be extended to an arbitrary number of qutrits. We also present how the logical qubit states can be defined for qutrits with an asymmetrical V configuration and that they preserve their robustness properties. The effective master equation is deduced from a physical system composed of two parametrically coupled cavities with one of them interacting dispersively with an ensemble of three-level atoms (the qutrits). A proof that the logical qubit is also part of a stationary solution of the physical system under the considered approximations is given. In principle, this physical system can be implemented by means of two coplanar waveguide resonators, a superconducting quantum interference device parametrically coupling them, and a cloud of alkali atoms close to one of the resonators.

An elastic arch is an archetypal bistable system. Here, we combine elastica theory and photomechanical experiments to elucidate the mechanics of an active arch with a spatiotemporally varying preferred curvature $\overline{\kappa }\left(s\right)$. Our shallow-arch theory completely describes any such system via the decomposition of its $\overline{\kappa }\left(s\right)$ into Euler-buckling modes. Intuitively, if $\overline{\kappa }\left(s\right)$ overlaps with the fundamental mode, it snaps the arch up/down. Conversely, nonoverlapping $\overline{\kappa }\left(s\right)$ drives a second-order transition to a higher-order shape. Furthermore, the form of $\overline{\kappa }\left(s\right)$ enables control over the instability’s character; we find the forms for snapping with maximum energy release and at the lowest stimulation (both binary patterns) and design forms for symmetric and asymmetric switching pathways. Analogous control can also be achieved in boundary-driven instabilities of passive arches by fabricating them with suitable $\overline{\kappa }\left(s\right)$. We thus anticipate that our results will improve switchable/snapping elements in micro-electromechanical systems, robotics, and mechanical metamaterials.

Classical shadow tomography has become a powerful tool in learning about quantum states prepared on a quantum computer. Recent works have used classical shadows to variationally enforce $N$-representability conditions on the two-particle reduced density matrix. In this paper, we build upon previous research by choosing an improved estimator within classical shadow tomography and rephrasing the optimization constraints, resulting in an overall enhancement in performance under comparable measurement shot budgets. We further explore the specific regimes where these methods outperform the unbiased estimator of the stand-alone classical shadow protocol and quantify the potential savings in numerical studies.

Symmetry constraints provide a powerful means to control the dynamics of open quantum systems. However, the set of accessible control parameters is often limited. Here, we show that a tunable phase in the collective light-matter coupling of a cavity QED system induces a phase-dependent strong symmetry of the Liouvillian, enabling dynamical control of the open quantum system evolution. We demonstrate that tuning this phase substantially reduces the critical driving strength for dissipative phase transitions between stationary and nonstationary phases. We illustrate this mechanism in two experimentally relevant cavity QED settings: a two-species ensemble of two-level atoms and a single-species ensemble of three-level atoms. Our results establish phase control as a versatile tool for engineering dissipative phase transitions, with implications for quantum state preparation.

We investigate how the space-time entanglement of photon pairs generated by multimode parametric down-conversion (PDC) propagates away from the source. We show that the entangled two-photon probability, tightly confined in space and time at the source, quickly broadens and decays out of a focal plane, behaving as a focused coherent beam of approximately twice the wavelength of the twin photons. This behavior is in strong contrast with the much slower decay rate of the classical mutual coherence of the PDC radiation, which follows the prescription of the generalized Van Cittert-Zernicke theorem. Besides their fundamental interest, our results could be relevant for the design of experiments, such as quantum-enhanced two-photon processes, that exploit the spatiotemporal entanglement of the pairs.

Establishing adaptive particles that sense their state, anticipate their evolution, and compute control inputs onboard has been a major challenge in nonequilibrium physics. We address this challenge by realizing an autonomous brainbot, building on a recently developed programmable bristlebot. First, we construct a physics-informed digital twin of the device, based on a kinematic model that reproduces measured trajectory statistics and generates long, statistically faithful synthetic trajectories. The kinematics forms the foundation for implementing onboard model predictive control, enabling autonomous trajectory tracking, demonstrated by accurate execution of a nontrivial target path. This provides a proof of principle for a brainbot that senses its state, predicts its evolution, and computes control inputs onboard, unlike conventional active particles with fixed motility, thereby transforming the brainbot into an agentic physical entity. By integrating physical modeling, data-driven parameter identification, and control into a unified framework, our approach provides a scalable platform for machine-learning-enabled multiagent studies and lays the groundwork for intelligent, adaptive active matter.