Critical slowing down is considered one of the main signs that a dynamical system is close to a tipping point. For this reason, early-warning indicators have been developed to identify it, mainly based on the temporal evolution of the system under analysis. Yet, it has been shown that critical slowing down also displays spatial signatures, such as an increase in the spatial correlation. However, these signatures are based only on heuristic observations and the analysis of numerical simulations and do not have a sound theoretical foundation. In this work I will derive analytical expressions for typical spatial early-warning indicators of critical transitions in spatially extended systems, such as spatial correlation, spatial variance, and spatial permutation entropy, in the linearized limit. As a result, I will show that the common belief that the spatial correlation increases when a bifurcation is imminent is false. Other indicators, instead, might represent more robust alternatives, such as the spatial permutation entropy or the spatial variance.

The Kondo lattice is one of the classic examples of strongly correlated electronic systems. We conduct a controlled study of the Kondo lattice in one dimension, highlighting the role of excitations created by the composite fermion operator. Using time-dependent matrix product state methods, we compute various correlation functions and contrast them with both large-N mean-field theory and the strong-coupling expansion. We show that the composite fermion operator creates long-lived, charge-e and spin-1/2 excitations, which cover the low-lying single-particle excitation spectrum of the system. Furthermore, spin excitations can be thought to be composed of such fractionalized quasiparticles with a residual interaction which tend to disappear at weak Kondo coupling.

We demonstrate a bistable optical trap by tightly focusing a vortex laser beam. The optical potential has the form of a Mexican hat with an additional minimum at the center. The bistable trapping corresponds to a nonequilibrium steady state, where the microsphere continually hops, due to thermal activation, between an axial equilibrium state and an orbital state driven by the optical torque. We develop a theoretical model for the optical force field, based entirely on experimentally accessible parameters, combining a Debye-type nonparaxial description of the focused vortex beam with Mie scattering by the microsphere. The theoretical prediction that the microsphere and the annular laser focal spot should have comparable sizes is confirmed experimentally by taking different values for the topological charge of the vortex beam. Spherical aberration introduced by refraction at the interface between the glass slide and the sample is considered and allows us to finetune between axial, bistable, and orbital states as the sample is shifted with respect to the objective focal plane. We find overall agreement between theory and experiment for a rather broad range of topological charges. Our results open the way for applications in stochastic thermodynamics, as they establish a control parameter—the height of the objective focal plane with respect to the glass slide—that allows us to shape the optical force field in real time and in a controllable way.

We present the magnetic, thermodynamic, and muon spin relaxation ($\mu \mathrm{SR}$) results of the dimer-based triangular antiferromagnet ${\mathrm{Ba}}_6{\mathrm{Y}}_2{\mathrm{Rh}}_2{\mathrm{Ti}}_2{\mathrm{O}}_{17-\delta }$. The magnetic susceptibility data show the sub-Curie-Weiss behavior $\chi \left(T\right)\propto T^{-{\alpha }_{\chi }}$ below 100 K, suggesting random magnetism. The isothermal magnetization results reveal the presence of weakly interacting structural orphan spins about $6.1\%$ at 2 K, arising from the oxygen deficiency. The comprehensive $\mu \mathrm{SR}$ experiments exhibit the coexisting relaxing and nonrelaxing components along with the thermally activated behavior in the muon spin relaxation rate, reflecting the fluctuating orphan spins in the dimer singlet background. In addition, we observe the scaling behavior of $M(H,T)$ in $H/T$ and $P_z\left(t\right)$ in $t/H_{\text{LF}}$ with the scaling exponents ${\alpha }_{\chi }={\alpha }_{\text{M}}=0.75$ and ${\alpha }_{\mu }=0.72$, respectively, but not for the magnetic specific heat data. The failure of the scaling relation in $C_{\text{m}}(H,T)/T$ implies low-energy excitations dressed by the conventional orphan spins. Based on these observations, we find that the magnetic ground state resembles random singlets and discuss the possible configurations of the spin dimer unit ${\mathrm{Rh}}_2{\mathrm{O}}_9$. Our results shed light on the role of quenched disorder in the dimer-based frustrated magnets.

Recent experiments [Persky et al., Nature (London) 607, 692 (2022)] demonstrate a magnetic memory effect in $4Hb\text{−}{\mathrm{TaS}}_2$ above its superconducting transition temperature, where Abriokosov vortices are spontaneously generated by lowering the temperature at zero magnetic field after field training the normal state. Motivated by the experiment, we propose the chiral quantum spin liquid (QSL) stabilized in the constituent layers of $4Hb\text{−}{\mathrm{TaS}}_2$ as a mechanism. We model $4Hb\text{−}{\mathrm{TaS}}_2$ as coupled layers of the chiral QSL and the superconductor. Through the Kondo coupling between the localized moments and conduction electrons, there is mutual transmutation between spinons and vortices during the thermal-cycling process, which yields the magnetic memory effect observed in experiments. We also propose a mechanism to stabilize chiral and nematic superconductivity in $4Hb\text{−}{\mathrm{TaS}}_2$ through the Kondo coupling of conduction electrons to the chiral QSL. Our picture suggests $4Hb\text{−}{\mathrm{TaS}}_2$ as an exciting platform to explore the interplay between QSL and superconductivity through the Kondo effect.

We investigate a tripartite quantum Rabi model (TQRM) wherein a bosonic mode concurrently couples to two spin-$1/2$ particles through a spin-spin interaction, resulting in a spin-spin-boson coupling—a departure from conventional quantum Rabi models featuring bipartite spin-boson couplings. The symmetries of the TQRM depend on the detuning parameter, representing the energy difference between the spin states. At zero detuning a parity symmetry renders the TQRM reducible to a quantum Rabi model. A subradiant-to-superradiant transition in the ground state is predicted as the tripartite coupling strength increases. For nonzero detuning the total spin emerges as the sole conserved quantity in the TQRM. It is found that superradiance prevails in the ground state as long as the tripartite coupling remains nonzero. We derive the Braak $\mathcal{G}$ function of the TQRM analytically, with which the eigenspectra are obtained. The TQRM can be realized in a viable trapped Rydberg ion quantum simulator, where the required tripartite couplings and single-body interactions in the TQRM are naturally present. Our study opens opportunities to explore and create correlations and entanglement in the spin and motional degrees of freedoms with the TQRM.

The layered perovskite ${\mathrm{Sr}}_2{\mathrm{RuO}}_4$ serves as a model material of the two-dimensional (2D) Fermi liquid but also exhibits various emergent phenomena including the non-Fermi-liquid (NFL) behavior under external perturbations such as uniaxial pressure and chemical substitutions. Here we present the thermoelectric transport of electron-doped system ${\mathrm{Sr}}_{2-y}{\mathrm{La}}_y{\mathrm{RuO}}_4$, in which a filling-induced Lifshitz transition occurs at the Van Hove singularity (VHS) point of $y\approx 0.2$. We find that the sign of the low-temperature thermopower becomes negative only near the VHS point, where the NFL behavior has been observed in the earlier study. This observation is incompatible with either a numerical calculation within a constant relaxation-time approximation or a toy-model calculation for the 2D Lifshitz transition adopting an elastic carrier scattering. As a promising origin of the observed negatively enhanced thermopower, we propose a skewed NFL state, in which an inelastic scattering with a considerable odd-frequency term plays a crucial role to negatively enhance the thermopower.

The quest to identify and observe Majorana fermions in physics and condensed-matter systems remains an important challenge. Here, we introduce a qubit (spin-$1/2$) from the occurrence of two delocalized zero-energy Majorana fermions in a model of two spins-$1/2$ on the Bloch sphere within the fractional one-half topological state. We address specific protocols in time with circularly polarized light and the protection of this delocalized spin-$1/2$ state related to quantum information protocols. We also show how disorder can play a positive and important role allowing singlet-triplet transitions and resulting in an additional elongated region for the fractional phase, demonstrating the potential of this platform related to applications in topologically protected quantum information. We generalize our approach with an array and Majorana fermions at the edges in a ring geometry.

In this theoretical study, we explore the dispersion and basic properties of optical microcavities filled with liquid crystal (LC) media that contain embedded quantum wells. As a result of the strong coupling between cavity photons and excitons, exciton polariton quasiparticles arise in these structures. LC-filled microcavities have an advantage of the ability to manipulate the spin (polarization) of the photonic component of the polariton states by controlling the orientation of LC molecules using an external electric field. This enables the engineering of controllable synthetic Hamiltonians for the polariton eigenmodes in microcavity structures. The introduction of synthetic spin-orbit interaction via placing of the quantum wells at particular positions in the LC-filled cavity enables control over the propagation of exciton polaritons, leading to various spatial effects. Through numerical calculations, we successfully reproduce the birefringence and zitterbewegung phenomena exhibited by exciton polaritons propagating within the microcavity plane. We also examine the conditions required for strong coupling when utilizing perovskite layers as hosts for excitons. While the strong coupling regime can be also achieved in this material system, the manifestations of the synthetic spin-orbit interaction are suppressed owing to stronger disorder and nonradiative processes.

Ultrafast heating of solids with modern x-ray free electron lasers (XFELs) leads to a unique set of conditions characterized by the simultaneous presence of heated electrons in a cold ionic lattice. In this work, we analyze the effect of electronic heating on the dynamic structure factor (DSF) in bulk aluminum (Al) with a face-centered cubic lattice and in silicon (Si) with a crystal diamond structure using first-principles linear-response time-dependent density functional theory simulations. We find a thermally induced red shift of the collective plasmon excitation in both materials. In addition, we show that the heating of the electrons in Al can lead to the formation of a double-plasmon peak due to the extension of the Landau damping region to smaller wave numbers. Finally, we demonstrate that thermal effects generate a measurable and distinct signature (peak-valley structure) in the DSF of Si at small frequencies. Our simulations indicate a variety of new features in the spectrum of x-ray-driven solids, specifically at finite momentum transfer, which can be probed in upcoming x-ray Thomson scattering experiments at various XFEL facilities.

Ascertaining whether a classical model can efficiently replace a given quantum model—dequantization—is crucial in assessing the true potential of quantum algorithms. In this work, we introduced the dequantizability of the function class of variational quantum-machine-learning (VQML) models by employing the tensor network formalism, effectively identifying every VQML model as a subclass of matrix product state (MPS) model characterized by constrained coefficient MPS and tensor product-based feature maps. From this formalism, we identify the conditions for which a VQML model's function class is dequantizable or not. Furthermore, we introduce an efficient quantum kernel-induced classical kernel which is as expressive as given any quantum kernel, hinting at a possible way to dequantize quantum kernel methods. This presents a thorough analysis of VQML models and demonstrates the versatility of our tensor-network formalism to properly distinguish VQML models according to their genuine quantum characteristics, thereby unifying classical and quantum machine-learning models within a single framework.

Tests and calibrations described in E. E. Kading et al. [Phys. Rev. Res. 2, 023279 (2020)] and the extraction of quantitative results from the experiment reported therein are considered unreliable.

We implement two types of matter-wave interferometers using trapped Bose-condensed Feshbach molecules, from weak to strong interactions. In each case, we focus on investigating interaction effects and their implications for the performance. In the Ramsey-type interferometer where interference between the two motional quantum states in an optical lattice is observed, interparticle interactions are found to induce energy shifts in the states. Consequently, this results in a reduction of the interferometer frequency and introduces a phase shift during the lattice pulses used for state manipulation. Furthermore, nonuniformity leads to dephasing and collisional effects contribute to the degradation of contrast. In the Michelson-type interferometer, where matter waves are spatially split and recombined in a waveguide, interference is observed in the presence of significant interaction, however coherence degrades with increasing interaction strength. Notably, coherence is also observed in thermal clouds, indicating the white-light nature of the implemented Michelson-type interferometer.

Unique properties of multimode non-Hermitian lattice dynamics can be utilized to construct exponentially sensitive sensors. However, the impact of noise remains unclear, which may severely degrade their sensitivity. We analytically characterize and highlight the impact of loss and gain on the sensitivity revival and stability of non-Hermitian sensors. Defying the general belief that the superiority of quantum sensing will vanish in the presence of loss, we find that by proactively tuning the loss, the exponential sensitivity can be surprisingly regained when the sensing dynamics is stable. Furthermore, we prove that gain is crucial to fully revive the ideally exponential sensitivity and to ensure the stability of non-Hermitian sensing by making a balanced loss and gain. Our paper opens a way to significantly enhance the sensitivity by proactively tuning the loss and gain, which may promote future quantum sensing and quantum engineering.

Genetic information often exhibits hierarchical and nested relationships, achieved through the reuse of repetitive subsequences such as duplicons and transposable elements, a concept termed “evolutionary tinkering” by François Jacob. Current bioinformatics tools often struggle to capture these, particularly the nested, relationships. To address this, we utilized ladderpath, an approach within the broader category of algorithmic information theory, introducing two key measures: order rate $\eta$ for characterizing sequence pattern repetitions and regularities, and ladderpath-complexity $\kappa$ for assessing hierarchical and nested richness. Our analysis of amino acid sequences revealed that humans have more sequences with higher $\kappa$ values, and proteins with many intrinsically disordered regions exhibit increased $\eta$ values. Additionally, it was found that extremely long sequences with low $\eta$ are rare. We hypothesize that this arises from varied duplication and mutation frequencies across different evolutionary stages, which in turn suggests a zigzag pattern for the evolution of protein complexity. This is supported by simulations and studies of protein families such as ubiquitin and NBPF, implying species-specific or environment-influenced protein elongation strategies. The ladderpath approach offers a quantitative lens to understand evolutionary tinkering and reuse, shedding light on the generative aspects of biological structures.

We investigate the collective non-Markovian dynamics of two fully excited two-level atoms coupled to a one-dimensional waveguide in the presence of delay. We demonstrate that analogous to the well-known superfluorescence phenomena, where an inverted atomic ensemble synchronizes to enhance its emission, there is a “subfluorescence” effect that synchronizes the atoms into an entangled dark state depending on the interatomic separation. The phenomenon can lead to a two-photon bound state in the continuum. Our results are pertinent to long-distance quantum networks, presenting a mechanism for spontaneous entanglement generation between distant quantum emitters.

Graphene-based superlattices offer a unique materials playground to exploit and control a higher number of electronic degrees of freedom, such as charge, spin, or valley for disruptive technologies. Recently, orbital effects, emerging in multivalley band structures lacking inversion symmetry, have been discussed as possible mechanisms for developing orbitronics. Here, we report nonlocal transport measurements in small gap hBN/graphene/hBN moiré superlattices which reveal very strong magnetic field-induced chiral response which is stable up to sizable temperatures. The measured sign dependence of the nonlocal signal with respect to the magnetic field orientation clearly indicates the manifestation of emerging orbital magnetic moments. The interpretation of experimental data is well supported by numerical simulations, and the reported phenomenon stands as a formidable way of in situ manipulation of the transverse flow of orbital information that could enable the design of orbitronic devices.

Three-dimensional interconnected nanowire networks have recently attracted notable attention for the fabrication of new devices for energy harvesting/storage, sensing, catalysis, magnetic and spintronic applications, and for the design of new hardware neuromorphic computing architectures. However, the complex branching of these nanowire networks makes it challenging to investigate these 3D nanostructured systems theoretically. Here, we present a theoretical description and simulations of the geometric properties of these 3D interconnected nanowire networks with selected characteristics. Our analysis reveals that the nanowire segment length between two crossing zones follows an exponential distribution. This suggests that shorter nanowire segments have a more pronounced influence on the nanowire network properties compared to their longer counterparts. Moreover, our observations reveal a homogeneous distribution in the smallest distance between the cores of two crossing nanowires. The results are highly reproducible and unaffected by changes in the nanowire network characteristics. The density of crossing zones and interconnected nanowire segments is found to vary as the square of the nanowire density multiplied by their diameter, further multiplied by a factor dependent on the packing factor. Finally, densities of interconnected segments up to ${10}^{13}{\mathrm{cm}}^{-2}$ can be achieved for 22-$\mu \mathrm{m}$-thick nanowire networks with high packing factors. This has important implications for neuromorphic computing applications, suggesting that the realization of ${10}^{14}$ interconnections, which corresponds to the approximate number of synaptic connections in the human brain, is achievable with a nanowire network of about $10{\mathrm{cm}}^2$.