Anomalous diffusion or, more generally, anomalous transport, with nonlinear dependence of the mean-squared displacement on the measurement time, is ubiquitous in nature. It has been observed in processes ranging from microscopic movement of molecules to macroscopic, large-scale paths of migrating birds. Using data from multiple empirical systems, spanning 12 orders of magnitude in length and 8 orders of magnitude in time, we employ a method to detect the individual underlying origins of anomalous diffusion and transport in the data. This method decomposes anomalous transport into three primary effects: long-range correlations (“Joseph effect”), fat-tailed probability density of increments (“Noah effect”), and nonstationarity (“Moses effect”). We show that such a decomposition of real-life data allows us to infer nontrivial behavioral predictions and to resolve open questions in the fields of single-particle tracking in living cells and movement ecology.

Coordinated directional switches often emerge in moving biological groups replete with individual-level interactions. Recent self-propelled particles models can somewhat mimic the patterns of directional switches, but they usually do not include the effects of time delays in the interactions. Here, we focus on investigating the influence of time-delay interactions on the collective motion of swarming locusts, an experimentally well-studied system that exhibits ordered switches between clockwise and counterclockwise movement. We show, both analytically and numerically, that time delays of different types can affect the directional switches. Specifically, for the sufficiently small response delay, increasing the transmission delay can increase the mean switching time, while, for the large response delay, increasing the transmission delay may destroy the ordered directional switches. Our results decipher the role of time-delay interactions in the collective motion, which could be beneficial to the design of collective intelligent devices.

Besides magnetic and charge order, regular arrangements of orbital occupation constitute a fundamental order parameter of condensed matter physics. Even though orbital order is difficult to identify directly in experiments, its presence was firmly established in a number of strongly correlated, three-dimensional Mott insulators. Here, reporting resonant x-ray-scattering experiments on the layered van der Waals compound $1T\text{−}{\mathrm{TiSe}}_2$, we establish that the known charge density wave in this weakly correlated, quasi-two-dimensional material corresponds to an orbital ordered phase. Our experimental scattering results are consistent with first-principles calculations that bring to the fore a generic mechanism of close interplay between charge redistribution, lattice displacements, and orbital order. It demonstrates the essential role that orbital degrees of freedom play in ${\mathrm{TiSe}}_2$, and their importance throughout the family of correlated van der Waals materials.

Controlling the phase separation phenomenon can enhance the properties of glass materials, such as transparency and strength. However, the initial and intermediate stages of phase separation of amorphous glass are yet to be understood completely. In this study, we performed an in situ observation on glass through scanning transmission electron microscopy, which possesses a high spatial resolution and chemical sensitivity. We visualized the phase-separated structure in the initial and intermediate stages of phase separation and observed a local and rapid change in the phase-separated structures and the formation of regions with advanced and delayed degrees of phase separation. The results were compared with the phase-field simulation and it was concluded that the characteristic change of the phase-separated structures is attributable to the multimetastability of the amorphous phase.

We report on the two-dimensional (2D) dynamics of a levitated nanoparticle in an optical cavity. The motion of the nanosphere is strongly coupled to the cavity field by coherent scattering and heavily cooled in the plane orthogonal to the tweezer axis. Due to the characteristics of the 2D motion and the strong optomechanical coupling, the motional sideband asymmetry that reveals the quantum nature of the dynamics is not limited to mere scale factors between Stokes and anti-Stokes peaks, as customary in quantum optomechanics, but assumes a peculiar spectral dependence. We introduce and discuss an effective thermal occupancy that quantifies how close the system is to a minimum uncertainty state and allows us to consistently characterize the particle motion. By rotating the polarization angle of the tweezer beam we tune the system from a 1D cooling regime, where we achieve a best thermal occupancy of $0.51\pm 0.05$, to a regime in which the fully 2D dynamics of the particle exhibit strong nonclassical properties. We achieve a strong 2D confinement with thermal occupancy of $3.4\pm 0.4$ along the warmest direction and around one in the orthogonal one. These results represent a major improvement over previous experiments considering both the 1D and the 2D motion and pave the way toward the preparation of tripartite optomechanical entangled states and novel applications to directional force and displacement quantum sensing.

Efficient and cost-effective Si-compatible lasers are a longstanding wish of the optoelectronic industry. In principle, there are two options. For many applications, lasers based on III-V compounds provide compelling solutions, even if the integration is complex and therefore costly. However, where low costs and also high integration density are crucial, group-IV-based lasers—made of Ge and GeSn, for example—could be an alternative, provided their performance can be improved. Such progress will come with better materials but also with the development of a more profound understanding of their optical properties. In this work, we demonstrate, using Ge microbridges with strain up to 6.6%, a powerful method for determining the population inversion gain and the material and optical losses of group IV lasers. This is done by deriving the values for the injection carrier densities and the cavity losses from the measurement of the change of the refractive index and the mode linewidth, respectively. We observe a laser threshold consistent with optical gain. Material loss values are obtained from a tight-binding calculation. Lasing in Ge—at steady-state—is found to be limited to low temperatures in a narrow regime of tensile strain at the crossover to the direct-band-gap band structure. We explain this observation by parasitic inter-valence-band absorption that increases rapidly with higher injection densities and temperature. $N$-doping seems to reduce the material loss at low excitation, but it does not extend the lasing regime. We also discuss the impact of the optically inactive carriers in the L-valley on the linewidth of group IV lasers.

The accuracy of atomic isotope shift factors limits the extraction of nuclear charge radii from isotope shift measurements because determining these factors is experimentally and theoretically challenging. Here, the isotope shift of the ${\mathrm{Cd}}^{+}5s{}^2{S}_{1/2}\to 5p{}^2{P}_{3/2}$ transition is measured precisely using laser-induced fluorescence from a sympathetically cooled large ${\mathrm{Cd}}^{+}$ ion crystal. A King-plot analysis is performed based on the new measurement to obtain accurate atomic field shift $F$ and mass shift $K$ factors that have been cross-checked by state-of-the-art configuration interaction plus many-body perturbation theory. The nuclear charge radii ($R_{\mathrm{ch}}$) of ${}^{100\text{–}130}\mathrm{Cd}$ extracted using these $F$ and $K$ values demonstrate a near fivefold precision increase in the neutron-rich region. This work proves that accurate extraction of $R_{\mathrm{ch}}$ from isotope shifts is possible. New $R_{\mathrm{ch}}$ values reveal hidden discrepancies with previous density functional predictions in the neutron-rich region and pose strong challenges to advancements in nuclear models.

In spin qubit arrays the exchange coupling can be harnessed to implement two-qubit gates and to realize intermediate-range qubit connectivity along a spin bus. In this work, we propose a scheme to characterize the exchange coupling between electrons in adjacent quantum dots. We investigate theoretically the transmission of a microwave resonator coupled to a triple quantum dot occupied by two electrons. We assume that the right quantum dot (QD) is always occupied by one electron while the second electron can tunnel between the left and center QDs. If the two electrons are in adjacent dots they interact via the exchange coupling. By means of analytical calculations we show that the transmission profile of the resonator directly reveals the value of the exchange coupling strength between two electrons. From perturbation theory up to second order we conclude that the exchange can still be identified in the presence of magnetic gradients. A valley splitting comparable to the interdot tunnel coupling will lead to further modifications of the cavity transmission dips that also depend on the valley phases.

Bistable valency in individual atoms presents an approach toward single-atom memory, as well as a building block to create tunable and stochastic multiwell energy landscapes. Yet, this concept of orbital memory has thus far only been observed for cobalt atoms on the surface of black phosphorus, which are switched using tip-induced ionization. Here, we show that individual iron atoms on the surface of black phosphorus exhibit orbital memory using a combination of scanning tunneling microscopy and spectroscopy with ab initio calculations based on density functional theory. Unlike cobalt, the iron orbital memory can be switched in its nonionized ground state. Based on calculations, we confirm that each iron valency has a distinct magnetic moment that is characterized by a distinguishable charge distribution due to the different orbital population. By studying the stochastic switching of the valency with varying tunneling conditions, we propose that the switching mechanism is based on a two-electron tunneling process.

The occurrence of a smectic-B (Sm-B) phase is demonstrated in concentrated aqueous solutions of “gapped” DNA constructs consisting of fully paired duplexes bridged by a flexible, unpaired strand of nucleotides. The Sm-B phase, identified by small and wide angle x-ray scattering measurements and optical microscopy, develops from a smectic-A (Sm-A) phase with increasing DNA concentration at room temperature. It transitions (reversibly) to the Sm-A when the temperature is raised above $\sim 50{}^{\circ }\mathrm{C}$.

Quantum algorithms have been successfully applied in quantum chemistry to obtain the ground-state energy of small molecules. Although accurate near the equilibrium geometry, the results can become unreliable when the chemical bonds are broken at large distances. For any adiabatic approach, this is usually caused by serious issues, such as energy gap closing or level crossing along the adiabatic evolution path. In this work, we propose a quantum algorithm based on adiabatic evolution to obtain molecular eigenstates and eigenenergies in quantum chemistry, which exploits a smooth geometric deformation by continuously varying bond lengths and bond angles. We demonstrate its utility in several examples on a noiseless quantum simulator, including ${\mathrm{H}}_2\mathrm{O}, {\mathrm{CH}}_2$, and a chemical reaction of ${\mathrm{H}}_2+{\mathrm{D}}_2\to$ 2HD, by uniformly stretching chemical bonds. We find that this new algorithm solves the problems related to energy gap closing and level crossing along the adiabatic evolution path at large atomic distances. The new method performs more stably and achieves better accuracy than our previous adiabatic method [Yu and Wei, Phys. Rev. Research 3, 013104 (2021)]. Furthermore, our fidelity analysis demonstrates that even with finite bond length changes, our algorithm still achieves high fidelity for the ground state.

The on-site Coulomb potential, $U$, and the covalent state of electronic orbitals play key roles for the Cooper pair symmetry and exotic electromagnetic properties of high-$T_{\mathrm{c}}$ superconducting cuprates. In this paper, we demonstrate a way to determine the value of $U$ and present the whole picture of the covalent state of Cu spins in the mother system of the La-based high-$T_{\mathrm{c}}$ superconducting cuprate, ${\mathrm{La}}_2{\mathrm{CuO}}_4$, by combining the muon spin rotation $\left(\mu \mathrm{SR}\right)$ and the density functional theory (DFT) calculation. We reveal local deformations of the ${\mathrm{CuO}}_6$ octahedron followed by changes in Cu-spin distributions caused by the injected muon. Adjusting the DFT and $\mu \mathrm{SR}$ results, $U$ and the minimum charge-transfer energy between the upper Hubbard band and the O $2p$ band were optimized to be 4.87(4) and 1.24(1) eV, respectively.

Long-range interactions play a key role in several phenomena of quantum physics and chemistry. To study these phenomena, analog quantum simulators provide an appealing alternative to classical numerical methods. Gate-defined quantum dots have been established as a platform for quantum simulation, but for those experiments the effect of long-range interactions between the electrons did not play a crucial role. Here we present a detailed experimental characterization of long-range electron-electron interactions in an array of gate-defined semiconductor quantum dots. We demonstrate significant interaction strength among electrons that are separated by up to four sites, and show that our theoretical prediction of the screening effects matches well the experimental results. Based on these findings, we investigate how long-range interactions in quantum dot arrays may be utilized for analog simulations of artificial quantum matter. We numerically show that about ten quantum dots are sufficient to observe binding for a one-dimensional $\mathrm{H}{}_2$-like molecule. These combined experimental and theoretical results pave the way for future quantum simulations with quantum dot arrays and benchmarks of numerical methods in quantum chemistry.

We study unitary evolution of bipartite entanglement in a circuit with nearest-neighbor random gates. Deriving a compact nonunitary description of purity dynamics on qudits we find a sudden transition in the purity relaxation rate the origin of which is in the underlying boundary localized eigenmodes—the skin effect. We provide the full solution of the problem, being one of the simplest iterations of two-site matrices, namely, that each is a sum of only two projectors. This leads to rich dynamics influenced by the Jordan normal form of the kernel and, most importantly, a spectrum that is completely discontinuous in the thermodynamic limit. It provides a simple example of how a seemingly innocuous many-body unitary evolution can harbor interesting mathematical effects: an effective nonsymmetric Toeplitz transfer matrix description causes a phantom relaxation, such that the correct relaxation rate is not given by the matrix spectrum, but rather by its pseudospectrum.

Spin-orbit torque (SOT) characterizations on magnetic heterostructures with perpendicular anisotropy are demonstrated on a projected vector field magnet via hysteresis loop shift measurement and harmonic Hall measurement with planar Hall correction. Accurate magnetic field calibration of the vector magnet is realized with the help of deep learning models, which can capture the nonlinear behavior between the generated magnetic field and the currents applied to the magnet. The trained models can successfully predict the applied current combinations under the circumstances of magnetic field scans, angle scans, and hysteresis loop shift measurements. The validity of the models is further verified, complemented by the comparison of the SOT characterization results obtained from the deep-learning-trained vector magnet system with those obtained from a conventional setup comprised of two separated electromagnets. The dampinglike (DL) SOT efficiencies ($|{\xi }_{\mathrm{DL}}|$) extracted from the vector magnet and the traditional measurement configuration are consistent, where $|{\xi }_{\mathrm{DL}}|\approx$ 0.22 for amorphous W and $|{\xi }_{\mathrm{DL}}|\approx$ 0.02 for $\alpha$-W. In this paper, we provide an advanced method to meticulously control a vector magnet and to conveniently perform various SOT characterizations.

Observing ultrafast laser-induced structural changes in nanoscale systems is essential for understanding the dynamics of intense light-matter interactions. For laser intensities on the order of ${10}^{14}\mathrm{W}/{\mathrm{cm}}^2$, highly collisional plasmas are generated at and below the surface. Subsequent transport processes such as heat conduction, electron-ion thermalization, surface ablation, and resolidification occur at picosecond and nanosecond timescales. Imaging methods, e.g., using x-ray free-electron lasers (XFEL), were hitherto unable to measure the depth-resolved subsurface dynamics of laser-solid interactions with appropriate temporal and spatial resolution. Here we demonstrate picosecond grazing-incidence small-angle x-ray scattering (GISAXS) from laser-produced plasmas using XFEL pulses. Using multilayer (ML) samples, both the surface ablation and subsurface density dynamics are measured with nanometer depth resolution. Our experimental data challenges the state-of-the-art modeling of matter under extreme conditions and opens new perspectives for laser material processing and high-energy density science.

The orbital Hall effect provides an alternative means to the spin Hall effect to convert a charge current into a flow of angular momentum. Recently, compelling signatures of orbital Hall effects have been identified in $3d$ transition metals. Here, we report a systematic study of the generation, transmission, and conversion of orbital currents in heterostructures comprising $3d$, $5d$, and $4f$ metals. We show that the orbital Hall conductivity of Cr reaches giant values of the order of $5\times {10}^5$ $\left[\frac{\hslash }{2e}\right]$ ${\mathrm{\Omega }}^{-1}{\mathrm{m}}^{-1}$ and that Pt presents a strong orbital Hall effect in addition to the spin Hall effect. Measurements performed as a function of thickness of nonmagnetic Cr, Mn, and Pt layers and ferromagnetic Co and Ni layers reveal how the orbital and spin currents compete or assist each other in determining the spin-orbit torques acting on the magnetic layer. We further show how this interplay can be drastically modulated by introducing $4f$ spacers between the nonmagnetic and magnetic layers. Gd and Tb act as very efficient orbital-to-spin current converters, boosting the spin-orbit torques generated by Cr by a factor of 4 and reversing the sign of the torques generated by Pt. To interpret our results, we present a generalized drift-diffusion model that includes both spin and orbital Hall effects and describes their interconversion mediated by spin-orbit coupling.