Atomic surface structure imaging is instrumental for the understanding of surface-related phenomena. Here, we show that conventional tapping mode atomic force microscopy with high cantilever eigenmodes and subnanometer amplitudes allow routine atomic imaging at atmospheric pressures. We identify the reasons for failure of atomic resolution imaging employing low eigenmodes. Strong tip-surface interactions cause significant differences between the oscillatory behaviors of the inclination of the cantilever as detected by conventional instruments and of the vertical position of the tip, which prevents correct functioning of instrumental feedback control loops. However, high effective spring constants of high eigenmodes make it possible to overcome the problem. Furthermore, the combination of high effective elastic constants of high cantilever eigenmodes with the high flexibility of the cantilever substantially enhances the imaging stability, thereby universally allowing atomic imaging of solid surfaces in gaseous environments and at elevated temperatures. Demonstrated imaging examples include single sulfur vacancies at the surface of ${\mathrm{MoS}}_2$ crystals imaged at temperatures ranging from room temperature to 250°C and potassium ions on hydrophilic and highly adhesive muscovite mica surfaces. Moreover, the high imaging stability allows knocking atoms off the ${\mathrm{MoS}}_2$ surface by hard tapping, indicating the potential for ultrahigh resolution lithography.

Photoabsorption spectra of neutral potassium clusters in helium nanodroplets are recorded by depletion spectroscopy using a supercontinuum laser source equipped with a variable bandpass filter. The results provide insight into the evolution of electronic spectra from molecular transitions to localized surface plasmon resonances in nanometer-sized clusters. Size selected spectra for potassium clusters ${\mathrm{K}}_n$ are acquired from $n=2–110$. Indications for the transition from molecularlike absorption to a collective resonance are already observed below $n=20$. For larger clusters, a splitting of the plasmon mode into two components is observed at around $n=600$. Supported by simulations, this is explained by the presence of nonspherical potassium nanoparticles grown via multicenter aggregation inside the helium droplets. The presented supercontinuum laser-based experimental approach provides a new route for the mass-selective spectroscopic characterization of different materials and material combinations isolated in helium nanodroplets in a size regime ranging from single atoms and molecules to small sub-10-nm particles.

We investigate long-range correlations (LRCs) induced by shear flow using the molecular dynamics (MD) simulation. We observe the LRCs by comparing the MD result with the linearized fluctuating hydrodynamics (LFH). We find that the MD result has large finite-size effects, and it prevents the occurrence of LRCs in small systems. We examine the finite-size effects using sufficiently large systems consisting of more than ten million particles, and verify the existence of shear-induced LRCs without ambiguity. Furthermore, we show that MD result is quantitatively consistent with the LFH solution for the large system. As we reduce the system size $L$ or increase the shear rate $\dot{\gamma }$, the hydrodynamic description gradually breaks down in the long-wavelength region. We define a characteristic wave number $k^{\mathrm{vio}}$ associated with the breakdown and find the nontrivial scaling relations $k^{\mathrm{vio}}\propto L^{-\omega }$ and $k^{\mathrm{vio}}\propto \dot{\gamma }$, where $\omega$ is an exponent depending on $\dot{\gamma }$. These relations enable us to estimate the finite-size effects in a larger-size simulation from a smaller system.

We propose a method, based on matrix product states, for studying the time evolution of many-body quantum lattice systems under continuous and site-resolved measurement. Both the frequency and the strength of generalized measurements can be varied within our scheme, thus allowing us to explore the corresponding two-dimensional phase diagram. The method is applied to one-dimensional chains of nearest-neighbor interacting hard-core bosons. A transition from an entangling to a disentangling (area-law) phase is found. However, by resolving time-dependent density correlations in the monitored system, we find important differences between different regions at the phase boundary. In particular, we observe a peculiar phenomenon of measurement-induced particle clusterization that takes place only for frequent moderately strong measurements, but not for strong infrequent measurements.

Epidemic models are crucial to understand how an infectious disease spreads in a population and to devise the best containment strategies. Compartmental models can provide a fine-grained description of the evolution of an epidemic when microscopic information on the network of contacts among individuals is available. However, coarser-grained descriptions prove also to be useful in many aspects. They allow to derive closed expressions for key parameters, such as the basic reproduction number, to understand the relationship between the model parameters, and also to derive fast and reliable predictions of macroscopic observables for a disease outbreak. The so-called population models can be developed at different levels of coarse-graining, so it is crucial to determine: (i) to which extent and how the existing correlations in the contact network have to be included in these models and (ii) what is their impact on the model ability to reproduce and predict the time evolution of the populations at the various stage of the disease. In this work, we address these questions through a systematic analysis of two discrete-time SEAIR (susceptible-exposed-asymptomatic-infected-recovered) population models: the first one developed assuming statistical independence at the level of individuals, and the other one assuming independence at the level of pairs. We provide a detailed derivation and analysis of both models, focusing on their capability to reproduce an epidemic process on different synthetic networks, and then comparing their predictions under scenarios of increasing complexity. We find that, although both models can fit the time evolution of the compartment populations obtained through microscopic simulations, the epidemic parameters adopted by the individual-based model for this purpose may significantly differ from those of the microscopic simulations. However, pair-based model provides not only more reliable predictions of the dynamical evolution of the variables but also a good estimation of the epidemic parameters. The difference between the two models is even more evident in the particularly challenging scenario when one or more variables are not measurable, and therefore are not available for model tuning. This occurs for instance with asymptomatic infectious individuals in the case of COVID-19, an issue that has become extremely relevant during the recent pandemic. Under these conditions, the pairwise model again proves to perform much better than the individual-based representation, provided that it is fed with adequate information which, for instance, to be collected, may require a more detailed contact tracing. Overall, our results thus hallmark the importance of acquiring the proper empirical data to fully unfold the potentialities of models incorporating more sophisticated assumptions on the correlations among nodes in the contact network.

We demonstrate that multipartite entanglement, witnessed by the quantum Fisher information, can characterize topological quantum phase transitions in the spin-$\frac{1}{2}$ toric code model (TCM) on a square lattice with external fields. We show that the quantum Fisher information density of the ground state can be written in terms of the expectation values of gauge-invariant Wilson loops for different sizes of square regions and identify ${\mathbb{Z}}_2$ topological order by its scaling behavior. Furthermore, we use this multipartite entanglement witness to investigate thermalization and disorder-assisted stabilization of topological order after a quantum quench. Moreover, with an upper bound of the quantum Fisher information, we demonstrate the absence of finite-temperature topological order in the two-dimensional TCM in the thermodynamic limit. Our results provide insights to topological phases, which are robust against external disturbances and are candidates for topologically protected quantum computation.

Cooper pair splitting (CPS) is a way to create spatially separated, entangled electron pairs. To this day, CPS is often identified in experiments as a spatial current correlation. However, such correlations can arise even in the absence of CPS, when a quantum dot is strongly coupled to the superconductor, and a subgap Shiba state is formed. Here, we present a detailed experimental characterization of those spatial current correlations, as the tunnel barrier strength between the quantum dot and the neighboring normal electrode is tuned. The correlation of the nonlocal signal and the barrier strength reveals a competition between CPS and the nonlocal probing of the Shiba state. We describe our experiment with a simple transport model and obtain the tunnel couplings of our device by fitting the model's prediction to the measured conductance correlation curve. Furthermore, we use our theory to extract the contribution of CPS to the nonlocal signal.

We present a study on the lifting of degeneracy of the size-quantized energy levels in an electrostatically defined quantum point contact in bilayer graphene by the application of in-plane magnetic fields. We observe a Zeeman spin splitting of the first three subbands, characterized by effective Landé $g$ factors that are enhanced by confinement and interactions. In the gate-voltage dependence of the conductance, a shoulderlike feature below the lowest subband appears, which we identify as a 0.7 anomaly stemming from the interaction-induced lifting of the band degeneracy. We employ a phenomenological model of the 0.7 anomaly to the gate-defined channel in bilayer graphene subject to in-plane magnetic field. Based on the qualitative theoretical predictions for the conductance evolution with increasing magnetic field, we conclude that the assumption of an effective spontaneous spin splitting is capable of describing our observations, while the valley degree of freedom remains degenerate.

By solving the exact master equation of open quantum systems, we formulate the quantum thermodynamics from weak to strong couplings. The open quantum systems exchange matters, energies, and information with their reservoirs through quantum particle tunnelings that are described by the generalized Fano-Anderson Hamiltonians. We find that the exact solution of the reduced density matrix of these systems approaches a Gibbs-type state in the steady-state limit for the systems in arbitrary initial states as well as for both the weak and strong system-reservoir coupling strengths. When the couplings become strong, thermodynamic quantities of the system must be renormalized. The renormalization effects are obtained nonperturbatively after exactly tracing over all reservoir states through the coherent state path integrals. The renormalized system Hamiltonian is characterized by the renormalized system energy levels and interactions, corresponding to the quantum work done by the system. The renormalized temperature is introduced to characterize the entropy production counting the heat transfer between the system and the reservoir. We further find that only with the renormalized system Hamiltonian and other renormalized thermodynamic quantities can the exact steady state of the system be expressed as the standard Gibbs state. Consequently, the corresponding exact steady-state particle occupations in the renormalized system energy levels obey the Bose-Einstein and the Fermi-Dirac distributions for bosonic and fermionic systems, respectively. In the very weak system-reservoir coupling limit, the renormalized system Hamiltonian and the renormalized temperature are reduced to the original bare Hamiltonian of the system and the initial temperature of the reservoir. Thus, the conventional statistical mechanics and thermodynamics are thereby rigorously deduced from quantum dynamical evolution. In the last, this nonperturbative renormalization method is also extended to general interacting open quantum systems.

The relativistic dynamical inversion technique, a novel tool for finding analytical solutions to the Dirac equation, is written in explicitly covariant form. It is then shown how the technique can be used to make a change from Cartesian to spherical coordinates of a given Dirac spinor. Moreover, the most remarkable feature of the method presented here, which is the ease of performing a nontrivial change of reference frames, is demonstrated. Such a feature constitutes a potentially powerful tool for finding novel solutions to the Dirac equation. Furthermore, a whole family of normalizable analytic solutions to the Dirac equation is constructed. More specifically, we find exact solutions for the case of a Dirac electron in the presence of a magnetic field as well as a solution comprising a combination of a spherically symmetric electric field and magnetic fields. These solutions shed light on the possibility of separating the positive- and negative-energy parts of localized Dirac spinors in the presence as well as in the absence of magnetic fields. The presented solutions provide an illustration of the connection between the geometrical properties of the spinor and spin-orbit coupling for normalizable spinorial wave functions.

Inspired by the success of field-effect transistors in electronics, electric field controlled magnetization dynamics has emerged as an important integrant in low-power spintronic devices. Here, we demonstrate electric field induced parametric excitation for CoFeB/MgO junctions by using interfacial in-plane magnetic anisotropy (IMA). When the IMA and the external magnetic field are parallel to each other, magnons are efficiently excited by electric field induced parametric resonance. The corresponding wavelengths are estimated to be tuned down to exchange interaction length scales by changing the input power and frequency of the applied voltage. A generalized phenomenological model is developed to explain the underlying role of the electric field torque. Electric field control of IMA is shown to be the origin for excitation of both uniform and parametric resonance modes in the in-plane magnetized sample, a crucial element for purely electric field induced magnetization dynamics. Electric field excitation of exchange magnons, with no Joule heating, offers a good opportunity for developing nanoscale magnonic devices and exploring various nonlinear dynamics in nanomagnetic systems.

We introduce a family of neural quantum states for the simulation of strongly interacting systems in the presence of spatial periodicity. Our variational state is parametrized in terms of a permutationally invariant part described by the Deep Sets neural-network architecture. The input coordinates to the Deep Sets are periodically transformed such that they are suitable to directly describe periodic bosonic systems. We show example applications to both one- and two-dimensional interacting quantum gases with Gaussian interactions, as well as to ${}^4\mathrm{He}$ confined in a one-dimensional geometry. For the one-dimensional systems we find very precise estimations of the ground-state energies and the radial distribution functions of the particles. In two dimensions we obtain good estimations of the ground-state energies, comparable to results obtained from more conventional methods.

Nonuniform elastic strain is known to induce pseudo-Landau levels in Dirac materials. But these pseudo-Landau levels are hardly resolvable in an analytic fashion when the strain is strong because of the emerging complicated space dependence in both the strain-modulated Fermi velocity and the strain-induced pseudomagnetic field. We here analytically characterize the solution to the pseudo-Landau levels in strongly bent graphene nanoribbons by treating the effects of the nonuniform Fermi velocity and pseudomagnetic field on equal footing. The analytic solution is detectable through angle-resolved photoemission spectroscopy and allows quantitative comparison between theories and various experimental signatures of transport, such as the Shubnikov-de Haas oscillation in the complete absence of magnetic fields and the negative strain-resistivity resulting from the valley anomaly. The analytic solution can be generalized to various Dirac materials and will shed light on the related experimental explorations and straintronics applications.

Efficient methods for loading given classical data into quantum circuits are essential for various quantum algorithms. In this paper, we propose an algorithm called Approximate Amplitude Encoding that can effectively load all the components of a given real-valued data vector into the amplitude of quantum state, while the previous proposal can load only the absolute values of those components. The key of our algorithm is to variationally train a shallow parameterized quantum circuit, using the results of two types of measurement: the standard computational-basis measurement plus the measurement in the Hadamard-transformed basis, introduced in order to handle the sign of the data components. The variational algorithm changes the circuit parameters so as to minimize the sum of two costs corresponding to those two measurement basis, both of which are given by the efficiently computable maximum mean discrepancy. We also consider the problem of constructing the singular value decomposition entropy via the stock market data set to give a financial market indicator; a quantum algorithm (the variational singular value decomposition algorithm) is known to produce a solution faster than classical, which yet requires the sign-dependent amplitude encoding. We demonstrate, with an in-depth numerical analysis, that our algorithm realizes loading of time series of real stock prices on quantum state with small approximation error, and thereby it enables constructing an indicator of the financial market based on the stock prices.

The AC Stark shift of electronic levels is ubiquitous in the interaction of intense light fields with atoms and molecules. As the light intensity changes on the rising and falling edges of a femtosecond laser pulse, it shifts the Rydberg states in and out of multiphoton resonances with the ground state. The two resonant pathways for transient excitation arising at the leading and the trailing edges of the pulse generate Young's type interference, generally referred to as the Stückelberg oscillations. Here we report the observation of the Stückelberg oscillations in the intensity of the coherent free-induction decay following resonant multiphoton excitation. Moreover, combining the experimental results with accurate numerical simulations and a simple model, we use the Stückelberg oscillations to recover the population dynamics of strongly driven Rydberg states inside the laser pulse by all-optical measurements after the end of the pulse. We demonstrate the potential of this spectroscopy to characterize lifetimes of Rydberg states dressed by laser fields with strengths far exceeding the Coulomb field between the Rydberg electron and the core.