Networks with fat-tailed degree distributions are omnipresent across many scientific disciplines. Such systems are characterized by so-called hubs, specific nodes with high numbers of connections to other nodes. By this property, they are expected to be key to the collective network behavior, e.g., in Ising models on such complex topologies. This applies in particular to the transition into a globally ordered network state, which thereby proceeds in a hierarchical fashion, and with a nontrivial local structure. Standard mean-field theory of Ising models on scale-free networks underrates the presence of the hubs, while nevertheless providing remarkably reliable estimates for the onset of global order. Here we expose that a spurious self-feedback effect, inherent to mean-field theory, underlies this apparent paradox. More specifically, we demonstrate that higher order interaction effects precisely cancel the self-feedback on the hubs, and we expose the importance of hubs for the distinct onset of local versus global order in the network. Due to the generic nature of our arguments, we expect the mechanism that we uncover for the archetypal case of Ising networks of the Barabási-Albert type to be also relevant for other systems with a strongly hierarchical underlying network structure.

An ultrasoft colloidal particle fluctuates due to its flexibility. Such fluctuation is essential for colloidal structure and dynamics, but is challenging to quantify experimentally. We use dendrimers as a model system to study the fluctuation of ultrasoft colloids. By considering the dynamic polydispersity in the small-angle neutron scattering (SANS) model and introducing the fluctuation of invasive water into the contrast in SANS, we reveal the fluctuating amplitudes of the size and shape of the dendrimer of generation 6 at finite concentrations. The size fluctuation is suppressed while the shape fluctuation increases as the weight fraction of dendrimers passes 11%. With neutron spin echo data, we suggest that such a crossover originates from the competition between the inter- and intraparticle dynamics. Further investigation on lower-generation samples shows a contrary result, which suggests a structural basis for these dynamic phenomena.

Data-driven discovery of partial differential equations (PDEs) has achieved considerable development in recent years. Several aspects of problems have been resolved by sparse regression-based and neural-network-based methods. However, the performance of existing methods lacks stability when dealing with complex situations, including sparse data with high noise, high-order derivatives, and shock waves, which bring obstacles to calculating derivatives accurately. Therefore, a robust PDE discovery framework, called the robust deep-learning genetic algorithm (R-DLGA), that incorporates the physics-informed neural network (PINN) is proposed in this paper. In the framework, preliminary results of potential terms provided by the DLGA are added into the loss function of the PINN as physical constraints to improve the accuracy of derivative calculation. It assists in optimizing the preliminary result and obtaining the ultimately discovered PDE by eliminating the error compensation terms. The stability and accuracy of the proposed R-DLGA in several complex situations are examined for proof and concept, and the results prove that the proposed framework can calculate derivatives accurately with the optimization of the PINN and possesses surprising robustness for complex situations, including sparse data with high noise, high-order derivatives, and shock waves.

We study the near-threshold molecular and collisional physics of a strong ${}^{40}\mathrm{K}$ $p$-wave Feshbach resonance through a combination of measurements, numerical calculations, and modeling. Dimer spectroscopy employs both radio-frequency spin-flip association in the MHz band and resonant association in the kHz band. Systematic uncertainty in the measured binding energy is reduced by a model that includes both the Franck-Condon overlap amplitude and inhomogeneous broadening. Coupled-channels calculations based on mass-scaled ${}^{39}\mathrm{K}$ potentials compare well to the observed binding energies and also reveal a low-energy $p$-wave shape resonance in the open channel. Contrary to conventional expectation, we observe a nonlinear variation of the binding energy with magnetic field, and explain how this arises from the interplay of the closed-channel ramping state with the near-threshold shape resonance in the open channel. We develop an analytic two-channel model that includes both resonances as well as the dipole-dipole interactions which, we show, become important at low energy. Using this parametrization of the energy dependence of the scattering phase, we can classify the studied ${}^{40}\mathrm{K}$ resonance as broad. Throughout the paper, we compare to the well-understood $s$-wave case and discuss the significant role played by van der Waals physics. The resulting understanding of the dimer physics of $p$-wave resonances provides a solid foundation for future exploration of few- and many-body orbital physics.

Micromechanical oscillators provide periodic output signals for clocks and sensors by vibrating in a single mechanical mode. The mode is conventionally excited into self-sustained oscillations and stabilized with an external electronic feedback loop. A paradigm is emerging for sustaining vibrations by coupling the mechanical mode with internal degrees of freedom, such as photons, electrons, or auxiliary mechanical modes. An open question in these hybrid vibrational systems is the corresponding internal sources of nonlinearity that can stabilize the oscillations, and their impact on oscillator performance. Here, we delineate two kinds of amplitude-stabilization mechanisms in micromechanical oscillators, geometric nonlinear damping and repulsive contact, and show that these mechanisms can coexist in the same device and their interplay and resonance frequency stability can be tuned in situ by adjusting the feedback strength. An auxiliary source of viscous dissipation and nonlinear dissipation accompanies the repulsive contact, which stabilizes the amplitude during sidewall collisions. The onset of self-sustained oscillations yields distinct spectral-temporal signatures that can be used to identify the amplitude stabilization nonlinearities.

Optical lattice experiments with ultracold atoms allow for the experimental realization of contemporary problems in many-body physics. Yet, devising models that faithfully describe experimental observables is often difficult and problem dependent; there is currently no theoretical method which accounts for all experimental observations. Leveraging the large data volume and presence of strong correlations, machine learning provides a novel avenue for the study of such systems. It has recently been proven successful in analyzing properties of experimental data of ultracold quantum gases. Here we show that generative deep learning succeeds in the challenging task of modeling such an experimental data distribution. Our method is able to produce synthetic experimental snapshots of a doped two-dimensional Fermi-Hubbard model that are indistinguishable from previously reported experimental realizations. We demonstrate how our generative model interprets physical conditions such as temperature at the level of individual configurations. We use our approach to predict snapshots at conditions and scales which are currently experimentally inaccessible, mapping the large-scale behavior of optical lattices at unseen conditions.

The controls enacting logical operations on quantum systems are described by time-dependent Hamiltonians that often include rapid oscillations. In order to accurately capture the resulting time dynamics in numerical simulations, a very small integration time step is required, which can severely impact the simulation run time. Here, we introduce a semianalytic method based on the Dyson expansion that allows us to time-evolve driven quantum systems much faster than standard numerical integrators. This solver, which we name Dysolve, efficiently captures the effect of the highly oscillatory terms in the system Hamiltonian, significantly reducing the simulation's run time as well as its sensitivity to the time-step size. Furthermore, this solver provides the exact derivative of the time-evolution operator with respect to the drive amplitudes. This key feature allows for optimal control in the limit of strong drives and goes beyond common pulse-optimization approaches that rely on rotating-wave approximations. As an illustration of our method, we show results of the optimization of a two-qubit gate using transmon qubits in the circuit QED architecture.

Models whose ground states can be written as an exact matrix-product state (MPS) provide valuable insights into phases of matter. While MPS-solvable models are typically studied as isolated points in a phase diagram, they can belong to a connected network of MPS-solvable models, which we call the MPS skeleton. As a case study where we can completely unearth this skeleton, we focus on the one-dimensional BDI class—noninteracting spinless fermions with time-reversal symmetry. This class, labeled by a topological winding number, contains the Kitaev chain and is Jordan-Wigner-dual to various symmetry-breaking and symmetry-protected topological (SPT) spin chains. We show that one can read off from the Hamiltonian whether its ground state is an MPS: defining a polynomial whose coefficients are the Hamiltonian parameters, MPS-solvability corresponds to this polynomial being a perfect square. We provide an explicit construction of the ground state MPS, its bond dimension growing exponentially with the range of the Hamiltonian. This complete characterization of the MPS skeleton in parameter space has three significant consequences: (i) any two topologically distinct phases in this class admit a path of MPS-solvable models between them, including the phase transition which obeys an area law for its entanglement entropy; (ii) we illustrate that the subset of MPS-solvable models is dense in this class by constructing a sequence of MPS-solvable models which converge to the Kitaev chain (equivalently, the quantum Ising chain in a transverse field); (iii) a subset of these MPS states can be particularly efficiently processed on a noisy intermediate-scale quantum computer.

Magnetic proximity has been observed in a variety of solid-state magnetic devices, but has been less discussed at the molecular scale. In this study, the magnetotransport calculation is carried out using the generalized Landau-Lifshitz-Gilbert (LLG) equation combined with density functional theory (DFT) and our self-developed junpy calculated spin-torque effect. Except for the current driven spin torque, which is a promising approach for magnetization switch in magnetic random access memory, the equilibrium fieldlike spin torque also plays a crucial role in the strain-controlled exchange bias with current-controlled magnetic coercivity in single-molecule magnetic junctions. The tight-binding model is further employed to clarify the critical role of the interfacial spin filter effect arising from the hybridization between the linker and Co apex. These multidisciplinary DFT+junpy+LLG results may provide important and practical implications in the dual control of magnetic proximity and magnetization switching in molecular spintronics at low temperature, either by tensile strain or via smaller applied current density of the order of $\mathrm{MA}/{\mathrm{cm}}^2$.

We determine the correlation energy of BN, ${\mathrm{SiO}}_2$, and ice polymorphs employing a recently developed random phase approximation with exchange (RPAx) approach. The RPAx provides larger and more accurate polarizabilities as compared to the random phase approximation (RPA), and captures the effects of anisotropy. In turn, the correlation energy, defined as an integral over the density-density response function, gives improved binding energies without the need for error cancellation. Here, we demonstrate that these features are crucial for predicting the relative energies between low- and high-pressure polymorphs of different coordination number as, e.g., between $\alpha$-quartz and stishovite in ${\mathrm{SiO}}_2$, and layered and cubic BN. Furthermore, a reliable ${\left({\mathrm{H}}_2\mathrm{O}\right)}_2$ potential energy surface is obtained, necessary for describing the various phases of ice. The RPAx gives results comparable to other high-level methods such as coupled cluster and quantum Monte Carlo, also in cases where the RPA breaks down. Although a higher computational cost than RPA, we observe a faster convergence with respect to the number of eigenvalues in the response function.

Electron transport in a nanowire exhibits a distinct behavior following the irradiation of intense laser pulse. Using particle-in-cell simulation, we observe a large-amplitude particle-driven wakefield excitation followed by electron acceleration in the solid density. Besides, we observed the quiver of the electrons across the nanowire under the action of the surrounding laser electric field facilitating deeper wakefield propagation in the nanowire with $2.5\times$ energy gain over a flat target. These results open insights into the laser-energy coupling with nanostructure targets and radiation sources, and motivate the wakefield acceleration in solid density plasma.

Delta-kick cooling (DKC) is used to compress the momentum distribution of ultracold quantum matter. It combines expansion dynamics with the use of kick pulses, designed via classical methods, that bring the system to rest. We introduce an exact approach to DKC for arbitrary scale-invariant dynamics of quantum gases, lifting the original restrictions to free evolution and noninteracting systems, to account for the control of atomic clouds in a time-dependent harmonic trap that can be either repulsive (inverted) or confining. We show that DKC assisted by a repulsive potential outperforms the conventional scheme, and that sudden trap-frequency quenches combined with DKC are equivalent to time-optimal bang-bang protocols. We further show that reverse engineering of the scale-invariant dynamics under smooth trap-frequency modulations can be combined with DKC to introduce a new class of shortcuts to adiabaticity assisted by kicks.

It has long been speculated that quasi-two-dimensional superconductivity can reappear above its semiclassical upper critical field due to Landau quantization; yet this reentrant property has never been observed. Here, we argue that twisted bilayer graphene at a magic angle (MATBG) is an ideal system in which to search for this phenomenon because its Landau levels are doubly degenerate and its superconductivity appears already at carrier densities small enough to allow the quantum limit to be reached at relatively modest magnetic fields. We study this problem theoretically by combining a simplified continuum model for the electronic structure of MATBG with a phenomenological attractive pairing interaction and discuss obstacles to the observation of quantum Hall superconductivity presented by disorder, thermal fluctuations, and competing phases.

For a generic quantum many-body system, the quantum ergodic regime is defined as the limit in which the spectrum of the system resembles that of a random matrix theory (RMT) in the corresponding symmetry class. In this paper, we analyze the time dependence of correlation functions of operators. We study them in the ergodic limit as well as their approach to the ergodic limit, which is controlled by nonuniversal massive modes. An effective field theory (EFT) corresponding to the causal symmetry and its breaking describes the ergodic phase. We demonstrate that the resulting Goldstone-mode theory has a topological expansion, analogous to the one described by Altland and Sonner [SciPost Phys. 11, 034 (2021)] with added operator sources, whose leading nontrivial topologies give rise to the universal ramp seen in correlation functions. The ergodic behavior of operators in our EFT is seen to result from a combination of RMT-like spectral statistics and Haar averaging over wave functions. Furthermore, we capture analytically the plateau behavior by taking into account the contribution of a second saddle point. Our main interest is quantum many-body systems with holographic duals, and we explicitly establish the validity of the EFT description in the Sachdev-Ye-Kitaev class of models, starting from their microscopic description. By studying the tower of massive modes above the Goldstone sector, we get a detailed understanding of how the ergodic EFT phase is approached, and we derive the relevant Thouless timescales. We point out that the topological expansion can be reinterpreted in terms of contributions of bulk wormholes and baby universes.

Lasing in the bad cavity regime has promising applications in precision metrology due to the reduced sensitivity to cavity noise originating from cavity length fluctuations. Here we investigate the spectral properties and phase behavior of pulsed lasing on the ${}^{1}S_0\text{−}{}^{3}P_1$ line of ${}^{88}\mathrm{Sr}$ in a mK thermal ensemble, as first described by S. A. Schäffer et al. [Phys. Rev. A 101, 013819 (2020)]. The system operates in a regime where the Doppler-broadened atomic transition linewidth is several times larger than the cavity linewidth. We find that for some detunings of the cavity resonance, the influence of the cavity noise on the peak lasing frequency can be eliminated to first order despite the system not being deep in the bad cavity regime. Experimental results are compared to a model based on a Tavis-Cummings Hamiltonian, which enables us to investigate the interplay between different thermal velocity classes as the underlying mechanism for the reduction in cavity noise. These velocity-dependent dynamics can occur in pulsed lasing and during the turn-on behavior of lasers in the superradiant crossover regime.

We investigate the localization properties of a spin chain with an antiferromagnetic nearest-neighbor coupling, subject to an external quasiperiodic on-site magnetic field. The quasiperiodic modulation interpolates between two paradigmatic models, namely the Aubry-André and the Fibonacci models. We find that stronger many-body interactions extend the ergodic phase in the former, whereas they shrink it in the latter. Furthermore, the many-body localization transition points at the two limits of the interpolation appear to be continuously connected along the deformation of the quasiperiodic modulation. As a result, the position of the many-body localization transition depends on the interaction strength for an intermediate degree of deformation. Moreover, in the region of parameter space where the single-particle spectrum contains both localized and extended states, many-body interactions induce an anomalous effect: weak interactions localize the system, whereas stronger interactions enhance ergodicity. We map the model's localization phase diagram using the decay of the quenched spin imbalance in relatively long chains. This is accomplished employing a time-dependent variational approach applied to a matrix product state decomposition of the many-body state. Our model serves as a rich playground for testing many-body localization under tunable potentials.

We report on the observation and coherent excitation of atoms on the narrow inner-shell orbital transition, connecting the erbium ground state $\left[\mathrm{Xe}\right]4f^{12}{(}^3{\text{H}}_6)6s^2$ to the excited state $\left[\mathrm{Xe}\right]4f^{11}({{(}^4{\text{I}}_{15/2})}^0)5d{(}^5{\text{D}}_{3/2})6s^2{(15/2,3/2)}_7^0$. This transition corresponds to a wavelength of 1299 nm and is optically closed. We perform high-resolution spectroscopy to extract the $g_J$ factor of the 1299-nm state and to determine the frequency shift for four bosonic isotopes. We further demonstrate coherent control of the atomic state and extract a lifetime of 178(19) ms, which corresponds to a linewidth of 0.9(1) Hz. The experimental findings are in good agreement with our semi-empirical model. In addition, we present theoretical calculations of the atomic polarizability, revealing several different magic-wavelength conditions. Finally, we make use of the vectorial polarizability and confirm a possible magic wavelength at 532 nm.

The possible symmetries of the superconducting pair amplitude is a consequence of the fermionic nature of the Cooper pairs. For spin-$1/2$ systems this leads to the $\mathcal{SPOT}=-1$ classification of superconductivity, where $\mathcal{S}, \mathcal{P}, \mathcal{O}$, and $\mathcal{T}$ refer to the exchange operators for spin, parity, orbital, and time between the paired electrons. However, this classification no longer holds for higher spin fermions, where each electron also possesses a finite orbital angular momentum strongly coupled with the spin degree of freedom, giving instead a conserved total angular moment. For such systems, we here instead introduce the $\mathcal{JPT}=-1$ classification, where $\mathcal{J}$ is the exchange operator for the $z$ component of the total angular momentum quantum numbers. We then specifically focus on spin-$3/2$ fermion systems and several superconducting cubic half-Heusler compounds that have recently been proposed to be spin-$3/2$ superconductors. By using a generic Hamiltonian suitable for these compounds we calculate the superconducting pair amplitudes and find finite pair amplitudes for all possible symmetries obeying the $\mathcal{JPT}=-1$ classification, including all possible odd-frequency (odd-$\omega$) combinations. Moreover, one of the very interesting properties of spin-$3/2$ superconductors is the possibility of them hosting a Bogoliubov Fermi surface (BFS), where the superconducting energy gap is closed across a finite area. We show that a spin-$3/2$ superconductor with a pair potential satisfying an odd-gap time-reversal product and being noncommuting with the normal-state Hamiltonian hosts both a BFS and has finite odd-$\omega$ pair amplitudes. We then reduce the full spin-$3/2$ Hamiltonian to an effective two-band model and show that odd-$\omega$ pairing is inevitably present in superconductors with a BFS and vice versa.

In this paper, we explore properties of pseudoentropy in quantum field theories and spin systems from several approaches. pseudoentropy is a generalization of entanglement entropy such that it depends on both an initial and final state and has a clear gravity dual via the AdS/CFT. We numerically analyze a class of free scalar field theories and the XY spin model. This reveals basic properties of pseudoentropy in quantum many-body systems, namely, the area-law behavior, the saturation behavior, and the nonpositivity of difference between the pseudoentropy and averaged entanglement entropy in the same quantum phase. In addition, our numerical analysis finds an example where the strong subadditivity of pseudoentropy gets violated. Interestingly, we find that the nonpositivity of the difference can be violated only if the initial and final state belong to different quantum phases. We also present analytical arguments, which support these properties by both conformal field theoretic and holographic calculations. When the initial and final state belong to different topological phases, we expect a gapless mode localized along an interface, which enhances the pseudoentropy, leading to the violation of the nonpositivity of the difference. Moreover, we also compute the time evolution of pseudoentropy after a global quantum quench, where we observe that the imaginary part of pseudoentropy shows an interesting characteristic behavior.