The theory of semiparametric estimation offers an elegant way of computing the Cramér-Rao bound for a parameter of interest in the midst of infinitely many nuisance parameters. Here I apply the theory to the problem of incoherent imaging under the effects of diffraction and photon shot noise, where the object may consist of an arbitrary number of point sources and the moments of their distribution are the parameters of interest. Using a Hilbert-space formalism designed for Poisson processes, I derive exact semiparametric Cramér-Rao bounds and efficient estimators for both direct imaging and a quantum-inspired measurement method called spatial-mode demultiplexing (SPADE). The results establish the superiority of SPADE even when little prior information about the object is available.

We present an experimental determination of the band gap of ${\mathrm{ThF}}_4$ performed by two different techniques. The first measurement was performed by combining x-ray photoemission spectroscopy and bremsstrahlung isochromat spectroscopy. The second measurement exploited the position of the inelastic threshold in reflection electron energy loss spectroscopy. Both measurements gave compatible values of the band gap, with the average $\mathrm{\Delta }E=10.2\left(2\right)\mathrm{eV}$. This value was found to be in excellent agreement with theoretical calculations. The measured band gap is significantly larger than the ${}^{229m}\mathrm{Th}$ excitation energy, making ${\mathrm{ThF}}_4$ a possible candidate material for a solid-state nuclear clock based on the vacuum ultraviolet $\gamma$ decay.

The recent proposals of experiments with single Andreev bound states make relevant a detailed analysis of these states in multiterminal superconducting nanostructures. We evaluate the energy splitting of degenerate Andreev bound states that overlap in a superconducting lead, and find that the splitting is reduced in comparison with their energy by a small factor $\sqrt{R{G}_Q}$, with $R{G}_Q$ being the dimensionless resistance of the overlap region in the normal state. This permits quantum manipulation of the quasiparticles in these states. We provide a simple scheme of such manipulation.

A Brownian particle floating in a narrow corrugated (sinusoidal) channel with fluctuating cross section exhibits non-Gaussian normal diffusion. Its displacements are distributed according to a Gaussian law for very short and asymptotically large observation times, whereas a robust exponential distribution emerges for intermediate observation times of the order of the channel fluctuation correlation time. For intermediate to large observation times, the particle undergoes normal diffusion with one and the same effective diffusion constant. These results are analytically interpreted without having recourse to heuristic assumptions. Such a simple model thus reproduces recent experimental and numerical observations obtained by investigating complex biophysical systems.

We reformulate the variational problem describing equilibrium beach profiles in the thermodynamic approach of Jenkins and Inman [J. Geophys. Res.: Oceans 111, C02003 (2006)]. A first integral of the resulting Euler-Lagrange equation coincides formally with the Friedmann equation ruling closed universes in relativistic cosmology, leading to a useful analogy. Using the machinery of Friedmann-Lemaître-Robertson-Walker cosmology, qualitative properties and analytic solutions of beach profiles, which are the subject of a controversy, are elucidated.

We construct a model of short-range interacting Ising spins on a translationally invariant two-dimensional lattice that mimics a reversible circuit that multiplies or factorizes integers, depending on the choice of boundary conditions. We prove that, for open boundary conditions, the model exhibits no finite-temperature phase transition. Yet we find that it displays glassy dynamics with astronomically slow relaxation times, numerically consistent with a double exponential dependence on the inverse temperature. The slowness of the dynamics arises due to errors that occur during thermal annealing that cost little energy but flip an extensive number of spins. We argue that the energy barrier that needs to be overcome in order to heal such defects scales linearly with the correlation length, which diverges exponentially with inverse temperature, thus yielding the double exponential behavior of the relaxation time.

Recently, we introduced Relative Resolution (RelRes) as a hybrid formalism for fluid mixtures [Chaimovich et al., J. Chem. Phys. 143, 243107 (2015)]. The essence of this approach is that it switches molecular resolution in terms of relative separation: While nearest neighbors are characterized by a detailed fine-grained model, other neighbors are characterized by a simplified coarse-grained model. Once the two models are analytically connected with each other via energy conservation, RelRes can capture the structural and thermal behavior of various multicomponent and multiphase systems across state space. This current work is a natural continuation of our original communication. Most importantly, we present the comprehensive mathematics of RelRes, casting it as a multipole approximation at appropriate distances; the current set of equations technically applies for any arbitrary system in soft matter (e.g., water). Besides, we continue examining the capability of this multiscale approach in molecular simulations of various (nonpolar) uniform liquids, specifically examining a $2:1$ mapping for dumbbell-like molecules, as well as a $6:1$ mapping and a $6:2$ mapping for butterflylike molecules. In turn, we exhaustively show that RelRes can successfully retrieve for these systems their static and dynamic behavior, given that the fine-grained and coarse-grained potentials are switched at the boundary between the first and second coordination shells, the location at which orientational correlations vanish. We finally conclude by discussing how RelRes is the inherent variant of the “cell-multipole” approach for molecular simulations and, thus, this multiscale framework is especially promising for studying biological systems.

We present a theoretical framework to understand the collective dynamics of an ensemble of electrophoretically driven colloidal particles that are forced to assemble around a single topological defect in a nematic liquid crystal by an alternating current electric field. Our generic model combines phoretic propulsion with electrostatic interactions and liquid-crystal-mediated hydrodynamics, which are effectively cast into a long-range interparticle repulsion, while nematic elasticity plays a subdominant role. Simulations based on this model fully capture the collective organization process observed in the experiments and other striking effects as the emergence of conformal ordering and a nearly frequency-independent repulsive interaction above $10\mathrm{Hz}$. Our results demonstrate the importance of hydrodynamic interactions on the assembly of driven microscale matter in anisotropic media.

The vast majority of soft and biological materials, gels, and tissues are made from micrometer-size slender structures such as biofilaments and colloidal and molecular chains, which are believed to crucially control their mechanics. These constituents show intriguing extreme mechanics, mechanical instabilities, and plasticity, which, besides attracting significant theoretical attention, have not been studied experimentally and as such remain poorly understood. Here we investigate, by experiments, simulations, and theory, the mechanical instabilities of a slender self-assembled colloidal structure, observing a form of stochastic buckling where thermal fluctuations and associated entropic force effects are amplified in the vicinity of a buckling instability. We fully characterize how the persistence length and plasticity control the stochastic buckling transition, leading to intriguing higher-order buckling modes. These results elucidate the interplay of geometrical, thermal, and plastic interactions in the nonlinear mechanics of thermal self-assembled structures, crucial to the mechanical response and function of fiber-based soft and biological materials, as well as the rational design of micro- and nanoscale architectures.

Before global-scale quantum networks become operational, it is important to consider how to evaluate their performance so that they can be built to achieve the desired performance. We propose two practical figures of merit for the performance of a quantum network: the average connection time and the average largest entanglement cluster size. These quantities are based on the generation of elementary links in a quantum network, which is a crucial initial requirement that must be met before any long-range entanglement distribution can be achieved and is inherently probabilistic with current implementations. We obtain bounds on these figures of merit for a particular class of quantum repeater protocols consisting of repeat-until-success elementary link generation followed by joining measurements at intermediate nodes that extend the entanglement range. Our results lead to requirements on quantum memory coherence times, requirements on repeater chain lengths in order to surpass the repeaterless rate limit, and requirements on other aspects of quantum network implementations. These requirements are based solely on the inherently probabilistic nature of elementary link generation in quantum networks, and they apply to networks with arbitrary topology.

We investigate the topological properties of Floquet-engineered twisted bilayer graphene above the so-called magic angle driven by circularly polarized laser pulses. Employing a full Moiré-unit-cell tight-binding Hamiltonian based on first-principles electronic structure, we show that the band topology in the bilayer, at twisting angles above $1.{05}^{\circ }$, essentially corresponds to the one of single-layer graphene. However, the ability to open topologically trivial gaps in this system by a bias voltage between the layers enables the full topological phase diagram to be explored, which is not possible in single-layer graphene. Circularly polarized light induces a transition to a topologically nontrivial Floquet band structure with the Berry curvature analogous to a Chern insulator. Importantly, the twisting allows for tuning electronic energy scales, which implies that the electronic bandwidth can be tailored to match realistic driving frequencies in the ultraviolet or midinfrared photon-energy regimes. This implies that Moiré superlattices are an ideal playground for combining twistronics, Floquet engineering, and strongly interacting regimes out of thermal equilibrium.

Microcavity exciton-polaritons, strongly mixed light-matter states, are promising candidates for novel solid-state photonic devices such as classical and quantum simulators, qubits, and topologically protected photonic on-chip circuitry. Although different schemes for creation of confined polariton states and lattices have been proposed, a unified approach for the advanced preparation and dynamic manipulation of individual confined states, as well as for the control of interactions between remote states, is still missing. Here, we introduce a solid-state platform for dynamic polariton control based on the combination of intracavity potential traps, defined by a spatial modulation of the microcavity thickness, with dynamic control via nonlinear polariton-polariton interactions, as well as time and spatially dependent strain fields. We first demonstrate important functionalities of the platform, such as dynamic control of the energy and internal degrees of freedom, as well as the energy matching of neighboring traps. We then show the coherent modulation and symmetry control of a lattice of coupled traps by strain fields, which enables the creation of dynamic states within the band gap of the lattice. Important characteristics of the acoustic modulation are that it maintains the coherence of macroscopic polariton states and does not depend on polariton density, thus being applicable down to the single-polariton level. These functionalities of the strongly nonlinear, tunable, and spatially compact polariton platform are well described by a theoretical framework and represent important steps towards tunable polaritonic devices based on lattices of interacting polariton traps.

Understanding collective electronic states such as superconductivity and charge density waves is pivotal for fundamental science and applications. The layered transition metal dichalcogenide $1T-\mathrm{TiS}{\mathrm{e}}_2$ hosts a unique charge density wave (CDW) phase transition whose origins are still not fully understood. Here, we present ultrafast time- and angle-resolved photoemission spectroscopy (TR-ARPES) measurements complemented by time-resolved reflectivity (TRR) which allows us to establish the contribution of excitonic and electron-phonon interactions to the CDW. We monitor the energy shift of the valence band (VB) and coupling to coherent phonons as a function of laser fluence. The VB shift, directly related to the CDW gap closure, exhibits a markedly slower recovery dynamics at fluences above $F_{\mathrm{th}}=60\mu \mathrm{J}\mathrm{c}{\mathrm{m}}^{-2}$. This observation coincides with a shift in the relative weight of coherently coupled phonons to higher-frequency modes in TRR, suggesting a phonon bottleneck. Using a rate equation model, the emergence of a high-fluence bottleneck is attributed to an abrupt reduction in coupled phonon damping and an increase in exciton dissociation rate linked to the loss of CDW superlattice phonons. Thus, our work establishes the important role of both excitonic and phononic interactions in the CDW phase transition and the advantage of combining complementary femtosecond techniques to understand the complex interactions in quantum materials.

Understanding the ultrafast coupling and relaxation mechanisms between valleys in transition metal dichalcogenide semiconductors is of crucial interest for future valleytronic devices. Recent ultrafast pump-probe experiments showed an unintuitive significant bleaching at the excitonic $B$ transition after optical excitation of the energetically lower excitonic $A$ transition. Here, we present a possible microscopic explanation for this surprising effect. It is based on the joint action of exchange coupling and phonon-mediated thermalization into dark exciton states and does not involve a population of the $B$ exciton. Our work demonstrates how intra- and intervalley coupling on a femtosecond timescale governs the optical valley response of 2D semiconductors.

The effect of an external perpendicular magnetic field on the magnetization and crystallization of magnetic particles trapped in multilayered arrays is investigated theoretically. General ground-state symmetry considerations corroborated by numerical results allow us to develop an exact analytical theory. When dealing with monolayers, the continuous degeneracy of the in-plane dipole orientation is broken and accompanied by a rhombic crystal structure at finite applied magnetic field. On the other hand, bilayer systems are more robust against applied magnetic fields and preserve the in-plane hexagonal lattice symmetry. The onset of disaggregation is predicted as well in both scenarios. Our findings can be experimentally verified in colloidal suspensions (typically ferrofluids or magnetorheological fluids) and provide enlightening hints to further understanding the phase behavior of magnetic multilayers in more conventional molecular and atomic materials such as thin metal films obtained by epitaxy in the presence of an external magnetic field.

Confining light to scales beyond the diffraction limit, quantum plasmonics supplies an ideal platform to explore strong light-matter couplings. The light-induced localized surface plasmons (LSPs) on the metal-dielectric interface acting as a quantum bus have wide potential in quantum information processing; however, the loss nature of light in the metal hinders their application. Here we propose a mechanism to make the reversible energy exchange and the multipartite quantum correlation of a collective of quantum emitters (QEs) mediated by the LSPs persistent. Via investigating the quantized interaction between the QEs and the LSPs supported by a spherical metal nanoparticle, we find that the diverse signatures of the quantized QE-LSP coupling in the steady state, including the complete decay, population trapping, and persistent oscillation, are essentially determined by the different number of bound states formed in the energy spectrum of the QE-LSP system. Enriching our understanding on the light-matter interactions in a lossy medium, our result is instructive in the design of quantum devices using plasmonic nanostructures.

Synchronization, the temporal coordination of coupled oscillators, allows fireflies to flash in unison, neurons to fire collectively, and human crowds to fall in step on the London millenium bridge. Here, we interpret active (or self-propelled) chiral microswimmers with a distribution of intrinsic frequencies as motile oscillators and show that they can synchronize over very large distances, even for local coupling in two dimensions (2D). This opposes canonical nonactive oscillators on static or time-dependent networks, leading to synchronized domains only. A consequence of this activity-induced synchronization is the emergence of a “mutual flocking phase,” where particles of opposite chirality cooperate to form superimposed flocks moving at a relative angle to each other, providing a chiral active matter analogue to the celebrated Toner-Tu phase. The underlying mechanism employs a positive feedback loop involving the two-way coupling between oscillators' phase and self-propulsion and could be exploited as a design principle for synthetic active materials and chiral self-sorting techniques.

We propose a qubit efficient scheme to study ground-state properties of quantum many-body systems on near-term noisy intermediate-scale quantum computers. One can obtain a tensor network representation of the ground state using a number of qubits smaller than the physical degrees of freedom. By increasing the number of qubits, one can exponentially increase the bond dimension of the tensor network variational ansatz on a quantum computer. Moreover, we construct circuits blocks which respect $\mathrm{U}\left(1\right)$ and $\mathrm{SU}\left(2\right)$ symmetries of the physical system and show that they can significantly speed up the training process and alleviate the gradient vanishing problem. To demonstrate the feasibility of the qubit efficient variational quantum eigensolver in a practical setting, we perform first-principles classical simulation of differentiable programming of the circuits. Using only six qubits, one can obtain the ground state of a $4\times 4$ square lattice frustrated Heisenberg model with fidelity over 97%. Arbitrarily-long-range correlations can also be measured on the same circuit after variational optimization.

Multidimensional stochastic integrate-and-fire (IF) models are a standard spike-generator model in studies of firing variability, neural information transmission, and neural network dynamics. Most popular is a version with Gaussian noise and adaptation currents that can be described via Markovian embedding by a set of $d+1$ stochastic differential equations corresponding to a Fokker-Planck equation (FPE) for one voltage and $d$ auxiliary variables. For the specific case $d=1$, we find a set of partial differential equations that govern the stationary probability density, the stationary firing rate, and, central to our study, the spike-train power spectrum. We numerically solve the corresponding equations for various examples by a finite-difference method and compare the resulting spike-train power spectra to those obtained by numerical simulations of the IF models. Examples include leaky IF models driven by either high-pass-filtered (green) or low-pass-filtered (red) noise (surprisingly, already in this case, the Markovian embedding is not unique), white-noise-driven IF models with spike-frequency adaptation (deterministic or stochastic) and models with a bursting mechanism. We extend the framework to general $d$ and study as an example an IF neuron driven by a narrow-band noise (leading to a three-dimensional FPE). The many examples illustrate the validity of our theory but also clearly demonstrate that different forms of colored noise or adaptation entail a rich repertoire of spectral shapes. The framework developed so far provides the theory of the spike statistics of neurons with known sources of noise and adaptation. In the final part, we use our results to develop a theory of spike-train correlations when noise sources are not known but emerge from the nonlinear interactions among neurons in sparse recurrent networks such as found in cortex. In this theory, network input to a single cell is described by a multidimensional Ornstein-Uhlenbeck process with coefficients that are related to the output spike-train power spectrum. This leads to a system of equations which determine the self-consistent spike-train and noise statistics. For a simple example, we find a low-dimensional numerical solution of these equations and verify our framework by simulation results of a large sparse recurrent network of integrate-and-fire neurons.

We investigate the quantum transition to a correlated state of coupled oscillators in the regime where they display period tripling in response to a drive at triple the eigenfrequency. Correlations are formed between the discrete oscillation phases of individual oscillators. The evolution toward the ordered state is accompanied by the transient breaking of the symmetry between seemingly equivalent configurations. We attribute this to the nontrivial geometric phase that characterizes period tripling. We also show that the Wigner distribution of a single damped quantum oscillator can display a minimum at the classically stable zero-amplitude state.