### Bifurcating subsystem symmetric entanglement renormalization in two dimensions

We introduce the subsystem symmetry-preserving real-space entanglement renormalization group and apply it to study bifurcating flows generated by linear and fractal subsystem symmetry-protected topological phases in two spatial dimensions. We classify all bifurcating fixed points that are given by subsystem symmetric cluster states with two qubits per unit cell. In particular, we find that the square lattice cluster state is a quotient-bifurcating fixed point, while the cluster states derived from Yoshida's first order fractal spin liquid models are self-bifurcating fixed points. We discuss the relevance of bifurcating subsystem symmetry-preserving renormalization group fixed points for the classification and equivalence of subsystem symmetry-protected topological phases.

### The Fractonal Quantum Hall Effect: Fracton Phases from Chiral Layers

We present a coupled-wire construction of a model with chiral fracton topological order. The model combines the known construction of $\nu=1/m$ Laughlin fractional quantum Hall states with a planar p-string condensation mechanism. The bulk of the model is gapped and supports immobile fracton excitations that generate a hierarchy of mobile composite excitations. Open boundaries of the model are chiral and gapless, and can be used to demonstrate a fractional quantized Hall conductance where fracton composites act as charge carriers in the bulk. The planar p-string mechanism used to construct and analyze the model generalizes to a wide class of models including those based on layers supporting non-Abelian topological order.

### Visualizing Quasiparticles from Quantum Entanglement for general 1D phases

In this work, we present a quantum information framework for the entanglement behavior of the low energy quasiparticle (QP) excitations in various quantum phases in one-dimensional (1D) systems. We first establish an exact correspondence between the correlation matrix and the QP entanglement Hamiltonian for free fermions and find an extended in-gap state in the QP entanglement Hamiltonian as a consequence of the position uncertainty of the QP. A more general understanding of such an in-gap state can be extended to a Kramers theorem for the QP entanglement Hamiltonian, which also applies to strongly interacting systems. Further, we present a set of ubiquitous entanglement spectrum features, dubbed entanglement fragmentation, conditional mutual information, and measurement induced non-local entanglement for QPs in 1D symmetry protected topological phases. Our result thus provides a new framework to identify different phases of matter in terms of their QP entanglement.

### Fracton topological phases from coupled wires

In three dimensions, gapped phases can support "fractonic" quasiparticle excitations, which are either completely immobile or can only move within a low-dimensional submanifold, a peculiar topological phenomenon going beyond the conventional framework of topological quantum field theory. In this work we explore fractonic topological phases using three-dimensional coupled wire constructions, which have proven to be a successful tool to realize and characterize topological phases in two dimensions. We find that both gapped and gapless phases with fractonic excitations can emerge from the models. In the gapped case, we argue that fractonic excitations are mobile along the wire direction, but their mobility in the transverse plane is generally reduced. We show that the excitations in general have infinite-order fusion structure, distinct from previously known gapped fracton models. Like the 2D coupled wire constructions, many models exhibit gapless (or even chiral) surface states, which can be described by infinite-component Luttinger liquids. However, the universality class of the surface theory strongly depends on the surface orientation, thus revealing a new type of bulk-boundary correspondence unique to fracton phases.

### Spin-valley collective modes of the electron liquid in graphene

We develop the theory of collective modes supported by a Fermi liquid of electrons in pristine graphene. Under reasonable assumptions regarding the electron-electron interaction, all the modes but the plasmon are over-damped. In addition to the $SU(2)$ symmetric spin mode, these include also the valley imbalance modes obeying a $U(1)$ symmetry, and a $U(2)$ symmetric valley spin imbalance mode. We derive the interactions and diffusion constants characterizing the over-damped modes. The corresponding relaxation rates set fundamental constraints on graphene valley- and spintronics applications.

### Non-abelian Thouless pumping in a photonic lattice

Non-abelian gauge fields emerge naturally in the description of adiabatically evolving quantum systems having degenerate levels. Here we show that they also play a role in Thouless pumping in the presence of degenerate bands.To this end we consider a photonic Lieb lattice having two degenerate non-dispersive modes and we show that, when the lattice parameters are slowly modulated, the propagation of the photons bear the fingerprints of the underlying non-abelian gauge structure. The non-dispersive character of the bands enables a high degree of control on photon propagation. Our work paves the way to the generation and detection of non-abelian gauge fields in photonic and optical lattices.

### Efimov effect at the Kardar-Parisi-Zhang roughening transition

Surface growth governed by the Kardar-Parisi-Zhang (KPZ) equation in dimensions higher than two undergoes a roughening transition from smooth to rough phases with increasing the nonlinearity. It is also known that the KPZ equation can be mapped onto quantum mechanics of attractive bosons with a contact interaction, where the roughening transition corresponds to a binding transition of two bosons with increasing the attraction. Such critical bosons in three dimensions actually exhibit the Efimov effect, where a three-boson coupling turns out to be relevant under the renormalization group so as to break the scale invariance down to discrete one. On the basis of these facts linking the two distinct subjects in physics, we predict that the KPZ roughening transition in three dimensions shows either the discrete scale invariance or no intrinsic scale invariance.

### Polymer Informatics with Multi-Task Learning

Modern data-driven tools are transforming application-specific polymer development cycles. Surrogate models that can be trained to predict the properties of new polymers are becoming commonplace. Nevertheless, these models do not utilize the full breadth of the knowledge available in datasets, which are oftentimes sparse; inherent correlations between different property datasets are disregarded. Here, we demonstrate the potency of multi-task learning approaches that exploit such inherent correlations effectively, particularly when some property dataset sizes are small. Data pertaining to 36 different properties of over $13, 000$ polymers (corresponding to over $23,000$ data points) are coalesced and supplied to deep-learning multi-task architectures. Compared to conventional single-task learning models (that are trained on individual property datasets independently), the multi-task approach is accurate, efficient, scalable, and amenable to transfer learning as more data on the same or different properties become available. Moreover, these models are interpretable. Chemical rules, that explain how certain features control trends in specific property values, emerge from the present work, paving the way for the rational design of application specific polymers meeting desired property or performance objectives.

### Effect of two parallel intruders on net work during granular penetrations

The impact of single passive intruders into granular particles has been studied in detail. However, the impact force produced by multiple intruders separated at a distance from one another, and hence the effect of their presence in close proximity to one another, is largely unexplored. Here, we use numerical simulations and laboratory experiments to study the force response of two parallel rods intruding vertically into granular media while varying the gap spacing between them. We also explored the effect of variations in friction, intruder size, and particle size on the force response. The net work ($W$) of the two rods over the depth of intrusion was measured, and the instantaneous velocities of particles over the duration of intrusion were calculated by simulations. We found that the work done by the intruders changes with distance between them. We observed a peak in $W$ at a gap spacing of $\sim$3 particle diameters, which was up to 25% greater than $W$ at large separation (\textgreater 11 particle diameters), beyond which the net work plateaued. This peak was likely due to less particle flow between intruders as we found a larger number of strong forces---identified as force chains---in the particle domain at gaps surrounding the peak force. Although higher friction caused greater force generation during intrusion, the gap spacing between the intruders at which the peak work was generated remained unchanged. Larger intruder sizes resulted in greater net work with the peak in $W$ occurring at slightly larger intruder separations. Taken together, our results show that peak work done by two parallel intruders remained within a narrow range, remaining robust to most other tested parameters.

### Nanoscale plasticity and neuromorphic dynamics in silicon suboxide RRAM

Resistive random-access memories, also known as memristors, whose resistance can be modulated by the electrically driven formation and disruption of conductive filaments within an insulator, are promising candidates for neuromorphic applications due to their scalability, low-power operation and diverse functional behaviours. However, understanding the dynamics of individual filaments, and the surrounding material, is challenging, owing to the typically very large cross-sectional areas of test devices relative to the nanometre scale of individual filaments. In the present work, conductive atomic force microscopy is used to study the evolution of conductivity at the nanoscale in a fully CMOS-compatible silicon suboxide thin film. Distinct filamentary plasticity and background conductivity enhancement are reported, suggesting that device behaviour might be best described by composite core (filament) and shell (background conductivity) dynamics. Furthermore, constant current measurements demonstrate an interplay between filament formation and rupture, resulting in current-controlled voltage spiking in nanoscale regions, with an estimated optimal energy consumption of 25 attojoules per spike. This is very promising for extremely low-power neuromorphic computation and suggests that the dynamic behaviour observed in larger devices should persist and improve as dimensions are scaled down.

### Exact Self-Consistent Effective Hamiltonian Theory

We propose a general variational fermionic many-body wavefunction that generates an effective Hamiltonian in a quadratic form, which can then be exactly solved. The theory can be constructed within the density functional theory framework, and a self-consistent scheme is proposed for solving the exact density functional theory. We apply the theory to structurally-disordered systems, symmetric and asymmetric Hubbard dimers, and the corresponding lattice models. The single fermion excitation spectra show a persistent gap due to the fermionic-entanglement-induced pairing condensate. For disordered systems, the density of states at the edge of the gap diverges in the thermodynamic limit, suggesting a topologically ordered phase. A sharp resonance is predicted as the gap is not dependent on the temperature of the system. For the symmetric Hubbard model, the gap for both half-filling and doped case suggests that the quantum phase transition between the antiferromagnetic and superconducting phases is continuous.

### Orientation-dependent stabilization of MgCr$_2$O$_4$ spinel thin films

AB$_2$O$_4$ normal spinels with a magnetic B site can host a variety of magnetic and orbital frustrations leading to spin-liquid phases and field-induced phase transitions. Here we report the first epitaxial growth of (111)-oriented MgCr$_2$O$_4$ thin films. By characterizing the structural and electronic properties of films grown along (001) and (111) directions, the influence of growth orientation has been studied. Despite distinctly different growth modes observed during deposition, the comprehensive characterization reveals no measurable disorder in the cation distribution nor multivalency issue for Cr ions in either orientation. Contrary to a naive expectation, the (111) stabilized films exhibit a smoother surface and a higher degree of crystallinity than (001)-oriented films. The preference in growth orientation is explained within the framework of heteroepitaxial stabilization in connection to a significantly lower (111) surface energy. These findings open broad opportunities in the fabrication of 2D kagome-triangular heterostructures with emergent magnetic behavior inaccessible in bulk crystals.

### Symmetry properties of superconducting order parameter in Sr$_2$RuO$_4$

Soon after the discovery of superconductivity in Sr2RuO4 (SRO) in 1994, it was conjectured that its order parameter (OP) has a form similar to that realized in the superfluid He-3, namely, odd parity and spin triplet. The chiral p-wave pairing realized in He-3 A-phase was favored by several early experiments, in particular, the muon spin rotation and the Knight shift measurements published in 1998. However, the original Knight shift result was called into question in early 2019, raising the question as to whether the chiral p-wave, or even the spin-triplet pairing itself, is indeed realized in SRO. In this brief pedagogical review, we will address this question by counterposing the currently accepted results of Knight shift, polarized neutron scattering (PNS), spin counterflow half-quantum vortex (HQV), and Josephson experiments with predictions made both by standard BCS theory and by more general arguments based only on (1) the symmetry of the Hamiltonian including the spin-orbital terms, (2) thermodynamics, and (3) the qualitative experimental features of SRO. We also introduce a notation for triplet states alternative to the more popular d-vector one which we believe well suited to SRO. We conclude that the most recent Knight shift and PNS experiments do not exclude in the bulk the odd-parity, spin-triplet "helical" states allowed by the symmetry group of SRO but do exclude the chiral p-wave state. On the other hand, the Josephson and the HQV experiments showed that the pairing in SRO cannot be of the even-parity, spin-singlet type, and in the surface region or in samples of mesoscopic size, the d-vector must have a c-axis component, thus excluding apparently all bulk p-wave states except the chiral p-wave. Possible resolution of this rather glaring prima facie contradiction is discussed, taking into account other important experiments on SRO touched upon only briefly in this article.

### Effect of disorder on topological charge pumping in the Rice-Mele model

Recent experiments with ultracold quantum gases have successfully realized integer-quantized topological charge pumping in optical lattices. Motivated by this progress, we study the effects of static disorder on topological Thouless charge pumping. We focus on the half-filled Rice-Mele model of free spinless fermions and consider random diagonal disorder. In the instantaneous basis, we compute the polarization, the entanglement spectrum, and the local Chern marker. As a first main result, we conclude that the space-integrated local Chern marker is best suited for a quantitative determination of topological transitions in a disordered system. In the time-dependent simulations, we use the time-integrated current to obtain the pumped charge in slowly periodically driven systems. As a second main result, we observe and characterize a disorder-driven breakdown of the quantized charge pump. There is an excellent agreement between the static and the time-dependent ways of computing the pumped charge. The topological transition occurs well in the regime where all states are localized on the given system sizes and is therefore not tied to a delocalization-localization transition of Hamiltonian eigenstates. For individual disorder realizations, the breakdown of the quantized pumping occurs for parameters where the spectral bulk gap inherited from the band gap of the clean system closes, leading to a globally gapless spectrum. As a third main result and with respect to the analysis of finite-size systems, we show that the disorder average of the bulk gap severely overestimates the stability of quantized pumping. A much better estimate is the typical value of the distribution of energy gaps, also called mode of the distribution.

### How do defects limit the ultrahigh thermal conductivity of BAs? A first principles study

The promise enabled by BAs high thermal conductivity in power electronics cannot be assessed without taking into account the reduction incurred when doping the material. Using first principles calculations, we determine the thermal conductivity reduction induced by different group IV impurities in BAs as a function of concentration and charge state. We unveil a general trend, where neutral impurities scatter phonons more strongly than the charged ones. $\text{C}_{\text{B}}$ and $\text{Ge}_{\text{As}}$ impurities show by far the weakest phonon scattering and retain BAs $\kappa$ values of over $\sim$ 1000 $\text{W}\cdot\text{K}^{-1}\cdot\text{m}^{-1}$ even up to high densities making them ideal n-type and p-type dopants. Furthermore, going beyond the doping compensation threshold associated to Fermi level pinning triggers observable changes in the thermal conductivity. This informs design considerations on the doping of BAs, and it also suggests a direct way to determine the onset of compensation doping in experimental samples.

### Turbidimetric evaluation of the solubilization rate: dissolution of dodecane nanodrops in 7.5 mM sodium dodecylsulfate solutions at selected sodium chloride concentrations

The rate of micelle solubilization (SR) can be appraised following the decrease of the radius of a macroscopic drop of oil in contact with a surfactant solution [Todorov, 2002]. Alternatively, the time required for the dissolution of a liquid dispersion can be used for this purpose. Here, the decrease of the turbidity of a dodecane-in-water (d/w) nanoemulsion in 7.5 mM sodium dodecylsulfate (SDS) is studied at sodium chloride concentrations of 100, 300, 500, 700, 900, and 1000 mM NaCl. These salinities correspond to non-aggregating (< 300), aggregation-promoted (500) and surfactant precipitation regimes (> 700). It is found that SR is equal to 2.3 x 10^-11, half the value observed in the absence of salt for a neat aqueous surfactant solution above its critical micelle concentration (7.0 < cmc < 8.7 mM SDS [Deodhar, 2020]).

### Superconducting Niobium Calorimeter for Studies of Adsorbed Helium Monolayers

We developed a calorimeter with a vacuum container made of superconducting niobium (Nb) to study monolayers of helium adsorbed on graphite which are prototypical two-dimensional quantum matters below 1 K. Nb was chosen because of its small specific heat in the superconducting state. It is crucially important to reduce the addendum heat capacity ($C_{\rm{ad}}$) when the specific surface area of substrate is small. Here we show details of design, construction and results of $C_{\rm{ad}}$ measurements of the Nb calorimeter down to 40 mK. The measured $C_{\rm{ad}}$ was sufficiently small so that we can use it for heat capacity measurements on helium monolayers in a wide temperature range below 1 K. We found a relatively large excess heat capacity in $C_{\rm{ad}}$, which was successfully attributed to atomic tunneling of hydrogen (H) and deuterium (D) between trap centers near oxygen or nitrogen impurities in Nb. The tunnel frequencies of H and D deduced by fitting the data to the tunneling model are consistent with the previous experiments on Nb doped with H or D.

### Anomalous drag in electron-hole condensates with granulated order

We explain the strong interlayer drag resistance observed at low temperatures in bilayer electron-hole systems in terms of an interplay between local electron-hole-pair condensation and disorder-induced carrier density variations. Smooth disorder drives the condensate into a granulated phase where interlayer coherence is formed only in well separated and disconnected regions, or grains, and the densities of electrons and holes accidentally match. The drag resistance is then dominated by Andreev scattering of charge carries between layers at the grains that transfers momentum between layers. We show that this scenario can account for the observed dependence of the drag resistivity on temperature, and on the average charge imbalance between layers.

### Hierarchical classical metastability in an open quantum East model

We study in detail an open quantum generalisation of a classical kinetically constrained model -- the East model -- known to exhibit slow glassy dynamics stemming from a complex hierarchy of metastable states with distinct lifetimes. Using the recently introduced theory of classical metastability for open quantum systems, we show that the driven open quantum East model features a hierarchy of classical metastabilities at low temperature and weak driving field. We find that the effective long-time description of its dynamics is not only classical, but shares many properties with the classical East model, such as obeying an effective detailed balance condition, and lacking static interactions between excitations, but with this occurring within a modified set of metastable phases which are coherent, and with an effective temperature that is dependent on the coherent drive.

### Valley-polarization in biased bilayer graphene using circularly polarized light

Achieving a population imbalance between the two inequivalent valleys is a critical first step for any valleytronic device. A valley-polarization can be induced in biased bilayer graphene using circularly polarized light. In this paper, we present a detailed theoretical study of valley-polarization in biased bilayer graphene. We show that a nearly perfect valley-polarization can be achieved with the proper choices of external bias and pulse frequency. We find that the optimal pulse frequency $\omega$ is given by $\hbar\omega=2a,$ where $2a$ is the potential energy difference between the graphene layers. We also find that the valley-polarization originates not from the Dirac points themselves, but rather from a ring of states surrounding each. Intervalley scattering is found to significantly reduce the valley-polarization at high frequencies, and thermal populations are found to reduce the valley-polarization at small biases. This work provides insight into the origin of valley-polarization in bilayer graphene and will aid experimentalists seeking to study valley-polarization in the lab.

### Analytically approximate solution to the VLE problem with the SRK equation of state

Since a transcendental equation is involved in vapor liquid equilibrium (VLE) calculations with a cubic equation of state (EoS), any exact solution has to be carried out numerically with an iterative approach [1,2]. This causes significant wastes of repetitive human efforts and computing resources. Based on a recent study [3] on the Maxwell construction [4] and the van der Waals EoS [5], here we propose a procedure for developing analytically approximate solutions to the VLE calculation with the Soave-Redlich-Kwong (SRK) EoS [6] for the entire coexistence curve. This procedure can be applied to any cubic EoS and thus opens a new area for the EoS study. For industrial applications, a simple databank can be built containing only the coefficients of a newly defined function and other thermodynamic properties will be obtained with analytical forms. For each system there is only a one-time effort, and therefore, the wastes caused by the repetitive efforts can be avoided. By the way, we also show that for exact solutions, the VLE problem with any cubic EoS can be reduced to solving a transcendental equation with one unknown, which can significantly simplify the methods currently employed [2,7].

### Quantum Kinetic Theory of Nonlinear Nernst Effect

For a long period of time, we have been seeking how Berry curvature influnces the transport properties in materials breaking time-reversal symmetry. In time-reversal symmetric material, there will be no thermoelectric current induced by Berry curvature in linear regime. However, the nonlinear Hall current can be shown in non-magnetic and non-centrosymmetric materials, where Berry curvature dipole plays an important role. Most studies are developed from semi-classical Boltzmann equation. Here we show the quantum kinetic theory for nonlinear Nernst effect and introduce a new type of Berry curvature dipole: thermoelectric Berry curvature dipole. This new Berry curvature dipole will also induce the thermoelectric transport in nonlinear regime even in time-reversal invariant crystals. We will also apply our theory to topological crystalline insulator with tilted Dirac cone.

### 2D correlations in the van der Waals ferromagnet CrBr$_{3}$ using high frequency electron spin resonance spectroscopy

Broadening the knowledge and understanding on the magnetic correlations in van der Waals layered magnets is critical in realizing their potential next-generation applications. In this study, we employ high frequency (240 GHz) electron spin resonance (ESR) spectroscopy on plate-like CrBr$_{3}$ to gain insight into the magnetic interactions as a function of temperature (200 - 4 K) and the angle of rotation ${\theta}$. We find that the temperature dependence of the ESR linewidth is well described by the Ginzberg-Landau critical model as well as Berezinskii-Kosterlitz-Thouless (BKT) transition model, indicative of the presence of two-dimensional (2D) correlations. This suggests that the three-dimensional ferromagnet CrBr$_{3}$, which has been described as an Ising or Heisenberg ferromagnet, could present 2D magnetic correlations and BKT-like behavior even in its bulk form; an observation that, to the best of our knowledge, has not been reported in the literature. Furthermore, our findings show that the resonance field follows a $(3cos^2{\theta} - 1)$-like angular dependence, while the linewidth follows a $(3cos^2{\theta} - 1)^2$-like angular dependence. This observed angular dependence of the resonance field and linewidth further confirm an unanticipated 2D magnetic behavior in CrBr$_{3}$. This behavior is likely due to the interaction of the external magnetic field applied during the ESR experiment that allows for the mediation of long-range vortex-like correlations between the spin clusters that may have formed due to magnetic phase separation. This study demonstrates the significance of employing spin sensitive techniques such as ESR to better understand the magnetic correlations in similar van der Waals magnets.

### Spectroscopic Evidence of Superconductivity Pairing at 83 K in Single-Layer FeSe/SrTiO3 Films

Single-layer FeSe films grown on the SrTiO3 substrate (FeSe/STO) have attracted much attention because of their possible record-high superconducting critical temperature Tc and distinct electronic structures in iron-based superconductors. However, it has been under debate on how high its Tc can really reach due to the inconsistency of the results obtained from the transport, magnetic and spectroscopic measurements. Here we report spectroscopic evidence of superconductivity pairing at 83 K in single-layer FeSe/STO films. By preparing high-quality single-layer FeSe/STO films, we observe for the first time strong superconductivity-induced Bogoliubov back-bending bands that extend to rather high binding energy ~100 meV by high-resolution angle-resolved photoemission measurements. The Bogoliubov back-bending band provides a new definitive benchmark of superconductivity pairing that is directly observed up to 83 K in the single-layer FeSe/STO films. Moreover, we find that the superconductivity pairing state can be further divided into two temperature regions of 64-83 K and below 64 K. We propose the 64-83 K region may be attributed to superconductivity fluctuation while the region below 64 K corresponds to the realization of long-range superconducting phase coherence. These results indicate that either Tc as high as 83 K is achievable in iron-based superconductors, or there is a pseudogap formation from superconductivity fluctuation in single-layer FeSe/STO films.

### Hybridization of Bogoliubov-quasiparticles between adjacent CuO$_2$ layers in the triple-layer cuprate Bi$_2$Sr$_2$Ca$_2$Cu$_3$O$_{10+δ}$ studied by ARPES

Hybridization of Bogoliubov quasiparticles (BQPs) between the CuO$_2$ layers in the triple-layer cuprate high-temperature superconductor Bi$_2$Sr$_2$Ca$_2$Cu$_3$O$_{10+\delta}$ is studied by angle-resolved photoemission spectroscopy (ARPES). In the superconducting state, an anti-crossing gap opens between the outer- and inner-BQP bands, which we attribute primarily to interlayer single-particle hopping with possible contributions from interlayer Cooper pairing. We find that the $d$-wave superconducting gap of both BQP bands smoothly develops with momentum without abrupt jump in contrast to a previous ARPES study. Hybridization between the BQPs also gradually increases in going from the off-nodal to the anti-nodal region, which is explained by the momentum-dependence of the interlayer single-particle hopping. As possible mechanisms for the enhancement of the superconducting transition temperature, the hybridization between the BQPs, as well as the combination of phonon modes of the triple CuO$_2$ layers and spin fluctuations are discussed.

### Use of local-density approximation pseudopotentials in range separated hybrid exchange-correlation functional method to investigate Pb doped SnO$_2$

In this study, the structural, electronic and optical properties of Pb doped rutile SnO$_2$ were investigated using the range separated hybrid exchange-correlation functional method. In the calculations, LDA pseudopotentials were used instead of the standard PBE pseudopotentials. According to the results obtained in this present work, when the LDA pseudopotentials are used instead of PBE pseudopotentials in HSE06 method with a mixing parameter of %29, the electronic structure of rutile SnO$_2$ can be described as quite compatible with experimental data. At the same time, in the Pb doped SnO$_2$ cases, using the same method, electronic structure, and especially the band gap were described quite compatible with the experimental data. Consistent with experimental data, the band gap narrows as the Pb doping rate increases. The computational results obtained in this study show that the reason for this narrowing is the change in the conduction band edges. Due to this effect of the Pb atom, the bandgap can be narrowed in a controlled manner by using the addition amount of the Pb atom.

### Quasi-indirect measurement of electrocaloric temperature change in PbSc0.5Ta0.5O3 via comparison of adiabatic and isothermal electrical polarization data

The electrically driven adiabatic changes of temperature that may be achieved in the archetypal electrocaloric material PbSc0.5Ta0.5O3 are identified by comparing the isothermal changes of electrical polarization that arise when an applied field is varied slowly with the adiabatic changes of electrical polarization that arise when the applied field is varied quickly. By obtaining these electrical polarization data at many nearby starting temperatures, every 0.3 K, we find that a maximum temperature change of ~1.7 K arises due to a maximum field change of 26 kV cm-1, for starting temperatures 298-310 K. This quasi indirect method of measurement is compared with the well known indirect, quasi-direct and direct methods, and may become routine in the study of electrocaloric materials.

### Quantum gas microscopy for single atom and spin detection

A particular strength of ultracold quantum gases are the versatile detection methods available. Since they are based on atom-light interactions, the whole quantum optics toolbox can be used to tailor the detection process to the specific scientific question to be explored in the experiment. Common methods include time-of-flight measurements to access the momentum distribution of the gas, the use of cavities to monitor global properties of the quantum gas with minimal disturbance and phase-contrast or high-intensity absorption imaging to obtain local real space information in high-density settings. Even the ultimate limit of detecting each and every atom locally has been realized in two-dimensions using so-called quantum gas microscopes. In fact, these microscopes not only revolutionized the detection, but also the control of lattice gases. Here we provide a short overview of this technique, highlighting new observables as well as key experiments that have been enabled by quantum gas microscopy.

### Determination of Young's modulus of active pharmaceutical ingredients by relaxation dynamics at elevated pressures

A new approach is theoretically proposed to study the glass transition of active pharmaceutical ingredients and a glass-forming anisotropic molecular liquid at high pressures. We describe amorphous materials as a fluid of hard spheres. Effects of nearest-neighbor interactions and cooperative motions of particles on glassy dynamics are quantified through a local and collective elastic barrier calculated using the Elastically Collective Nonlinear Langevin Equation theory. Inserting two barriers into Kramer's theory gives structural relaxation time. Then, we formulate a new mapping based on the thermal expansion process under pressure to intercorrelate particle density, temperature, and pressure. This analysis allows us to determine the pressure and temperature dependence of alpha relaxation. From this, we estimate an effective elastic modulus of amorphous materials and capture effects of conformation on the relaxation process. Remarkably, our theoretical results agree well with experiments.

### Fractality and Topology of Self-Avoiding Walks

We have analyzed geometric and topological features of self-avoiding walks. We introduce a new kind of walk: the loop-deleted self-avoiding walk (LDSAW) motivated by the interaction of chromatin with the nuclear lamina. Its critical exponent is calculated and found to be different from that of the ordinary SAW. Taking the walks as point-clouds, the LDSAW is a subset of the SAW. We study the difference between the LDSAW and SAW by comparing their fractal dimensions and growth rates of the Betti number. In addition, the spatial distribution of the contacts inside a SAW, which is also a subset of SAW, is analyzed following the same routine. The results show that the contact-cloud has a multi-fractal property and different growth rates for the Betti number. Finally, for comparison, we have analyzed random subsets of the SAW, showing them to have the same fractal dimension as the SAW.

### Low-temperature Benchtop-synthesis of All-inorganic Perovskite Nanowires

A facile, low-temperature precipitation-based method is utilized to demonstrate the synthesis of ultra-thin and highly-uniform cesium lead bromide perovskite nanowires (NWs). The reactions facilitate the NWs crystalline nature over micron-size lengths, while they impart tailored nanowire widths that range from the quantum confinement regime (~ 7 nm) and down to 2.6 nm. This colloidal synthesis approach is the first of its kind that is carried out on the work-bench, without demanding chemical synthesis equipment. Importantly, the NWs photoluminescence is shown to become improved over time, with no tedious post-synthesis surface treatment requirement.

### Evolution of the crystal structure and magnetic properties of Sm-doped BiFeO3 ceramics across the phase boundary region

Samarium doped BiFeO3 compounds having nano-size crystallites were prepared by the ethylene glycol assisted sol-gel synthesis method. X-ray diffraction and SEM measurements as well as Raman spectroscopy and FTIR experiments were used to clarify the evolution of the crystal structure on microscopic and local scale levels in the compounds having formula Bi1-xSmxFeO3, where x equals from 0 to 1. Magnetization measurements along with the structural data were used to determine a correlation between magnetic properties and crystal structure of the compounds. The compounds with from x 0.1-0.2 are characterized by the sequence of the structural transitions driven by the dopant increase, from the polar rhombohedral phase to the non-polar orthorhombic phase via two-phase regions characterized by the presence of the anti-polar orthorhombic phase. The concentration regions ascribed to a coexistence of the rhombohedral and the anti-polar orthorhombic phases as well as theanti-polar orthorhombic and the non-polar orthorhombic phases are observed in the ranges from 0.12 to 0.15 and from 0.15 to 0.18 respectively. The compounds having single-phase rhombohedral structure are characterized by a release of remnant magnetization as compared to ceramics with similar chemical compositions but synthesized by the solid-state reaction method and having microscopic size crystallites. A correlation between the type of structural distortion, morphology of crystallites and an onset of remnant magnetization is discussed highlighting a difference in the evolution of crystal structure and magnetization observed for the Sm-doped ceramics prepared by modified sol-gel method and conventional solid-state reaction technique.

### Domain wall dynamics in antiferromagnetically-coupled double-lattice systems

In ferromagnetic materials, the rich dynamics of magnetic domain walls (DWs) under magnetic field or current have been successfully described using the well-known q-{\phi} analytical model. We demonstrate here that this simple unidimensional model holds for multiple-sublattice materials such as ferrimagnetic alloys or synthetic antiferromagnets (SAF) by using effective parameters, and is in excellent agreement with double-lattice micromagnetic simulations. We obtain analytical laws for the DW velocity and internal precession angle as a function of net magnetisation for different driving forces (magnetic field, spin transfer and spin-orbit torques) and different propagation regimes in ferrimagnetic alloys and SAFs. The model predicts that several distinctive dynamical features occur near or at the magnetic and the angular compensation points when the net magnetization or the net angular momentum of the system vanishes, and we discuss the experimental observations that have been reported for some of them. Using a higher degree-of-freedom analytical model that accounts for inter-sublattice distortions, we give analytical expressions for these distortions that agree with the micromagnetic simulations. This model shows that the DW velocity and precession rate are independent of the strength of the inter-sublattice exchange coupling, and justifies the use of the simpler effective parameters model.

### Excitons in bulk black phosphorus evidenced by photoluminescence at low temperature

Atomic layers of Black Phosphorus (BP) present unique opto-electronic properties dominated by a direct tunable bandgap in a wide spectral range from visible to mid-infrared. In this work, we investigate the infrared photoluminescence of BP single crystals at very low temperature. Near-bandedge recombinations are observed at 2 K, including dominant excitonic transitions at 0.276 eV and a weaker one at 0.278 eV. The free-exciton binding energy is calculated with an anisotropic Wannier-Mott model and found equal to 9.1 meV. On the contrary, the PL intensity quenching of the 0.276 eV peak at high temperature is found with a much smaller activation energy, attributed to the localization of free excitons on a shallow impurity. This analysis leads us to attribute respectively the 0.276 eV and 0.278 eV PL lines to bound excitons and free excitons in BP. As a result, the value of bulk BP bandgap is refined to 0.287 eV at 2K.

### Asymmetric Rydberg blockade of giant excitons in Cuprous Oxide

The ability to generate and control strong long-range interactions via highly excited electronic states has been the foundation for recent breakthroughs in a host of areas, from atomic and molecular physics [1, 2] to quantum optics [3, 4] and technology [5-7]. Rydberg excitons provide a promising solid-state realization of such highly excited states, for which record-breaking orbital sizes of up to a micrometer have indeed been observed in cuprous oxide semiconductors [8]. Here, we demonstrate the generation and control of strong exciton interactions in this material by optically producing two distinct quantum states of Rydberg excitons. This makes two-color pump-probe experiments possible that allow for a detailed probing of the interactions. Our experiments reveal the emergence of strong spatial correlations and an inter-state Rydberg blockade that extends over remarkably large distances of several micrometers. The generated many-body states of semiconductor excitons exhibit universal properties that only depend on the shape of the interaction potential and yield clear evidence for its vastly extended-range and power-law character.

### Magnetic and electronic phases of U$_\mathbf{2}$Rh$_\mathbf{3}$Si$_\mathbf{5}$

We present a detailed study of the magnetic and electronic properties of $\mathrm{U}_2\mathrm{Rh}_3\mathrm{Si}_5$, a material that has been demonstrated to exhibit a first order antiferromagnetic phase transition. From a high magnetic field study, together with extensive experiments in moderate fields, we establish the magnetic phase diagrams for all crystallographic directions. The possibility of an electronic phase in a narrow interval above the N\'eel temperature as a precursor of a magnetic phase is discussed.

### Nature of native atomic defects in ZrTe$_5$ and their impact on the low-energy electronic structure

Over the past decades, investigations of the anomalous low-energy electronic properties of ZrTe$_5$ have reached a wide array of conclusions. An open question is the growth method's impact on the stoichiometry of ZrTe$_5$ samples, especially given the very small density of states near its chemical potential. Here we report on high resolution scanning tunneling microscopy and spectroscopy measurements performed on samples grown via different methods. Using density functional theory calculations, we identify the most prevalent types of atomic defects on the surface of ZrTe$_5$, namely Te vacancies and intercalated Zr atoms. Finally, we precisely quantify their density and outline their role as ionized defects in the anomalous resistivity of this material.

### Prediction of $d$-wave bond-order and pseudogap in organic superconductor $κ$-(BEDT-TTF)$_2$X: Similarities to cuprate superconductors

Rich pseudogap phenomena due to unconventional orders, such as the inter-site order parameter called the bond-order (BO), attract increasing attention in condensed matter physics. Here, we investigate the occurrence of the unconventional orders in organic superconductor $\kappa$-(BEDT-TTF)$_2$X in an unbiased way, based on the combination of the functional renormalization group (fRG) method and the density-wave equation method. We revealed the strong development of the $d$-wave BO instability at wavelength $q=Q_{\rm B}=(\delta,\delta)$ ($\delta=0.38\pi$). Its origin is novel quantum interference among incommensurate paramagnons with $Q_{\rm S}^{\pm}\approx(\pi \pm \delta/2,\pi \pm \delta/2)$. The present prediction leads to the emergence of the Fermi arc structure and pseudogap in $\kappa$-(BEDT-TTF)$_2$X. The d-wave BO fluctuations at $q=Q_{\rm B}$ reinforce the $d$-wave superconducting state.

### Competition between fractional quantum Hall liquid and Wigner solid at small fillings: Role of layer thickness and Landau level mixing

What is the fate of the ground state of a two-dimensional electron system (2DES) at very low Landau level filling factors ($\nu$) where interaction reigns supreme? An ordered array of electrons, the so-called Wigner crystal, has long been believed to be the answer. It was in fact the search for the elusive Wigner crystal that led to the discovery of an unexpected, incompressible liquid state, namely the fractional quantum Hall state at $\nu=1/3$. Understanding the competition between the liquid and solid ground states has since remained an active field of fundamental research. Here we report experimental data for a new two-dimensional system where the electrons are confined to an AlAs quantum well. The exceptionally high quality of the samples and the large electron effective mass allow us to determine the liquid-solid phase diagram for the two-dimensional electrons in a large range of filling factors near $\simeq 1/3$ and $\simeq 1/5$. The data and their comparison with an available theoretical phase diagram reveal the crucial role of Landau level mixing and finite electron layer thickness in determining the prevailing ground states.

### Chiral edge currents in confined fibrosarcoma cells

During metastatic dissemination, streams of cells collectively migrate through a network of narrow channels within the extracellular matrix, before entering into the blood stream. This strategy is believed to outperform other migration modes, based on the observation that individual cancer cells can take advantage of confinement to switch to an adhesion-independent form of locomotion. Yet, the physical origin of this behaviour has remained elusive and the mechanisms behind the emergence of coherent flows in populations of invading cells under confinement are presently unknown. Here we demonstrate that human fibrosarcoma cells (HT1080) confined in narrow stripe-shaped regions undergo collective migration by virtue of a novel type of topological edge currents, resulting from the interplay between liquid crystalline (nematic) order, microscopic chirality and topological defects. Thanks to a combination of in vitro experiments and theory of active hydrodynamics, we show that, while heterogeneous and chaotic in the bulk of the channel, the spontaneous flow arising in confined populations of HT1080 cells is rectified along the edges, leading to long-ranged collective cell migration, with broken chiral symmetry. These edge currents are fuelled by layers of +1/2 topological defects, orthogonally anchored at the channel walls and acting as local sources of chiral active stress. Our work highlights the profound correlation between confinement and collective migration in multicellular systems and suggests a possible mechanism for the emergence of directed motion in metastatic cancer.

### The ground state of polaron in an ultracold dipolar Fermi gas

An impurity atom immersed in an ultracold atomic Fermi gas can form a quasiparticle, so-called Fermi polaron, due to impurity-fermion interaction. We consider a three-dimensional homogeneous dipolar Fermi gas as a medium, where the interatomic dipole-dipole interaction (DDI) makes the Fermi surface deformed into a spheroidal shape, and, using a Chevy-type variational method, investigate the ground-state properties of the Fermi polaron: the effective mass, the momentum distribution of a particle-hole (p-h) excitation, the drag parameter, and the medium density modification around the impurity. These quantities are shown to exhibit spatial anisotropies in such a way as to reflect the momentum anisotropy of the background dipolar Fermi gas. We have also given numerical results for the polaron properties at the unitarity limit of the impurity-fermion interaction in the case in which the impurity and fermion masses are equal. It has been found that the transverse effective mass and the transverse momentum drag parameter of the polaron both tend to decrease by $\sim 10\%$ when the DDI strength is raised from $0$ up to around its critical value, while the longitudinal ones exhibit a very weak dependence on the DDI.

### The difference between angular momentum and pseudo angular momentum

In condensed matter systems it is necessary to distinguish between the momentum of the constituents of the system and the pseudomomentum of quasiparticles. The same distinction is also valid for angular momentum and pseudo angular momentum. Based on Noether's theorem, we demonstrate that the recently discussed orbital angular momenta of phonons and magnons are pseudo angular momenta. This conceptual difference is important for a proper understanding of the transfer of angular momentum in condensed matter systems, especially in spintronics applications.

### Critical Behavior and Universal Signature of an Axion Insulator State

Recently, the search for an axion insulator state in 3D magnetic topological insulators (TIs) has attracted intensive interest due to its unqiue electromagnetic response. However, the detection of the axion insulator state remains difficult in experiments. We systematically investigate the disorder-induced phase transition of the axion insulator state in a 3D TI with antiparallel magnetization alignment surfaces. It is found that there exists a 2D disorder-induced phase transition which shares the same universality class with the quantum Hall plateau to plateau transition. Then, we provide a phenomenological theory which maps the random mass Dirac Hamiltonian of the axion insulator state into the Chalker-Coddington network model. Therefore, we propose to probe the axion insulator state by investigating the universal signature of such a phase transition in the 3D magnetic TI. Our findings not only show a global phase diagram of an axion insulator state, but also provide a new experimental routine to probe an axion insulator.

### Universal Aspects of Vortex Reconnections across the BCS-BEC Crossover

Reconnecting vortices in a superfluid allow for the energy transfer between different length scales and its subsequent dissipation. Present picture assumes that the dynamics of a reconnection is driven mostly by the phase of the order parameter, and this statement can be justified in the case of Bose-Einstein Condensates (BECs), where vortices have simple internal structure. Therefore, it is natural to postulate that the reconnection dynamics in the vicinity of the reconnection moment is universal. This expectation has been confirmed in numerical simulations for BECs and experimentally for superfluid ${}^4$He. Not much has been said about this relation in the context of Fermi superfluids. In this letter we aim at bridging this gap, and we report our findings, which reveal that the reconnection dynamics conforms with the predicted universal behaviour across the entire BCS-BEC crossover. The universal scaling survives also for spin-imbalanced systems, where unpaired fermions induce a complex structure of the colliding vortices.

### Chiral Majorana Hinge Modes in Superconducting Dirac Materials

Chiral Majorana hinge modes are characteristic of a second-order topological superconductor in three dimensions. Here we systematically study pairing symmetry in the point group D_{2h}, and find that the leading pairing channels can be of s-, d-, and s+id-wave pairing in Dirac materials. Except for the odd-parity s-wave pairing superconductivity, the s+id-wave pairing superconductor is topologically nontrivial and possesses Majorana hinge and surface modes. The chiral Majorana hinge modes can be characterized by a winding number of the quadrupole moment, or quantized quadruple moment at the symmetrically invariant point. Our findings suggest the strong spin-orbital coupling, crystalline symmetries and electron-electron interaction in the Dirac materials may provide a microscopic mechanism to realize chiral Majorana hinge modes without utilizing the proximity effect or external fields.

### Solvable model of a generic driven mixture of trapped Bose-Einstein condensates and properties of a many-boson Floquet state at the limit of an infinite number of particles

A solvable model of a periodically-driven trapped mixture of Bose-Einstein condensates, consisting of $N_1$ interacting bosons of mass $m_1$ driven by a force of amplitude $f_{L,1}$ and $N_2$ interacting bosons of mass $m_2$ driven by a force of amplitude $f_{L,2}$, is presented. The model generalizes the harmonic-interaction model for mixtures to the time-dependent domain. The resulting many-particle ground Floquet wavefunction and quasienergy, as well as the time-dependent densities and reduced density matrices, are prescribed explicitly and analyzed at the many-body and mean-field levels of theory for finite systems and at the limit of an infinite number of particles. We prove that the time-dependent densities per particle are given at the limit of an infinite number of particles by their respective mean-field quantities, and that the time-dependent reduced one-particle and two-particle density matrices per particle of the driven mixture are $100\%$ condensed. Interestingly, the quasienergy per particle {\it does not} coincide with the mean-field value at this limit, unless the relative center-of-mass coordinate of the two Bose-Einstein condensates is not activated by the driving forces $f_{L,1}$ and $f_{L,2}$. As an application, we investigate the imprinting of angular momentum and its fluctuations when steering a Bose-Einstein condensate by an interacting bosonic impurity, and the resulting modes of rotations. Whereas the expectation values per particle of the angular-momentum operator for the many-body and mean-field solutions coincide at the limit of an infinite number of particles, the respective fluctuations can differ substantially. The results are analyzed in terms of the transformation properties of the angular-momentum operator under translations and boosts and the interactions between the particles. Implications are briefly discussed.

### Tearing apart cellulose nanofibers: the formation of unitary cellulose polymers

The atomic scale understanding of cellulose disassembly processes is an important issue in designing nanostructures using cellulose-based materials. In this work, we present a joint of experimental and theoretical study addressing the disassembly of cellulose nanofibrils. Through TEMPO-mediated oxidation processes, combined with atomic force microscopy results, we find the formation of nanofibers with diameters corresponding to a single cellulose polymer chain. Further first-principles calculations have been done to provide a total energy picture of interchain and intersheet interactions in pristine and oxidized cellulose nanofibrils. In the former, by using a number of different van der Waals approaches, we found the intersheet interaction stronger than the interchain one. In the oxidized systems, we have considered the formation of (charged) carboxylate groups along the inner sites of elementary fibrils. By mapping the total charge density, we show a net charge concentration on the carboxylate groups, supporting the emergence of repulsive electrostatic interactions between the cellulose fibers. Indeed, our total energy results show that the weakening of the binding strength between the fibrils is proportional net charge density of the carboxylate group. Moreover, by comparing interchain and intersheet binding energies, we found that most of the disassembly processes should take place by breaking the interchain O--H$\cdots$O hydrogen bond interactions.

### Spin vs. bond correlations along dangling edges of quantum critical magnets

Dangling edge spins of two-dimensional quantum critical antiferromagnets display strongly enhanced spin correlations with scaling dimensions that fall outside of the classical theory of surface critical phenomena. We provide large-scale quantum Monte Carlo results for both spin and bond correlation functions for the case of the columnar dimer model in particular. Unlike the spin correlations, we find the bond correlations to differ starkly between the spin-1/2 and spin-1 case. Furthermore, we compare the corresponding scaling dimensions to recent theoretical predictions. These predictions are, in part, supported by our numerical data, but cannot explain our findings completely. Our results thus put further constraints on completing the understanding of dangling edge correlations, as well as surface phenomena in strongly-correlated quantum systems in general.

### A cold-source paradigm for steep-slope transistors based on van der Waals heterojunctions

The availability of transistors capable of operating at low supply voltage is essential to improve the key performance metric of computing circuits, i.e., the number of operations per unit energy. In this paper, we propose a new device concept for energy-efficient, steep-slope transistors based on heterojunctions of 2D materials. We show that by injecting electrons from an isolated and weakly dispersive band into a strongly dispersive one, subthermionic subthreshold swings can be obtained, as a result of a cold-source effect and of a reduced thermalization of carriers. This mechanism is implemented by integrating in a MOSFET architecture two different monolayer materials coupled through a van der Waals heterojunction, combining the subthermionic behavior of tunnel field-effect transistors (FETs) with the robustness of a MOSFET architecture against performance-degrading factors, such as traps, band tails and roughness. A further advantage with respect to tunnel FETs is that only an n-type or p-type doping is required to fabricate the device. In order to demonstrate the device concept and to discuss the underlying physics and the design options, we study through abinitio and full-quantum transport simulations a possible implementation that exploits two recently reported 2D materials.

### Asymmetric electrocaloric effects in PbSc0.5Ta0.5O3 on field application and removal

Electrically driven thermal changes in PbSc0.5Ta0.5O3 bulk ceramics are investigated using temperature and electric-field dependent differential scanning calorimetry and infrared thermometry. On first application and removal of electric field, we find asymmetries in the magnitude of isothermal entropy change $\Delta$ S and adiabatic temperature change $\Delta$ T, due to hysteresis. On subsequent field cycling, we find further asymmetries in the magnitude of $\Delta$ T due to non-linearity in the isofield legs of entropy-temperature plots.

### Determination of the spin orientation of helical electrons in monolayer WTe2

Monolayer WTe2 is predicted to be a quantum spin Hall insulator (QSHI) and electron transport along its edges has been experimentally observed. However, the 'smoking gun' of QSHI, spin momentum locking of the edge electrons, has not been experimentally demonstrated. We propose a model to establish the relationship between the anisotropic magnetoresistance (AMR) and spin orientation of the helical electrons in WTe2. Based on the predictions of the model, angular dependent magnetoresistance measurements were carried out. The experimental results fully supported the model and the spin orientation of the helical edge electrons was determined. Our results not only demonstrate that WTe2 is indeed a QSHI, but also suggest a convenient method to determine the spin orientation of other QSHIs.

### Collisionless sound of bosonic superfluids in lower dimensions

The superfluidity of low-temperature bosons is well established in the collisional regime. In the collisionless regime, however, the presence of superfluidity is not yet fully clarified, in particular in lower spatial dimensions. Here we compare the Vlasov-Landau equation, which does not take into account the superfluid nature of the bosonic system, with the Andreev-Khalatnikov equations, which instead explicitly contain a superfluid velocity. We show that recent experimental data of the sound mode in a two-dimensional collisionless Bose gas of $^{87}$Rb atoms are in good agreement with both theories but the sound damping is better reproduced by the Andreev-Khalatnikov equations below the Berezinskii-Kosterlitz-Thouless critical temperature $T_c$ while above $T_c$ the comparison is not conclusive. For one dimensional bosonic fluids, where experimental data are not yet available, we find larger differences between the sound velocities predicted by the two transport theories and, also in this case, the existence of a superfluid velocity reduces the sound damping.

### Gaussian time-dependent variational principle for the finite-temperature anharmonic lattice dynamics

The anharmonic lattice is a representative example of an interacting bosonic many-body system. The self-consistent harmonic approximation has proven versatile for the study of the equilibrium properties of anharmonic lattices. However, the study of dynamical properties therewithin resorts to an ansatz, whose validity has not yet been theoretically proven. Here, we apply the time-dependent variational principle, a recently emerging useful tool for studying the dynamic properties of interacting many-body systems, to the anharmonic lattice Hamiltonian at finite temperature using the Gaussian states as the variational manifold. We derive an analytic formula for the position-position correlation function and the phonon self-energy, proving the dynamical ansatz of the self-consistent harmonic approximation. Our work expands the range of applicability of time-dependent variational principle to first-principles lattice Hamiltonians and lays the groundwork for the study of dynamical properties of the anharmonic lattice using a fully variational framework.

### Production and characterization of a fragmented spinor Bose-Einstein condensate

Understanding the ground state of many-body fluids is a central question of statistical physics. Usually for weakly interacting Bose gases, most particles occupy the same state, corresponding to a Bose--Einstein condensate. However, another scenario may occur with the emergence of several, macroscopically populated single-particle states. The observation of such fragmented states remained elusive so far, due to their fragility to external perturbations. Here we produce a 3-fragment condensate for a spin 1 gas of $\sim 100$ atoms, with anti-ferromagnetic interactions and vanishing collective spin. Using a spin-resolved detection approaching single-atom resolution, we show that the reconstructed many-body state is quasi-pure, while one-body observables correspond to a mixed state. Our results highlight the interplay between symmetry and interaction to develop entanglement in a quantum system.

### A colloquium on the variational method applied to excitons in 2D materials

In this colloquium, we review the research on excitons in van der Waals heterostructures from the point of view of variational calculations. We first make a presentation of the current and past literature, followed by a discussion on the connections between experimental and theoretical results. In particular, we focus our review of the literature on the absorption spectrum and polarizability, as well as the Stark shift and the dissociation rate. Afterwards, we begin the discussion of the use of variational methods in the study of excitons. We initially model the electron-hole interaction as a soft-Coulomb potential, which can be used to describe interlayer excitons. Using an \emph{ansatz}, based on the solution for the two-dimensional quantum harmonic oscillator, we study the Rytova-Keldysh potential, which is appropriate to describe intralayer excitons in two-dimensional (2D) materials. These variational energies are then recalculated with a different \emph{ansatz}, based on the exact wavefunction of the 2D hydrogen atom, and the obtained energy curves are compared. Afterwards, we discuss the Wannier-Mott exciton model, reviewing it briefly before focusing on an application of this model to obtain both the exciton absorption spectrum and the binding energies for certain values of the physical parameters of the materials. Finally, we briefly discuss an approximation of the electron-hole interaction in interlayer excitons as an harmonic potential and the comparison of the obtained results with the existing values from both first--principles calculations and experimental measurements.

### Theory of optically detected spin noise in nanosystems

Theory of spin noise in low dimensional systems and bulk semiconductors is reviewed. Spin noise is usually detected by optical means, continuously measuring the rotation angle of the polarization plane of the probe beam passing through the sample. Spin noise spectra yield rich information about the spin properties of the system including, for example, $g$-factors of the charge carriers, spin relaxation times, parameters of the hyperfine interaction, spin-orbit interaction constants, frequencies and widths of the optical resonances. The review describes basic models of spin noise, methods of its theoretical description, and their relation with the experimental results. We also discuss the relation between the spin noise spectroscopy, the strong and weak quantum measurements and the spin flip Raman scattering, and analyze similar effects including manifestations of the charge, current and valley polarization fluctuations in the optical response. Possible directions for further development of the spin noise spectroscopy are outlined.

### Synthesis of BeN4 polymorphs leading to a two-dimensional material with anisotropic Dirac fermions

High pressure chemistry is known to inspire the creation of unexpected new classes of compounds with exceptional properties. However, the application of pressure is counterintuitive for the synthesis of layered van der Waals bonded compounds, and consequently, in a search for novel two-dimensional materials. Here we report the synthesis at ~90 GPa of novel beryllium polynitrides, monoclinic and triclinic BeN4. The triclinic phase, upon decompression to ambient conditions, transforms into a compound with atomic-thick BeN4 layers consisting of polyacetylene-like nitrogen chains with conjugated {\pi}-systems and Be atoms in square-planar coordination. These layers are interconnected via weak van der Waals bonds which makes their exfoliation possible. Theoretical calculations for a single BeN4 layer show the presence of Dirac points in the electronic band structure. The BeN4 layer, i.e. beryllonitrene, represents a new class of 2D materials that can be built of a metal atom and polymeric nitrogen chains, leading to a high degree of electronic structure anisotropy.

### Broadening and sharpening of the Drude peak through antiferromagnetic fluctuations

Antiferromagnetic or charge density wave fluctuations couple with light through the recently discovered {\pi}-ton contribution to the optical conductivity, and quite generically constitute the dominant vertex corrections in low-dimensional correlated electron systems. Here we study the arguably simplest version of these {\pi}-tons based on the semi-analytical random phase approximation (RPA) ladder in the transversal particle-hole channel. The vertex corrections to the optical conductivity are calculated directly for real frequencies. We validate that the RPA qualitatively reproduces the {\pi}-ton vertex corrections to the Drude peak in the Hubbard model. Depending on the temperature we find vertex corrections to broaden or sharpen the Drude peak.

### Magnetoresistance oscillation study of the half-quantum vortex in doubly connected mesoscopic superconducting cylinders of Sr2RuO4

The observation of the highly unusual half-quantum vortex (HQV) in a single crystalline superconductor excludes unequivocally the spin-singlet symmetry of the superconducting order parameter. HQVs were observed previously in mesoscopic samples of Sr2RuO4 in cantilever torque magnetometry measurements, thus providing direct evidence for spin-triplet pairing in the material. In addition, it raised important questions on HQV, including its stability and dynamics. These issues have remained largely unexplored, in particular, experimentally. We report in this paper the detection of HQVs in mesoscopic, doubly connected cylinders of single-crystalline Sr2RuO4 of a mesoscopic size and the examination of the effect of the in-plane magnetic field needed for the observation of the HQV by magnetoresistance (MR) oscillations measurements. Several distinct features found in our data, especially a dip and secondary peaks in the MR oscillations seen only in the presence of a sufficiently large in-plane magnetic field as well as a large measurement current, are linked to the formation of the HQV fluxoid state in and crossing of an Abrikosov HQV through the sample. The conclusion is drawn from the analysis of our data using a model of thermally activated vortex crossing overcoming a free-energy barrier which is modulated by the applied magnetic flux enclosed in the cylinder as well as the measurement current. Evidence for the trapping of an HQV fluxoid state in the sample was also found. Our observation of the HQV in mesoscopic Sr2RuO4 provided not only additional evidence for spin-triplet superconductivity in Sr2RuO4 but also insights into the physics of HQV, including its spontaneous spin polarization, stability, and dynamics. Our study also revealed a possible effect of the measurement current on the magnitude of the spontaneous spin polarization associated with the HQV.

### Thermal transport in$T \bar{T}$-deformed conformal field theories: from integrability to holography

In this paper we consider the energy and momentum transport in (1+1)-dimension conformal field theories (CFTs) that are deformed by an irrelevant operator $T\bar{T}$, using the integrability based generalized hydrodynamics, and holography. The two complementary methods allow us to study the energy and momentum transport after the in-homogeneous quench, derive the exact non-equilibrium steady states and calculate the Drude weights and the diffusion constants. Our analysis reveals that both the energy and the momentum Drude weights satisfy universal formulae regardless of the underlying conformal field theory. These fundamental physical insights have important consequences for our understanding of the $T\bar{T}$-deformed CFTs. First of all, they provide the first check of the $T\bar{T}$-deformed $\mathrm{AdS}_3$/$\mathrm{CFT}_2$ correspondence from the dynamical standpoint. And secondly, we are able to identify a remarkable connection between the $T\bar{T}$-deformed CFTs and reversible cellular automata.

### Observation of a non-Hermitian phase transition in an optical quantum gas

Quantum gases of light, as photons or polariton condensates in optical microcavities, are collective quantum systems enabling a tailoring of dissipation from e.g. cavity loss. This makes them a tool to study dissipative phases, an emerging subject in quantum manybody physics. Here we experimentally demonstrate a non-Hermitian phase transition of a photon Bose-Einstein condensate to a new dissipative phase, characterized by a biexponential decay of the condensate's second-order coherence. The phase transition occurs due to the emergence of an exceptional point in the quantum gas. While Bose-Einstein condensation is usually connected to ordinary lasing by a smooth crossover, the observed phase transition separates the novel, biexponential phase from both lasing and an intermediate, oscillatory condensate regime. Our findings pave the way for studies of a wide class of dissipative quantum phases, for instance in topological or lattice systems.

### Self-assembling kinetics: Accessing a new design space via differentiable statistical-physics models

The inverse problem of designing component interactions to target emergent structure is fundamental to numerous applications in biotechnology, materials science, and statistical physics. Equally important is the inverse problem of designing emergent kinetics, but this has received considerably less attention. Using recent advances in automatic differentiation, we show how kinetic pathways can be precisely designed by directly differentiating through statistical-physics models, namely free energy calculations and molecular dynamics simulations. We consider two systems that are crucial to our understanding of structural self-assembly: bulk crystallization and small nanoclusters. In each case we are able to assemble precise dynamical features. Using gradient information, we manipulate interactions among constituent particles to tune the rate at which these systems yield specific structures of interest. Moreover, we use this approach to learn non-trivial features about the high-dimensional design space, allowing us to accurately predict when multiple kinetic features can be simultaneously and independently controlled. These results provide a concrete and generalizable foundation for studying non-structural self-assembly, including kinetic properties as well as other complex emergent properties, in a vast array of systems.

### Simulating Plasmon Resonances of Gold Nanoparticles with Bipyramidal Shapes by Boundary Element Methods

Computational modeling and accurate simulations of localized surface plasmon resonance (LSPR) absorption properties are reported for gold nanobipyramids (GNBs), a class of metal nanoparticle that features highly tunable, geometrydependent optical properties. GNB bicone models with spherical tips performed best in reproducing experimental LSPR spectra while the comparison with other geometrical models provided a fundamental understanding of base shapes and tip effects on the optical properties of GNBs. Our results demonstrated the importance of averaging all geometrical parameters determined from transmission electron microscopy images to build representative models of GNBs. By assessing the performances of LSPR absorption spectra simulations based on a quasi-static approximation, we provided an applicability range of this approach as a function of the nanoparticle size, paving the way to the theoretical study of the coupling between molecular electron densities and metal nanoparticles in GNB-based nanohybrid systems, with potential applications in the design of nanomaterials for bioimaging, optics and photocatalysis.

### Locality of temperature and correlations in the presence of non-zero-temperature phase transitions

While temperature is well understood as an intensive quantity in standard thermodynamics, it is less clear whether the same holds in the presence of strong correlations, especially in the case of quantum systems, which may even display correlations with no classical analogue. The problem lies in the fact that, under the presence of strong correlations, subsystems of a system in thermal equilibrium are, in general, not described by a thermal state at the same temperature as the global system and thus one cannot simply assign a local temperature to them. However, there have been identified situations in which correlations in thermal states decay sufficiently fast so that the state of their subsystems can be very well approximated by the reduced states of equilibrium systems that are only slightly bigger than the subsystems themselves, hence allowing for a valid local definition of temperature. In this work, we address the question of whether temperature is locally well defined for a bosonic system with local interactions that undergoes a phase transition at non-zero temperature. We consider a three-dimensional bosonic model in the grand canonical state and verify that a certain form of locality of temperature holds regardless of the temperature, and despite the presence of infinite-range correlations at and below the critical temperature of the phase transition.

### Link inference of noisy delay-coupled networks: Machine learning and opto-electronic experimental tests

We devise a machine learning technique to solve the general problem of inferring network links that have time-delays. The goal is to do this purely from time-series data of the network nodal states. This task has applications in fields ranging from applied physics and engineering to neuroscience and biology. To achieve this, we first train a type of machine learning system known as reservoir computing to mimic the dynamics of the unknown network. We formulate and test a technique that uses the trained parameters of the reservoir system output layer to deduce an estimate of the unknown network structure. Our technique, by its nature, is non-invasive, but is motivated by the widely-used invasive network inference method whereby the responses to active perturbations applied to the network are observed and employed to infer network links (e.g., knocking down genes to infer gene regulatory networks). We test this technique on experimental and simulated data from delay-coupled opto-electronic oscillator networks. We show that the technique often yields very good results particularly if the system does not exhibit synchrony. We also find that the presence of dynamical noise can strikingly enhance the accuracy and ability of our technique, especially in networks that exhibit synchrony.

### [66] 2010.15292

Interactions are essential for the creation of correlated quantum many-body states. While two-body interactions underlie most natural phenomena, three- and four-body interactions are important for the physics of nuclei [1], exotic few-body states in ultracold quantum gases [2], the fractional quantum Hall effect [3], quantum error correction [4], and holography [5, 6]. Recently, a number of artificial quantum systems have emerged as simulators for many-body physics, featuring the ability to engineer strong interactions. However, the interactions in these systems have largely been limited to the two-body paradigm, and require building up multi-body interactions by combining two-body forces. Here, we demonstrate a pure N-body interaction between microwave photons stored in an arbitrary number of electromagnetic modes of a multimode cavity. The system is dressed such that there is collectively no interaction until a target total photon number is reached across multiple distinct modes, at which point they interact strongly. The microwave cavity features 9 modes with photon lifetimes of $\sim 2$ ms coupled to a superconducting transmon circuit, forming a multimode circuit QED system with single photon cooperativities of $\sim10^9$. We generate multimode interactions by using cavity photon number resolved drives on the transmon circuit to blockade any multiphoton state with a chosen total photon number distributed across the target modes. We harness the interaction for state preparation, preparing Fock states of increasing photon number via quantum optimal control pulses acting only on the cavity modes. We demonstrate multimode interactions by generating entanglement purely with uniform cavity drives and multimode photon blockade, and characterize the resulting two- and three-mode W states using a new protocol for multimode Wigner tomography.

### Exploring Generative Adversarial Networks for Image-to-Image Translation in STEM Simulation

The use of accurate scanning transmission electron microscopy (STEM) image simulation methods require large computation times that can make their use infeasible for the simulation of many images. Other simulation methods based on linear imaging models, such as the convolution method, are much faster but are too inaccurate to be used in application. In this paper, we explore deep learning models that attempt to translate a STEM image produced by the convolution method to a prediction of the high accuracy multislice image. We then compare our results to those of regression methods. We find that using the deep learning model Generative Adversarial Network (GAN) provides us with the best results and performs at a similar accuracy level to previous regression models on the same dataset. Codes and data for this project can be found in this GitHub repository, https://github.com/uw-cmg/GAN-STEM-Conv2MultiSlice.

### Quasi-Locality Bounds for Quantum Lattice Systems. Part II. Perturbations of Frustration-Free Spin Models with Gapped Ground States

We study the stability with respect to a broad class of perturbations of gapped ground state phases of quantum spin systems defined by frustration-free Hamiltonians. The core result of this work is a proof using the Bravyi-Hastings-Michalakis (BHM) strategy that under a condition of Local Topological Quantum Order, the bulk gap is stable under perturbations that decay at long distances faster than a stretched exponential. Compared to previous work we expand the class of frustration-free quantum spin models that can be handled to include models with more general boundary conditions, and models with discrete symmetry breaking. Detailed estimates allow us to formulate sufficient conditions for the validity of positive lower bounds for the gap that are uniform in the system size and that are explicit to some degree. We provide a survey of the BHM strategy following the approach of Michalakis and Zwolak, with alterations introduced to accommodate more general than just periodic boundary conditions and more general lattices. We express the fundamental condition known as LTQO by means of the notion of indistinguishability radius, which we introduce. Using the uniform finite-volume results we then proceed to study the thermodynamic limit. We first study the case of a unique limiting ground state and then also consider models with spontaneous breaking of a discrete symmetry. In the latter case, LTQO cannot hold for all local observables. However, for perturbations that preserve the symmetry, we show stability of the gap and the structure of the broken symmetry phases. We prove that the GNS Hamiltonian associated with each pure state has a non-zero spectral gap above the ground state.

### Magnifying quantum phase fluctuations with Cooper-pair pairing

Remarkably, complex assemblies of superconducting wires, electrodes, and Josephson junctions are compactly described by a handful of collective phase degrees of freedom that behave like quantum particles in a potential. The inductive wires contribute a parabolic confinement, while the tunnel junctions add a cosinusoidal corrugation. Usually, the ground state wavefunction is localized within a single potential well -- that is, quantum phase fluctuations are small -- although entering the regime of delocalization holds promise for metrology and qubit protection. A direct route is to loosen the inductive confinement and let the ground state phase spread over multiple Josephson periods, but this requires a circuit impedance vastly exceeding the resistance quantum and constitutes an ongoing experimental challenge. Here we take a complementary approach and fabricate a generalized Josephson element that can be tuned in situ between one- and two-Cooper-pair tunneling, doubling the frequency of the corrugation and thereby magnifying the number of wells probed by the ground state. We measure a tenfold suppression of flux sensitivity of the first transition energy, implying a twofold increase in the vacuum phase fluctuations.

### Bosonic and fermionic Gaussian states from Kähler structures

We show that bosonic and fermionic Gaussian states (also known as "squeezed coherent states") can be uniquely characterized by their linear complex structure $J$ which is a linear map on the classical phase space. This extends conventional Gaussian methods based on covariance matrices and provides a unified framework to treat bosons and fermions simultaneously. Pure Gaussian states can be identified with the triple $(G,\Omega,J)$ of compatible K\"ahler structures, consisting of a positive definite metric $G$, a symplectic form $\Omega$ and a linear complex structure $J$ with $J^2=-1\!\!1$. Mixed Gaussian states can also be identified with such a triple, but with $J^2\neq -1\!\!1$. We apply these methods to show how computations involving Gaussian states can be reduced to algebraic operations of these objects, leading to many known and some unknown identities. This provides one of the most comprehensive comparisons of bosonic and fermionic Gaussian states in the literature.

### Quantum signatures of chaos in a cavity-QED-based stimulated Raman adiabatic passage

A nonlinear stimulated Raman adiabatic passage (STIRAP) is a fascinating physical process that dynamically explores chaotic and non-chaotic phases. In a recent paper Phys. Rev. Res. 2, 042004 (R) (2020), such a phenomenon is realized in a cavity-QED platform. There, the emergence of chaos and its impact on STIRAP efficiency are mainly demonstrated in the semiclassical limit. In the present paper I treat the problem in a fully quantum many-body framework. With the aim of extracting quantum signatures of a classically chaotic system, it is shown that an out-of-time-ordered correlator (OTOC) measure precisely captures chaotic/non-chaotic features of the system. The prediction by OTOC is in precise matching with classical chaos quantified by Lyapunov exponent (LE). Furthermore, it is shown that the quantum route corresponding to the semiclassical followed state encounters a dip in single-particle purity within the chaotic phase, depicting a consequence of chaos. A dynamics through the chaotic phase is associated with spreading of many-body quantum state and an irreversible increase in the number of participating adiabatic eigenstates.

### Nuclear scattering configurations of onia in different frames

In the scattering of a small onium off a large nucleus at high center-of-mass energies, when the parameters are set in such a way that the cross section at fixed impact parameter is small, events are triggered by rare partonic fluctuations of the onium, which are very deformed with respect to typical configurations. Using the color dipole picture of high-energy interactions in quantum chromodynamics, in which the quantum states of the onium are represented by sets of dipoles generated by a branching process, we describe the typical scattering configurations as seen from different reference frames, from the restframe of the nucleus to frames in which the rapidity is shared between the projectile onium and the nucleus. We show that taking advantage of the freedom to select a frame in the latter class makes possible to derive complete asymptotic expressions for some boost-invariant quantities, beyond the total cross section, from a procedure which leverages the limited available knowledge on the properties of the solutions to the Balitsky-Kovchegov equation that governs the rapidity-dependence of total cross sections. We obtain in this way an analytic expression for the rapidity-distribution of the first branching of the slowest parent dipole of the set of those which scatter. This distribution provides an estimator of the correlations of the interacting dipoles, and is also known to be related to the rapidity-gap distribution in diffractive dissociation, an observable measurable at a future electron-ion collider. Furthermore, our result may be formulated as a more general conjecture, that we expect to hold true for any one-dimensional branching random walk model, on the branching time of the most recent common ancestor of all the particles that end up to the right of a given position.

### Localized dynamics following a quantum quench in a non-integrable system: An example on the sawtooth ladder

Motivated by the recent discovery of ergodicity breaking in geometrically frustrated systems, we study the quench dynamics of interacting hardcore bosons on a sawtooth ladder. We identify a set of initial states for which this system exhibits characteristic signatures of localization like initial state memory retention and slow growth of entanglement entropy for a wide parameter regime. Remarkably, this localization persists even when the many-body spectrum is thermalizing. We argue that the localized dynamics originates from an interaction induced quantum interference. Our results show that the sawtooth ladder can be a fertile platform for realizing non-equilibrium quantum states of matter.

### $T{\overline T}$ deformations and the width of fundamental particles

We provide a simple geometric meaning for deformations of so-called $T{\overline T}$ type in relativistic and non-relativistic systems. Deformations by the cross products of energy and momentum currents in integrable quantum field theories are known to modify the thermodynamic Bethe ansatz equations by a "CDD factor". In turn, CDD factors may be interpreted as additional, fixed shifts incurred in scattering processes: a finite width added to the fundamental particles (or, if negative, to the free space between them). We suggest that this physical effect is a universal way of understanding $T{\overline T}$ deformations, both in classical and quantum systems. We first show this in non-relativistic systems, with particle conservation and translation invariance, using the deformation formed out of the densities and currents of particles and momentum. This holds at the level of the equations of motion, and for any interaction potential, integrable or not. We then argue, and show by similar techniques in free relativistic particle systems, that $T\overline T$ deformations of relativistic systems produce the equivalent phenomenon, accounting for length contractions. We also show that, in both the relativistic and non-relativistic cases, the width of particles is equivalent to a state-dependent change of metric, where the distance function discounts the particles' widths, or counts the additional free space. This generalises and explains the known field-dependent coordinate change describing $T\overline T$ deformations. The results connect such deformations with generalised hydrodynamics, where the relations between scattering shifts, widths of particles and state-dependent changes of metric have been established.

### Design of self-adaptive oscillating neurons using electrically reconfigurable skyrmion lattices

Taking inspiration from the brain, neuromorphic computing promises to actualize the transformative potential of Artificial Intelligence (AI) by providing a path for ultra-low power AI implementation. Moreover, mimicking the complex and advanced properties of the brain can deliver a more powerful form of computation than is currently available. Here, we design and simulate a novel artificial neuron that incorporates two advanced neural behaviors: oscillatory dynamics and neuromodulation. Neuromodulation is the self-adaptive ability of a neuron to regulate its dynamics in response to its environment and contextual cues. The artificial neuron is implemented with a lattice of five magnetic skyrmions in a bilayer of insulating thulium iron garnet (TmIG) and platinum (Pt). The oscillatory dynamics of the coupled skyrmions has a multi-frequent spectrum which provides the neuron with a rich basis for information representation. Neuromodulation is enabled by the reconfigurability of the skyrmion lattice: individual skyrmions can be manipulated by electrical currents to change their arrangement in the lattice, which shifts the resonant frequencies and modulates the amplitudes of oscillatory outputs of the neuron in response to the same external excitation. Bio-mimicking dynamics such as bursting are shown. The results can be used to implement advanced neuromorphic applications including burst-coding, motion detection, cognition, brain-machine interfaces and attention-based learning.

### Storing short single-photon-level optical pulses in Bose-Einstein condensates for high-performance quantum memory

Large-scale quantum networks require quantum memories featuring long-lived storage of non-classical light together with efficient, high-speed and reliable operation. The concurrent realization of these features is challenging due to inherent limitations of matter platforms and light-matter interaction protocols. Here, we propose an approach to overcome this obstacle, based on the implementation of the Autler-Townes-splitting (ATS) quantum-memory protocol on a Bose-Einstein condensate (BEC) platform. We demonstrate a proof-of-principle of this approach by storing short pulses of single-photon-level light as a collective spin-excitation in a rubidium BEC. For 20 ns long-pulses, we achieve an ultra-low-noise memory with an efficiency of 30% and lifetime of 15 $\mu$s. The non-adiabatic character of the ATS protocol (leading to high-speed and low-noise operation) in combination with the intrinsically large atomic densities and ultra-low temperatures of the BEC platform (offering highly efficient and long-lived storage) opens up a new avenue towards high-performance quantum memories.

### Effective field theory for hydrodynamics without boosts

We formulate the Schwinger-Keldysh effective field theory of hydrodynamics without boost symmetry. This includes a spacetime covariant formulation of classical hydrodynamics without boosts with an additional conserved particle/charge current coupled to Aristotelian background sources. We find that, up to first order in derivatives, the theory is characterised by the thermodynamic equation of state and a total of 29 independent transport coefficients, in particular, 3 hydrostatic, 9 non-hydrostatic non-dissipative, and 17 dissipative. Furthermore, we study the spectrum of linearised fluctuations around anisotropic equilibrium states with non-vanishing fluid velocity. This analysis reveals a pair of sound modes that propagate at different speeds along and opposite to the fluid flow, one charge diffusion mode, and two distinct shear modes along and perpendicular to the fluid velocity. We present these results in a new hydrodynamic frame that is linearly stable irrespective of the boost symmetry in place. This provides a unified covariant stable approach for simultaneously treating Lorentzian, Galilean, and Lifshitz fluids within an effective field theory framework and sets the stage for future studies of non-relativistic intertwined patterns of symmetry breaking.

### Momentum Entanglement for Atom Interferometry

The Standard Quantum Limit (SQL) restricts the sensitivity of atom interferometers employing unentangled ensembles. Inertially sensitive light-pulse atom interferometry beyond the SQL requires the preparation of entangled atoms in different momentum states. So far, such a source of entangled atoms that is compatible with state-of-the-art interferometers has not been demonstrated. Here, we report the transfer of entanglement from the spin degree of freedom of a Bose-Einstein condensate to well-separated momentum modes. A measurement of number and phase correlations between the two momentum modes yields a squeezing parameter of -3.1(8) dB. The method is directly applicable for a future generation of entanglement-enhanced atom interferometers as desired for tests of the Einstein Equivalence Principle and the detection of gravitational waves.