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Inference and inverse problems are closely related concepts, both fundamentally involving the deduction of unknown causes or parameters from observed data. Bayesian inference, a powerful class of methods, is often employed to solve a variety of problems, including those related to causal inference. Variational inference, a subset of Bayesian inference, is primarily used to efficiently approximate complex posterior distributions. Variational Autoencoders (VAEs), which combine variational inference with deep learning, have become widely applied across various domains. This study explores the potential of VAEs for solving inverse problems, such as Independent Component Analysis (ICA), without relying on an explicit inverse mapping process. Unlike other VAE-based ICA methods, this approach discards the encoder in the VAE architecture, directly setting the latent variables as trainable parameters. In other words, the latent variables are no longer outputs of the encoder but are instead optimized directly through the objective function to converge to appropriate values. We find that, with a suitable prior setup, the latent variables, represented by trainable parameters, can exhibit mutually independent properties as the parameters converge, all without the need for an encoding process. This approach, referred to as the Half-VAE, bypasses the inverse mapping process by eliminating the encoder. This study demonstrates the feasibility of using the Half-VAE to solve ICA without the need for an explicit inverse mapping process.

Exotic quantum phases, arising from a complex interplay of charge, spin, lattice and orbital degrees of freedom, are of immense interest to a wide research community. A well-known example of such an entangled behavior is the Jahn-Teller effect, where the lifting of orbital degeneracy proceeds through lattice distortions, often accompanied by ordering of spins and metal-insulator transitions. Static distortions, including cooperative behavior, have been associated with colossal magneto-resistance, multiferroicity, high-$T_\mathrm{C}$ superconductivity and other correlated phenomena. Realizations of the dynamic Jahn-Teller effect, on the other hand, are scarce since the preservation of vibronic symmetries requires subtle tuning of the local environment. Here we demonstrate that a highly-symmetrical 5d$^1$ double perovskite Ba$_2$MgReO$_6$, comprising of a 3D array of isolated ReO$_6$ octahedra, fulfils these requirements, resulting in a unique case of a dynamic Jahn-Teller system with strong spin-orbit coupling. Thermodynamic and resonant inelastic x-ray scattering experiments undoubtedly show that the Jahn-Teller instability leads to a ground-state doublet, invoking a paradigm shift for this family of compounds. The restoration of vibronic degrees of freedom arises from a quantum-mechanical zero-point motion, as revealed by detailed quantum chemistry calculations. The dynamic state of ReO$_6$ octahedra persists down to the lowest temperatures, where a multipolar order sets in, allowing for investigations of the interplay between a dynamic JT effect and strongly correlated electron behavior.

In the rich phases of van der Waals (vdW) materials featuring intertwined electronic order and collective phenomena, characterizing elementary dynamics that entail the low-energy Hamiltonian and electronic degrees of freedom is of paramount importance. Here we performed resonant inelastic X-ray scattering (RIXS) to elaborate the spin-orbital ground and excited states of the vdW antiferromagnetic insulator FePS$_{3}$, as well as their relation to magnetism. We observed the spectral enhancement of spin-orbital multiplet transitions about $\sim$ 100 and $\sim$ 220 meV, as well as quasielastic response, when entering the zig-zag antiferromagnetic phase, where the spectral changes develop an order-parameter-like evolution with temperature. By comparing with ligand field theory calculations, we discovered the essential role of trigonal lattice distortion and negative metal-ligand charge-transfer to account for these emergent excitations. Such spectral profiles are further examined upon confinement by mechanical exfoliation. We reveal their spectral robustness down to the few atomic layer limit, in accordance with the persistent antiferromagnetic state previously reported in optical measurements. Our study demonstrates the versatile RIXS capability that resolves magneto-crystalline anisotropy and charge-transfer energetics. These provide the crucial insight to understand how the spontaneous magnetic symmetry-breaking stabilizes in the quasi-two-dimensional limit for the vdW magnet FePS$_{3}$.

Turgor is the driving force of plant growth, making possible for roots to overcome soil resistance or for stems to counteract gravity. Maintaining a constant growth rate while avoiding the cell content dilution, which would progressively stop the inward water flux, imposes the production or import of osmolytes in proportion to the increase of volume. We coin this phenomenon stationary osmoregulation. The article explores the quantitative consequences of this hypothesis on the interaction of a cylindrical cell growing axially against an obstacle. An instantaneous axial compression of a pressurized cylindrical cell generates a force and a pressure jump which both decrease toward a lower value once water has flowed out of the cell to reach the water potential equilibrium. In a first part, the article derives analytical formula for these force and over-pressure both before and after relaxation. In a second part, we describe how the coupling of the Lockhart's growth law with the stationary osmoregulation hypothesis predicts a transient slowdown in growth due to contact before a re-acceleration in growth. We finally compare these predictions with the output of an elastic growth model which ignores the osmotic origin of growth: models only match in the early phase of contact for high stiffness obstacle.

Strongly-correlated transition-metal oxides are widely known for their various exotic phenomena. This is exemplified by rare-earth nickelates such as LaNiO$_{3}$, which possess intimate interconnections between their electronic, spin, and lattice degrees of freedom. Their properties can be further enhanced by pairing them in hybrid heterostructures, which can lead to hidden phases and emergent phenomena. An important example is the LaNiO$_{3}$/LaTiO$_{3}$ superlattice, where an interlayer electron transfer has been observed from LaTiO$_{3}$ into LaNiO$_{3}$ and is predicted to result in a high-spin state. However, macroscopic emergence of magnetic order has so far not been observed. Here, by using muon spin rotation, x-ray absorption, and resonant inelastic x-ray scattering, we present direct evidence of an emergent antiferromagnetic order with high magnon energy and exchange interactions at the LaNiO$_{3}$/LaTiO$_{3}$ interface. As the magnetism is purely interfacial, a single LaNiO$_{3}$/LaTiO$_{3}$ interface can essentially behave as an atomically thin quasi-two-dimensional antiferromagnet, potentially allowing its technological utilisation in advanced spintronic devices. Furthermore, its strong quasi-two-dimensional magnetic correlations and orbitally-polarized planar ligand holes make its electronic and magnetic configurations resemble the precursor states of superconducting cuprates and nickelates, but with an S $\rightarrow$ 1 spin state instead., Comment: 41 pages, 13 figures

The occurrence of charge-density-wave (CDW) order is a common thread in the phase diagram of cuprate high-transition-temperature ($T_c$) superconductors. In iron-based superconductors (FeSCs), nematic order and fluctuations play a decisive role in driving other emergent orders. CDW order has been observed by scanning tunneling microscopy for various FeSCs such as FeSe thin films, uniaxially strained LiFeAs, and tetragonal FeSe$_{0.81}$S$_{0.19}$. However, it remains elusive if the CDW in these materials is a bulk phenomenon as well as if and how it intertwines with the electronic nematicity. Using energy-resolved resonant X-ray scattering at the Fe-L$_3$ edge, we report the discovery of a local-strain-induced incommensurate isotropic CDW order in FeSe$_{0.82}$S$_{0.18}$. A highly anisotropic CDW response under uniaxial strain unambiguously manifests that the CDW is directly coupled to the nematicity. Transforming part of Fe$^{2+}$ to Fe$^{3+}$ on the surface of FeSe$_{1-x}$S$_{x}$ reveals that the same isotropic CDW can be induced, enhanced, and stabilized in the whole nematic regime measured ($x=0-0.19$). As Fe$^{3+}$ can create local lattice distortions on the surface, the CDW could arise from the interaction between the local strain around Fe$^{3+}$ and the nematic electron correlations. Our experimental observation of a local-strain-induced CDW gives vital information for understanding the interplay between electron correlations and the electronic nematicity in FeSCs., Comment: 7 pages, 4 figures

Relativistic positron sources with high spin polarization have important applications in nuclear and particle physics and many frontier fields. However, it is challenging to produce dense polarized positrons. Here we present a simple and effective method to achieve such a positron source by directly impinging a relativistic high-density electron beam on the surface of a solid target. During the interaction, a strong return current of plasma electrons is induced and subsequently asymmetric quasistatic magnetic fields as high as megatesla are generated along the target surface. This gives rise to strong radiative spin flips and multiphoton processes, thus leading to efficient generation of copious polarized positrons. With three-dimensional particle-in-cell simulations, we demonstrate the production of a dense highly-polarized multi-GeV positron beam with an average spin polarization above 40% and nC-scale charge per shot. This offers a novel route for the studies of laserless strong-field quantum electrodynamics physics and for the development of high-energy polarized positron sources.

Emergent quasiparticles with a Dirac dispersion in condensed matter systems can be described by the Dirac equation for relativistic electrons, in analogy with Dirac particles in high-energy physics. For example, electrons with a Dirac dispersion have been intensively studied in electronic systems such as graphene and topological insulators. However, charge is not a prerequisite for Dirac fermions, and the emergence of Dirac fermions without charge degree of freedom has been theoretically predicted to be realized in Dirac quantum spin liquids. These quasiparticles carry a spin of 1/2 but are charge-neutral, and so are called spinons. Here we show that the spin excitations of a kagome antiferromagnet, YCu$_3$(OD)$_6$Br$_2$[Br$_{0.33}$(OD)$_{0.67}$], are conical with a spin continuum inside, which is consistent with the convolution of two Dirac spinons. The predictions of a Dirac spin liquid model with a spinon velocity obtained from the spectral measurements are in agreement with the low-temperature specific heat of the sample. Our results thus provide spectral evidence for the Dirac quantum spin liquid state emerging in this kagome lattice antiferromagnet. However, the locations of the conical spin excitations differ from those calculated by the nearest neighbor Heisenberg model, suggesting the Dirac spinons have an unexpected origin., Comment: 6 pages, 4 figures

A fully stabilized soliton microcomb is critical for many applications of optical frequency comb based on microresonators. However, the current approaches for full frequency stabilization require either external acousto-optic or electro-optic devices or auxiliary lasers and multiple phase-locked loops, which compromises the convenience of the system. This study explores a compact atomic referenced fully stabilized soliton microcomb that directly uses a rubidium atomic optical frequency reference as the pump source, and complements the repetition rate (7.3 GHz) of the soliton microcomb was phase-locked to an atomic-clock-stabilized radio frequency (RF) reference by mechanically tuning the resonance of the optical resonator. The results demonstrate that the stability of the comb line (0.66 THz away from the pump line) is consistent with that of the Rb87 optical reference, attaining a level of approximately 4 Hz @100 s, corresponding to the frequency stability of 2E-14 @100 s. Furthermore,the frequency reproducibility of the comb line was evaluated over six days and it was discovered that the standard deviation (SD) of the frequency of the comb line is 10 kHz, resulting in a corresponding absolute deviation uncertainty of 1.3E-10, which is technically limited by the locking range of the soliton repetition rate. The proposed method gives a low-power and compact solution for fully stabilized soliton micorcombs., Comment: 6 pages, 5 figures

The roles of the fine-structure intramanifold resonances to the Zeeman shifts caused by the blackbody radiation (BBRz shifts) in the optical clock transitions are analyzed. The clock frequency measurement in the $^1S_0-^3P_0$ clock transition of the singly charged aluminium ion (Al$^+$) has already been reached the $10^{-19}$ level at which the BBRz effect can be significant in determining the uncertainty. In view of this, we probe first the BBRz shift in this transition rigorously and demonstrate the importance of the contributions from the intramanifold resonances explicitly. To carry out the analysis, we determine the dynamic magnetic dipole (M1) polarizabilities of the clock states over a wide range of angular frequencies by employing two variants of relativistic many-body methods. This showed the BBRz shift is highly suppressed due to blue-detuning of the BBR spectrum to the $^3P_0-^3P_1$ fine-structure intramanifold resonance in Al$^+$ and it fails to follow the usually assumed static M1 polarizability limit in the estimation of the BBRz shift. The resonance also leads to a reversal behavior of the temperature dependence and a cancellation in the shift. After learning this behavior, we extended our analyses to other optical clocks and found that these shifts are of the order of micro-hertz leading to fractional shifts in the clock transitions at the $10^{-20}$ level or below.

We use resonant inelastic X-ray scattering (RIXS) at the Fe-L$_3$ edge to study the spin excitations of uniaxial-strained and unstrained FeSe$_{1-x}$S$_{x}$ ($0\leq x\leq0.21$) samples. The measurements on unstrained samples reveal dispersive spin excitations in all doping levels, which show only minor doping dependence in energy dispersion, lifetime, and intensity, indicating that high-energy spin excitations are only marginally affected by sulfur doping. RIXS measurements on uniaxial-strained samples reveal that the high-energy spin-excitation anisotropy observed previously in FeSe is also present in the doping range $0< x\leq0.21$ of FeSe$_{1-x}$S$_{x}$. The spin-excitation anisotropy persists to a high temperature up to $T>200$ K in $x=0.18$ and reaches a maximum around the nematic quantum critical doping ($x_c\approx0.17$). Since the spin-excitation anisotropy directly reflects the existence of nematic spin correlations, our results indicate that high-energy nematic spin correlations pervade the regime of nematicity in the phase diagram and are enhanced by the nematic quantum criticality. These results emphasize the essential role of spin fluctuations in driving electronic nematicity and open the door for uniaxial strain tuning of spin excitations in quantum materials hosting strong magnetoelastic coupling and electronic nematicity., Comment: 6 pages, 4 figures, supplemental materials uploaded

Calcium fluoride (CaF$_2$) crystalline whispering gallery mode resonators (WGMRs) exhibit ultrahigh intrinsic quality factors and a low power anomalous dispersion in the communication and mid-infrared bands, making them attractive platforms for microresonator-based comb generation. However, their unique negative thermo-optic effects pose challenges when achieving thermal equilibrium. To our knowledge, our experiments serve as the first demonstration of soliton microcombs in Q > 109 CaF$_2$ WGMRs. We observed soliton mode-locking and bidirectional switching of soliton numbers caused by the negative thermo-optic effects. Additionally, various soliton formation dynamics are shown, including breathing and vibrational solitons, which can be attributed to thermo-photomechanical oscillations. Thus, our results enrich the soliton generation platform and provide a reference for generating solitons from WGMRs that comprise other materials with negative thermo-optic effects. In the future, the ultrahigh quality factor of CaF$_2$ crystal cavities may enable the generation of sub-milliwatt-level broad-spectrum soliton combs., Comment: 4 pages,5 pictures,description of soliton generation in a calcium fluoride whisper gallery mode microresonators with negative thermo-optical effect,ready for publication in optics letter

With the emphasis on healthcare, early childhood education, and fitness, non-invasive measurement and recognition methods have received more attention. Pressure sensing has been extensively studied due to its advantages of simple structure, easy access, visualization application, and harmlessness. This paper introduces a smart pressure e-mat (SPeM) system based on a piezoresistive material Velostat for human monitoring applications, including sleeping postures, sports, and yoga recognition. After a subsystem scans e-mat readings and processes the signal, it generates a pressure image stream. Deep neural networks (DNNs) are used to fit and train the pressure image stream and recognize the corresponding human behavior. Four sleeping postures and five dynamic activities inspired by Nintendo Switch Ring Fit Adventure (RFA) are used as a preliminary validation of the proposed SPeM system. The SPeM system achieves high accuracies on both applications, which demonstrates the high accuracy and generalization ability of the models. Compared with other pressure sensor-based systems, SPeM possesses more flexible applications and commercial application prospects, with reliable, robust, and repeatable properties.