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Creation and control of topological complex excitations play crucial roles in both fundamental physics and modern information science. Torons are a sophisticated class of 3D chiral polar topological structures with both skyrmionic quasiparticle textures and monopole point defects, so far only observed in liquid crystal nonpolar models. Here, we experimentally construct torons with the photonic spin of vector structured light and demonstrate the topological phase transitions among diverse topological states: torons, hopfions, skyrmioniums and monopole pairs. We can also continually tune the toron's chirality and the helical spin textures of emerging monopole pairs. The birth of photonic torons and tunable monopoles opens a flexible platform for studying nontrivial light-matter interaction and topological informatics.

Nonreciprocal thermophotonics, by breaking Lorentz reciprocity, exceeds current theoretical efficiency limits, unlocking opportunities to energy devices and thermal management. However, energy transfer in current systems is highly defect-sensitive. This sensitivity is further amplified at deep subwavelength scales by inevitable multi-source interactions, interface wrinkles, and manufacturing tolerances, making precise control of thermal photons increasingly challenging. Here, we demonstrate a topological one-way heat transport in a deep-subwavelength thermophotonic lattice. This one-way heat flow, driven by global resonances, is strongly localized at the geometric boundaries and exhibits exceptional robustness against imperfections and disorder, achieving nearly five orders of radiative enhancement. Our findings offer a blueprint for developing robust thermal systems capable of withstanding strong perturbations., Comment: 15 pages, 4 figures

Facial expressions are crucial to human communication, offering insights into emotional states. This study examines how specific facial features influence emotion classification, using facial perturbations on the Fer2013 dataset. As expected, models trained on data with the removal of some important facial feature experienced up to an 85% accuracy drop when compared to baseline for emotions like happy and surprise. Surprisingly, for the emotion disgust, there seem to be slight improvement in accuracy for classifier after mask have been applied. Building on top of this observation, we applied a training scheme to mask out facial features during training, motivating our proposed Perturb Scheme. This scheme, with three phases-attention-based classification, pixel clustering, and feature-focused training, demonstrates improvements in classification accuracy. The experimental results obtained suggests there are some benefits to removing individual facial features in emotion recognition tasks., Comment: 10 pages. 5 figures

Can thermal nonreciprocity improve the radiative cooling efficiency? Probably not., Comment: 12 pages, 3 figures

This paper compared physics-informed neural network (PINN), conventional neural network (NN) and traditional numerical discretization methods on solving differential equations (DEs) through literature investigation and experimental validation. We focused on the soft-constrained PINN approach and formalized its mathematical framework and computational flow for solving Ordinary DEs and Partial DEs (ODEs/PDEs). The working mechanism and its accuracy and efficiency were experimentally verified by solving typical linear and non-linear oscillator ODEs. We demonstrate that the DeepXDE-based implementation of PINN is not only light code and efficient in training, but also flexible across CPU/GPU platforms. PINN greatly reduces the need for labeled data: when the nonlinearity of the ODE is weak, a very small amount of supervised training data plus a few unsupervised collocation points are sufficient to predict the solution; in the minimalist case, only one or two training points (with initial values) are needed for first- or second-order ODEs, respectively. We also find that, with the aid of collocation points and the use of physical information, PINN has the ability to extrapolate data outside the time domain of the training set, and especially is robust to noisy data, thus with enhanced generalization capabilities. Training is accelerated when the gains obtained along with the reduction in the amount of data outweigh the delay caused by the increase in the loss function terms. The soft-constrained PINN can easily impose a physical law (e.g., conservation of energy) constraint by adding a regularization term to the total loss function, thus improving the solution performance to ODEs that obey this physical law. Furthermore, PINN can also be used for stiff ODEs, PDEs, and other types of DEs, and is becoming a favorable catalyst for the era of Digital Twins., Comment: 24 pages, 7 figures, 2 tables, etc. Ready for submission

Polarization and wavelength multiplexing are the two most widely employed techniques to improve the capacity in the metasurfaces. Existing works have pushed each technique to its individual limits. For example, the polarization multiplexing channels working at a single wavelength have been significantly increased by using noise engineering. However, it is still challenging to achieve the multiplexing limits of wavelength and polarization simultaneously. Besides, such multiplexing methods suffer from computational inefficiencies, hindering their application in tasks like image recognition that require extensive training computation. In this work, we introduce a gradient-based optimization algorithm using deep neural network (DNN) to achieve the limits of both polarization and wavelength multiplexing with high computational efficiency. We experimentally demonstrate this capability, achieving a record-breaking capacity of 15 holographic images across five wavelengths and the maximum of three independent polarization channels, as well as 18 holographic images across three wavelengths and six corelated polarization channels. Moreover, leveraging the high computational efficiency of our DNN-based method, which is well-suited for processing large datasets, we implement large-scale image recognition tasks across 36 classes encoded in a record of nine multiplexed channels (three wavelengths * three polarizations), achieving 96% classification accuracy in calculations and 91.5% in experiments. This work sets a new benchmark for high-capacity multiplexing with metasurfaces and demonstrates the power of gradient-based inverse design for realizing multi-functional optical elements.

Polarization entanglement holds significant importance for photonic quantum technologies. Recently emerging subwavelength nonlinear quantum light sources, e.g., GaP and LiNbO3 thin films, benefiting from the relaxed phase-matching constraints and volume confinement, has shown intriguing properties, such as high-dimensional hyperentanglement and robust entanglement anti-degradation. Van der Waals (vdW) NbOCl2 crystal, renowned for its superior optical nonlinearities, has emerged as one of ideal candidates for ultrathin quantum light sources [Nature 613, 53 (2023)]. However, polarization-entanglement is inaccessible in NbOCl2 crystal due to its unfavorable nonlinear susceptibility tensor. Here, by leveraging the twist-stacking degree of freedom inherently in vdW systems, we showcase the preparation of tunable polarization entanglement and quantum Bell states. Our work not only provides a new and tunable polarization-entangled vdW photon-pair source, but also introduces a new knob in engineering the entanglement state of quantum light at the nanoscale., Comment: 16 pages,4 figures

Charge-order states of broken symmetry, such as charge density wave (CDW), are able to induce exceptional physical properties, however, the precise understanding of the underlying physics is still elusive. Here, we combine fluctuational electrodynamics and density functional theory to reveal an unconventional thermophotonic effect in CDW-bearing TiSe$_2$, referred to as thermophotonic-CDW ($tp$-CDW). The interplay of plasmon polariton and CDW electron excitations give rise to an anomalous negative temperature dependency in thermal photons transport, offering an intuitive fingerprint for a transformation of the electron order. Additionally, the demonstrated nontrivial features of $tp$-CDW transition hold promise for a controllable manipulation of heat flow, which could be extensively utilized in various fields such as thermal science and electron dynamics, as well as in next-generation energy devices., Comment: 7 pages, 4 figures

We implement a stacking strategy in designing chiral metasurfaces with high rotational symmetry, enabling quasi-bound-in-the-continuum (quasi-BIC) resonances characterized by absolute chirality. The rotational symmetry allows a circularly polarized pump to be converted into a circularly polarized nonlinear signal. Meanwhile, our bilayered metasurface can be engineered to respond solely to one selected circular polarization. Consequently, integrating resonant chiral response and rotational symmetry endows a unique category of metasurfaces to upconvert any linear or unpolarized pump into a circularly polarized nonlinear signal. Our results reveal that when such a metasurface is subjected to a linearly polarized pump, the intensity ratio of the resultant circularly polarized signals varies with the order of the nonlinear process. Counterintuitively, this ratio scales as the fourth power of the local field enhancement in the second harmonic process and the second power in the third harmonic process. Our work offers a comprehensive theoretical description of the nonlinear processes in chiral structures with rotation and provides universal guidelines for designing nonlinear all-dielectric metasurfaces with a strong chiral response.

Solid-state quantum emitters are essential sources of single photons, and enhancing their emission rates is of paramount importance for applications in quantum communications, computing, and metrology. One approach is to couple quantum emitters with resonant photonic nanostructures, where the emission rate is enhanced due to the Purcell effect. Dielectric nanoantennas are promising as they provide strong emission enhancement compared to plasmonic ones, which suffer from high Ohmic loss. Here, we designed and fabricated a dielectric Fano resonator based on a pair of silicon (Si) ellipses and a disk, which supports the mode hybridization between quasi-bound-states-in-the-continuum (quasi-BIC) and Mie resonance. We demonstrated the performance of the developed resonant system by interfacing it with single photon emitters (SPEs) based on nitrogen-vacancy (NV-) centers in nanodiamonds (NDs). We observed that the interfaced emitters have a Purcell enhancement factor of ~10, with sub-ns emission lifetime and a polarization contrast of 9. Our results indicate a promising method for developing efficient and compact single-photon sources for integrated quantum photonics applications., Comment: 20 pages, 4 figures

Flexible control light field across multiple parameters is the cornerstone of versatile and miniaturized optical devices. Metasurfaces, comprising subwavelength scatterers, offer a potent platform for executing such precise manipulations. However, the inherent mutual constraints between parameters of metasurfaces make it challenging for traditional approaches to achieve full-parameter control across multiple wavelengths. Here, we propose a universal end-to-end inverse design framework to directly optimize the geometric parameter layout of meta-optics based on the target functionality of full-parameter control across multiple wavelengths. This framework employs a differentiable forward simulator integrating a neural network-based dispersive full-parameter Jones matrix and Fourier propagation to facilitate gradient-based optimization. Its superiority over sequential forward designs in dual-polarization channel color holography with higher quality and tri-polarization three-dimensional color holography with higher multiplexed capacity is showcased. To highlight the universality, we further present polarized spectral multi-information processing with six arbitrary polarizations and three wavelengths. This versatile, differentiable, system-level design framework is poised to expedite the advancement of meta-optics in integrated multi-information display, imaging, and communication, extending to multi-modal sensing applications.

Controlling and channelling light emissions from unpolarized quantum dots into specific directions with chiral polarization remains a key challenge in modern photonics. Stacked metasurface designs offer a potential compact solution for chirality and directionality engineering. However, experimental observations of directional chiral radiation from resonant metasurfaces with quantum emitters remain obscure. In this paper, we present experimental observations of unidirectional chiral emission from a twisted bi-layer metasurface via multi-dimensional control, including twist angle, interlayer distance, and lateral displacement between the top and bottom layers, as enabled by doublet alignment lithography (DAL). First, maintaining alignment, the metasurface demonstrates a resonant intrinsic optical chirality with near-unity circular dichroism of 0.94 and reflectance difference of 74%, where a high circular dichroism greater than 0.9 persists across a wide range of angles from -11 to 11 degrees. Second, engineered lateral displacement induces a unidirectional chiral resonance, resulting in unidirectional chiral emission from the quantum dots deposited onto the metasurface. Our bi-layer metasurfaces offer a universal compact platform for efficient radiation manipulation over a wide angular range, promising potential applications in miniaturized lasers, grating couplers, and chiral nanoantennas., Comment: 16 pages, 4 figures

Quantum steering is the phenomenon whereby one party (Alice) proves entanglement by "steering'' the system of another party (Bob) into distinct ensembles of states, by performing different measurements on her subsystem. Here, we investigate steering in a network scenario involving $n$ parties, who each perform local measurements on part of a global quantum state, that is produced using only two-party entangled states, and mixing with ancillary separable states. We introduce three scenarios which can be straightforwardly implemented in standard quantum optics architecture, which we call random $\frac{n}{2}$-pair entanglement, random pair entanglement and semi-random pair entanglement. We study steerability of the states across two-party marginals which arise in the three scenarios, and derive analytically the necessary and sufficient steering criteria for different sets of measurement settings. Strikingly, using the semi-random pair entanglement construction, one party can steer every one of the $n-1$ other parties, for arbitrarily large $n$, using only two measurements. Finally, exploiting symmetry, we study various small network configurations (three or four parties) in the three scenarios, under different measurements and produced by different two-party entangled states., Comment: 11 pages, 9 figures, Close to published version

Cavity optomechanical (COM) sensors, featuring efficient light-motion couplings, have been widely used for ultra sensitive measurements of various physical quantities ranging from displacements to accelerations or weak forces. Previous works, however, have mainly focused on reciprocal COM systems. Here, we propose how to further improve the performance of quantum COM sensors by breaking reciprocal symmetry in purely quantum regime. Specifically, we consider a spinning COM resonator and show that by selectively driving it in opposite directions, highly nonreciprocal optical squeezing can emerge, which in turn provides an efficient way to surpass the standard quantum limit that otherwise exists in conventional reciprocal devices. Our work confirms that breaking reciprocal symmetry, already achieved in diverse systems well beyond spinning systems, can serve as a new strategy to further enhance the abilities of advanced quantum sensors, for applications ranging from testing fundamental physical laws to practical quantum metrology., Comment: 7 pages,3 figures

An ancient and counterintuitive phenomenon know as the Mpemba effect (water can cool faster when initially heated up) showcases the critical role of initial conditions in relaxation processes. How to realize and utilize this effect for speeding up relaxation is an important but challenging task in purely quantum system till now. Here, we report the first experiment, as far as we know,about the strong Mpemba effect in a single trapped ion system in which an exponentially expedited relaxation in time is observed by preparing an optimal initial state with no excitation of the slowest decaying mode. Also, we find that the condition of realizing such effect coincides with the Liouvillian exceptional point, featuring the coalescence of both the eigenvalues and the eigenmodes of the system. Our work provides an efficient strategy to exponentially accelerate relaxations of quantum system to their stationary state, and suggests a link unexplored yet between the Mpemba effect and the non-Hermitian physics. It could open up the door to engineer a wide range of dissipative quantum systems by utilizing the anomalous Mpemba effect, for applications in quantum simulation and quantum information processing., Comment: Accepted by Nature Communications

Smith-Purcell radiation (SPR) occurs when an electron skims above a spatial grating, but the fixed momentum compensation from the static grating imposes limitations on the emission wavelength. It has been discovered that a temporally periodic system can provide energy compensation to generate light emissions in free space. Here, we introduce temporal SPR (t-SPR) emerging from a time grating and propose a generalized t-SPR dispersion equation to predict the relationship between radiation frequency, direction, electron velocity, modulation period, and harmonic orders. Compared to conventional SPR, t-SPR can: 1) Provide a versatile platform for manipulating SPR emission through temporal modulation (e.g., period, amplitude, wave shape). 2) Exhibit strong robustness to the electron-grating separation, alleviating the constraints associated with extreme electron near-field excitation. 3) Introduce additional energy channels through temporal modulation, enhancing and amplifying emission., Comment: 6 pages, 3 figures

Solid-state quantum emitters coupled to integrated photonic nanostructures are quintessential for exploring fundamental phenomena in cavity quantum electrodynamics and widely employed in photonic quantum technologies such as non-classical light sources, quantum repeaters, and quantum transducers, etc. One of the most exciting promises from integrated quantum photonics is the potential of scalability that enables massive productions of miniaturized devices on a single chip. In reality, the yield of efficient and reproducible light-matter couplings is greatly hindered by the spectral and spatial mismatches between the single solid-state quantum emitters and confined or propagating optical modes supported by the photonic nanostructures, preventing the high-throughput realization of large-scale integrated quantum photonic circuits for more advanced quantum information processing tasks. In this work, we introduce the concept of hyperspectral imaging in quantum optics, for the first time, to address such a long-standing issue. By exploiting the extended mode with a unique dispersion in a 1D planar cavity, the spectral and spatial information of each individual quantum dot in an ensemble can be accurately and reliably extracted from a single wide-field photoluminescence image with super-resolutions. With the extracted quantum dot positions and emission wavelengths, surface-emitting quantum light sources and in-plane photonic circuits can be deterministically fabricated with a high-throughput by etching the 1D confined planar cavity into 3D confined micropillars and 2D confined waveguides. Further extension of this technique by employing an open planar cavity could be exploited for pursuing a variety of compact quantum photonic devices with expanded functionalities for large-scale integration. Our work is expected to change the landscape of integrated quantum photonic technology., Comment: 5 pages, 8 figures,comments are welcome

While conventional surface waves propagate along the surface and decay perpendicularly from the interface, the ghost surface polaritons show oblique propagation direction with respect to the interface. Here, we have discovered topologically protected ghost surface polaritons by applying the lattice transformation optics method to gyromagnetic photonic crystals. By introducing the transformation optics method to periodic systems, we develop the lattice transformation optics method to engineer the band structures and propagation directions of the surface polaritons. We show that a simple shear transformation on the square lattice can tailor the propagation directions with ease. The reversed ghost surface polariton is discovered by setting a negative shear factor. Interestingly, we find the topological invariant Chern number will change sign when the orientation of the Brillouin zone flipped during the transformation. Our findings open up new avenues for studying ghost surface polaritons and provide a general engineering method for periodic systems., Comment: 8 pages, 6 figures

Flat optics consisting of nanostructures of high-refractive-index materials produce lenses with thin form factors that tend to operate only at specific wavelengths. Recent attempts to achieve achromatic lenses uncover a trade-off between the numerical aperture (NA) and bandwidth, which limits performance. Here we propose a new approach to design high NA, broadband and polarization-insensitive multilayer achromatic metalenses (MAM). We combine topology optimization and full wave simulations to inversely design MAMs and fabricate the structures in low-refractive-index materials by two-photon polymerization lithography. MAMs measuring 20 micrometer in diameter operating in the visible range of 400-800 nm with 0.5 NA and 0.7 NA were achieved with efficiencies of up to 42%. We demonstrate broadband imaging performance of the fabricated MAM under white light, and RGB narrowband illuminations. These results highlight the potential of the 3D printed multilayer structures for realizing broadband and multi-functional meta-devices with inverse design., Comment: 37 pages, 15 figures

The distribution and verification of quantum nonlocality across a network of users is essential for future quantum information science and technology applications. However, beyond simple point-to-point protocols, existing methods struggle with increasingly complex state preparation for a growing number of parties. Here, we show that, surprisingly, multiparty loophole-free quantum steering, where one party simultaneously steers arbitrarily many spatially separate parties, is achievable by constructing a quantum network from a set of qubits of which only one pair is entangled. Using these insights, we experimentally demonstrate this type of steering between three parties with the detection loophole closed. With its modest and fixed entanglement requirements, this work introduces a scalable approach to rigorously verify quantum nonlocality across multiple parties, thus providing a practical tool towards developing the future quantum internet.

Stacking bilayer structures is an efficient way to tune the topology of polaritons in in-plane anisotropic films, e.g., by leveraging the twist angle (TA). However, the effect of another geometric parameter, film thickness ratio (TR), on manipulating the plasmon topology in bilayers is elusive. Here, we fabricate bilayer structures of WTe2 films, which naturally host in-plane hyperbolic plasmons in the terahertz range. Plasmon topology is successfully modified by changing the TR and TA synergistically, manifested by the extinction spectra of unpatterned films and the polarization dependence of the plasmon intensity measured in skew ribbon arrays. Such TR- and TA-tunable topological transitions can be well explained based on the effective sheet optical conductivity by adding up those of the two films. Our study demonstrates TR as another degree of freedom for the manipulation of plasmonic topology in nanophotonics, exhibiting promising applications in bio-sensing, heat transfer and the enhancement of spontaneous emission., Comment: 18 pages, 4 figures

In this reply, we include new experimental results and verify that the observed non-linearity in rippled-MoS$_2$ (leading to mobility kink) is an intrinsic property of a disordered system, rather than contact effects (invasive probes) or other device issues. Noting that Peng Wu's hypothesis is based on a highly ordered ideal system, transfer curves are expected to be linear, and the carrier density is assumed be constant. Wu's model is therefore oversimplified for disordered systems and neglects carrier-density dependent scattering physics. Thus, it is fundamentally incompatible with our rippled-MoS$_2$, and leads to the wrong conclusion.

Metal halide perovskite quantum dots (PQDs) have emerged as promising materials due to their exceptional photoluminescence (PL) properties. A wide range of applications could benefit from adjustable luminescence properties, while preserving the physical and chemical properties of the PQDs. Therefore, post-synthesis engineering has gained attention recently, involving the use of ion-exchange or external stimuli, such as extreme pressure, magnetic and electric fields. Nevertheless, these methods typically suffer from spectrum broadening, intensity quenching or yield multiple bands. Alternatively, photonic antennas can modify the radiative decay channel of perovskites via the Purcell effect, with the largest wavelength shift being 8 nm to date, at an expense of 5-fold intensity loss. Here, we present an optical nanoantenna array with polarization-controlled quasi-bound-states-in-the-continuum (q-BIC) resonances, which can engineer and shift the photoluminescence wavelength over a ~39 nm range and confers a 21-fold emission enhancement of FAPbI3 perovskite QDs. The spectrum is engineered in a non-invasive manner via lithographically defined antennas and the pump laser polarization at ambient conditions. Our research provides a path towards advanced optoelectronic devices, such as spectrally tailored quantum emitters and lasers., Comment: 39 pages, 4 figures in the main text and 10 figures in the supporting information

Controlling light at the nanoscale by exploiting ultra-confined polaritons - hybrid light and matter waves - in various van der Waals (vdW) materials empowers unique opportunities for many nanophotonic on-chip technologies. So far, mainstream approaches have relied interfacial techniques (e.g., refractive optics, meta-optics and moire engineering) to manipulate polariton wavefront. Here, we propose that orbital angular momentum (OAM) of incident light could offer a new degree of freedom to structure vdW polaritons. With vortex excitations, we observed a new class of accelerating polariton waves - Airy-like hyperbolic phonon polaritons (PhPs) in high-symmetry orthorhombic vdW crystal {\alpha}-MoO3. In analogous to the well-known Airy beams in free space, such Airy-like PhPs also exhibit self-accelerating, nonspreading and self-healing characteristics. Interestingly, the helical phase gradient of vortex beam leads to asymmetry excitation of polaritons, as a result, the Airy-like PhPs possess asymmetric propagation feature even with a symmetric mode, analogous to the asymmetry hyperbolic shear polaritons in low-symmetry crystals. Our finding highlights the potential of OAM to manipulate polaritons in vdW materials, which could be further extended into a variety of applications such as active structured polaritonic devices.

Planar lenses with optimized but disordered structures can focus light beyond the diffraction limit. However, these disordered structures have inevitably destroyed wide-field imaging capability, limiting their applications in microscopy. Here we introduce information entropy S to evaluate the disorder of an objective chip by using the probability of its structural deviation from standard Fresnel zone plates. Inspired by the theory of entropy change, we predict an equilibrium point S0=0.5 to balance wide-field imaging (theoretically evaluated by the Strehl ratio) and subdiffraction-limit focusing. To verify this, a NA=0.9 objective chip with a record-long focal length of 1 mm is designed with S=0.535, which is the nearest to the equilibrium point among all reported planar lenses. Consequently, our fabricated chip can focus light with subdiffraction-limit size of 0.44{\lambda} and image fine details with spatial frequencies up to 4000 lp/mm in experiment. These unprecedented performances enable ultracompact reflective confocal microscopy for superresolution imaging., Comment: 42 pages, 4 figures

Matters Arising in Nature on "Evidence for a single layer van der Waals multiferroic". The search for two dimensional multiferroic materials is an exciting yet challenging endeavor. Recently, Song reported the exciting discovery of type II multiferroic order in an antiferromagnetic (AFM) NiI2 single layer and concluded the ferroelectric (FE) polarization induced by a helical magnetic order1. Their finding was presented from all optical experimental evidence, based on the methods of second harmonic generation (SHG) and linear dichroism (LD). However, the all optical characterizations cannot serve as unanimous evidence of the FE existence, particularly in conjunction with magnetic orders in a single layer NiI2 multiferroic. We have designed and built a Magneto-Optical-Electric Joint-measurement Scanning Imaging system (MOEJSI) for identification of two-dimensional vdW multiferroic., Comment: 7 pages

Singularities arise in diverse disciplines and play a key role in both exploring fundamental laws of physics and making highly-sensitive sensors. Higher-order (>3) singularities, with further improved performance, however, usually require exquisite tuning of multiple (>3) coupled degrees of freedom or nonlinear control, thus severely limiting their applications in practice. Here we propose theoretically and confirm using mechanics experiments that, cubic singularities can be realized in a coupled binary system without any nonlinearity, only by observing the phase tomography of the driven response. By steering the cubic phase-tomographic singularities in an electrostatically-tunable micromechanical system, enhanced cubic-root response to frequency perturbation and voltage-controlled nonreciprocity are demonstrated. Our work opens up a new phase-tomographic method for interacted-system research and sheds new light on building and engineering advanced singular devices with simple and well-controllable elements, with a wide range of applications including precision metrology, portable nonreciprocal devices, and on-chip mechanical computing.