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Recently, great progress has been made in the entanglement of multiple photons at various wavelengths and in different degrees of freedom for optical quantum information applied in diverse scenarios. However, multi-photon entanglement in the transmission window of green light under the water has not been reported yet. Here, by combining femtosecond laser based multi-photon entanglement and entanglement-maintaining frequency upconversion techniques, we successfully generate a green two-photon polarization-entangled Bell state and a green three-photon Greenberger-Horne-Zeilinger (GHZ) state, whose state fidelities are 0.893$\mathbf{\pm}$0.002 and 0.595$\mathbf{\pm}$0.023, respectively. Our result provides a scalable method to prepare green multi-photon entanglement, which may have wide applications in underwater quantum information., Comment: 8 pages, 4 figures

High-dimensional encoding of quantum information holds the potential to greatly increase the computational power of existing devices by enlarging the accessible state space for fixed register size and by reducing the number of required entangling gates. However, qudit-based quantum computation remains far less developed than conventional qubit-based approaches, in particular for photons, which represent natural multi-level information carriers that play a crucial role in the development of quantum networks. A major obstacle for realizing quantum gates between two individual photons is the restriction of direct interaction between photons in linear media. In particular, essential logic components for quantum operations such as native qudit-qudit entangling gates are still missing for optical quantum information processing. Here we address this challenge by presenting a protocol for realizing an entangling gate -- the controlled phase-flip (CPF) gate -- for two photonic qudits in arbitrary dimension. We experimentally demonstrate this protocol by realizing a four-dimensional qudit-qudit CPF gate, whose decomposition would require at least 13 two-qubit entangling gates. Our photonic qudits are encoded in orbital angular momentum (OAM) and we have developed a new active high-precision phase-locking technology to construct a high-dimensional OAM beam splitter that increases the stability of the CPF gate, resulting in a process fidelity within a range of $ [0.64 \pm 0.01, 0.82 \pm 0.01]$. Our experiment represents a significant advance for high-dimensional optical quantum information processing and has the potential for wider applications beyond optical system., Comment: 14 pages, 7 figures

Materials that exhibit strongly coupled magnetic order and electronic properties are crucial for both fundamental research and technological applications. However, finding a material that not only shows remarkable magnetoresistive responses but also has an easily tunable ground state remains a challenge. Here, we report successful manipulation of the magnetic and transport properties of EuCd$_2$P$_2$, which is transformed from an A-type antiferromagnet ($T_\mathrm{N}$ = 11 K) exhibiting colossal magnetoresistance into a ferromagnet ($T_\mathrm{C}$ = 47 K) with metallic behavior. The dramatic alteration results from a low hole concentration of $10^{19}$ cm$^{-3}$ induced by changing the growth conditions. Electronic structure and total energy calculations confirm the tunability of magnetism with a small carrier concentration for EuCd$_2$P$_2$. It is feasible to switch between the magnetic states by using field-effect to control the carrier density, thereby changing the magneto-electronic response. The controllable magnetism and electrical transport of EuCd$_2$P$_2$ make it a potential candidate for spintronics.

EuZn$_2$P$_2$ was reported to be an insulating antiferromagnet with $T_\mathrm{N}$ of 23.5 K. In this study, single crystals of EuZn$_2$P$_2$ exhibiting metallic behavior and a ferromagnetic order of 72 K ($T_\mathrm{C}$) are successfully synthesized via a salt flux method. The presence of hole carriers induced by the Eu vacancies in the lattice is found to be crucial for the drastic changes in magnetism and electrical transport. The carriers mediate the interlayer ferromagnetic interaction, and the coupling strength is directly related to $T_\mathrm{C}$, as evidenced by the linear dependence of $T_\mathrm{C}$ and the fitted Curie-Weiss temperatures on the Eu-layer distances for ferromagnetic Eu$M_2X_2$ ($M$ = Zn, Cd; $X$ = P, As). The ferromagnetic EuZn$_2$P$_2$ shows conspicuous negative magnetoresistance (MR) near $T_\mathrm{C}$, owing to strong magnetic scattering. The MR behavior is consistent with the Majumdar-Littlewood model, indicating that the MR can be enhanced by decreasing the carrier density. Our findings suggest that Eu$M_2X_2$ has highly tunable magnetism and charge transport, making it a promising material family for potential applications in spintronics.

This study presents an investigation of the isotropic superconductor Ti4Ir2O, focusing on its magnetic field vs. temperature phase diagram near and above the Pauli limit for superconductivity. The data exhibits characteristic features that align with the formation of a Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state, including a deviation of the upper critical field line from the standard WHH model upon approaching the Pauli limiting field and a phase transition line separating the ordinary low-field superconducting phase from an unusual high field superconducting state above the Pauli limit. We discuss why the upper critical field line in this isotropic superconductor can approach the Pauli limit, necessitating a particularly high orbital limit for superconductivity. The research also identifies peculiar features in the specific heat data set taken at 0.6 K, which may be an example of the segmentation of the FFLO phase with multiple q phases. The findings provide an explanation for the violation of the Pauli limit in this superconductor, adding a fully isotropic superconductor to the list of potential FFLO superconductors and providing new insights for contemporary theories of the FFLO state.

We propose a novel approach to enable the agile manipulation of light- and dark-seeking particles. Our approach involves introducing a two-curvilinear perfect optical vortex beam (TC-POVB) generated by superimposing a pair of curved beams. The TC-POVB exhibits the property of a perfect optical vortex, which means that its size remains constant regardless of its topological charge. Additionally, each curve of the TC-POVB can support a distinct orbital flow density (OFD). This enables the application of torques to produce a dark channel that satisfies the requirements for particle size and drives the revolution or rotation motion of the confined dark-seeking particles. To demonstrate the effectiveness of our approach, we manipulate light- and dark-seeking particles experimentally, making them perform various curvilinear trajectories simultaneously, including moving, revolving, and rotating.

We report the synthesis, crystal structure, and physical properties of a novel ternary compound, Th$_2$Cu$_4$As$_5$. The material crystallizes in a tetragonal structure with lattice parameters $a=4.0716(1)$ {\AA} and $c=24.8131(4)$ {\AA}. Its structure can be described as an alternating stacking of fluorite-type Th$_2$As$_2$ layers with antifluorite-type double-layered Cu$_4$As$_3$ slabs. The measurement of electrical resistivity, magnetic susceptibility and specific heat reveals that Th$_2$Cu$_4$As$_5$ undergoes bulk superconducting transition at 4.2 K. Moreover, all these physical quantities exhibit anomalies at 48 K, where the Hall coefficient change the sign. These findings suggest a charge-density-wave-like (CDW) transition, making Th$_2$Cu$_4$As$_5$ a rare example for studying the interplay between CDW and superconductivity., Comment: 11 pages, 6 figures, and 1 table

Unconventional superconductivity (USC) in a highly correlated kagome system has been theoretically proposed for years, yet the experimental realization is hard to achieve. The recently discovered vanadium-based kagome materials, which exhibit both superconductivity and charge density wave (CDW) orders, are nonmagnetic and weakly correlated, thus unlikely host USC as theories proposed. Here we report the discovery of a chromium-based kagome metal, CsCr$_3$Sb$_5$, which is contrastingly characterised by strong electron correlations, frustrated magnetism, and characteristic flat bands close to the Fermi level. Under ambient pressure, it undergoes a concurrent structural and magnetic phase transition at 55 K, accompanying with a stripe-like $4a_0$ structural modulation. At high pressure, the phase transition evolves into two transitions, probably associated with CDW and antiferromagnetic spin-density-wave orderings, respectively. These density-wave (DW)-like orders are gradually suppressed with pressure and, remarkably, a superconducting dome emerges at 3.65-8.0 GPa. The maximum of the superconducting transition temperature, $T_\mathrm{c}^{\mathrm{max}}=$ 6.4 K, appears when the DW-like orders are completely suppressed at 4.2 GPa, and the normal state exhibits a non-Fermi-liquid behaviour, reminiscent of USC and quantum criticality in iron-based superconductors. Our work offers an unprecedented platform for investigating possible USC in a correlated kagome system., Comment: 32 pages, 14 figures

Ordinary differential equations (ODEs), via their induced flow maps, provide a powerful framework to parameterize invertible transformations for the purpose of representing complex probability distributions. While such models have achieved enormous success in machine learning, particularly for generative modeling and density estimation, little is known about their statistical properties. This work establishes the first general nonparametric statistical convergence analysis for distribution learning via ODE models trained through likelihood maximization. We first prove a convergence theorem applicable to arbitrary velocity field classes $\mathcal{F}$ satisfying certain simple boundary constraints. This general result captures the trade-off between approximation error (`bias') and the complexity of the ODE model (`variance'). We show that the latter can be quantified via the $C^1$-metric entropy of the class $\mathcal F$. We then apply this general framework to the setting of $C^k$-smooth target densities, and establish nearly minimax-optimal convergence rates for two relevant velocity field classes $\mathcal F$: $C^k$ functions and neural networks. The latter is the practically important case of neural ODEs. Our proof techniques require a careful synthesis of (i) analytical stability results for ODEs, (ii) classical theory for sieved M-estimators, and (iii) recent results on approximation rates and metric entropies of neural network classes. The results also provide theoretical insight on how the choice of velocity field class, and the dependence of this choice on sample size $n$ (e.g., the scaling of width, depth, and sparsity of neural network classes), impacts statistical performance.

Theoretical studies predicted possible superconductivity in electron-doped chromium pnictides isostructural to their iron counterparts. Here, we report the synthesis and characterization of a new ZrCuSiAs-type Cr-based compound ThCrAsN, as well as its oxygen-doped variants. All samples of ThCrAsN$_{1-x}$O$_x$ show metallic conduction, but no superconductivity is observed above 30 mK even though the oxygen substitution reaches 75\%. The magnetic structure of ThCrAsN is determined to be G-type antiferromagnetic by magnetization measurements and first-principles calculations jointly. The calculations also indicate that the in-plane Cr--Cr direct interaction of ThCrAsN is robust against the heavy electron doping. The calculated density of states of the orbital occupations of Cr for ThCrAs(N,O) is strongly spin-polarized. Our results suggest the similarities between chromium pnictides and iron-based superconductors shouldn't be overestimated.

High-order quantum coherence reveals the statistical correlation of quantum particles. Manipulation of quantum coherence of light in temporal domain enables to produce single-photon source, which has become one of the most important quantum resources. High-order quantum coherence in spatial domain plays a crucial role in a variety of applications, such as quantum imaging, holography and microscopy. However, the active control of high-order spatial quantum coherence remains a challenging task. Here we predict theoretically and demonstrate experimentally the first active manipulation of high-order spatial quantum coherence by mapping the entanglement of spatially structured photons. Our results not only enable to inject new strength into current applications, but also provide new possibilities towards more wide applications of high-order quantum coherence., Comment: 11 pages, 5 figures

The first-principles calculations and measurements of the magnetic penetration depths, the upper critical field, and the specific heat were performed for a family of Mo$_5$Si$_{3-x}$P$_x$ superconducotrs. First-principles calculations suggest the presence of a flat band dispersion, which gradually shifts to the Fermi level as a function of phosphorus doping $x$. The flat band approaches the Fermi level at $x\simeq 1.3$, thus separating Mo$_5$Si$_{3-x}$P$_x$ between the purely steep band and the steep band/flat band superconducting regimes. The emergence of flat bands lead to an abrupt change of nearly all the superconducting quantities. In particular, a strong reduction of the coherence length $\xi$ and enhancement of the penetration depth $\lambda$ result in nearly factor of three increase of the Ginzburg-Landau parameter $\kappa=\lambda/\xi$ (from $\kappa\simeq 25$ for $x\lesssim 1.2$ to $\kappa\simeq 70$ for $x\gtrsim 1.4$) thus initiating the transition of Mo$_5$Si$_{3-x}$P$_x$ from a moderate to an extreme type-II superconductivity., Comment: 6 pages, 4 figures

Free space optical (FSO) communication can exploit mode-division multiplexing using orthogonal spatial modes of Laguerre Gaussian beams, such as orbital angular momentum (OAM) modes, wherein OAM multiplexing offers potentially infinite information capacity due to the arbitrary quantization of OAM. Combined with polarization-division multiplexing and wavelength-division multiplexing, OAM multiplexing is a promising solution for future capacity demands. However, the practically addressable number of spatial subchannels is severely limited by the receiver size and the rapid beam expansion with increasing mode order and communication distance. Based on the intrinsic and distinctive property that the divergent degree of the innermost ring of a Laguerre-Gaussian beam is significantly slower than that of the beam cross-section during propagation, here we propose theoretically and demonstrate experimentally a novel communication strategy innermost ring dominated OAM (IRD-OAM) multiplexingn that can overcome these limits and achieve up to 1238% capacity of conventional OAM multiplexing in a canonical FSO link system without any additional hardware modifications. Alternatively, our strategy can also enable longer communication distance (403% of that for conventional OAM multiplexing), or smaller receiver (26.9% in size compared to conventional OAM multiplexing), while maintaining the same capacity as conventional OAM multiplexing. Our work will hasten the development of future FSO communications with ultra high capacity, ultra long distance and highly-integrated devices for deep space, near Earth and Earth surface applications., Comment: 15 pages,6 Figures

We report the discovery and detailed investigation of superconductivity in Mo$_4$Ga$_{20}$As. Mo$_4$Ga$_{20}$As crystallizes in the space group of $I4/m$ (No. 87), with lattice parameters $a$ = 12.86352 \AA and $c$ = 5.30031 \AA. The resistivity, magnetization, and specific heat data reveal Mo$_4$Ga$_{20}$As to be a type-II superconductor with $T_c$ = 5.6 K. The upper and lower critical fields are estimated to be 2.78 T and 22.0 mT, respectively. In addition, electron-phonon coupling in Mo$_4$Ga$_{20}$As is possibly stronger than the BCS weak-coupling limit. First-principles calculations suggest the Fermi level being dominated by the Mo-4$d$ and Ga-4$p$ orbitals.

We report the effect of carbon doping in Ti-stabilized nonstoichiometric molybdenum diboride (Mo$_{0.96}$Ti$_{0.04}$)$_{0.8}$B$_{2}$, which exhibits bulk superconductivity below $T_{\rm c}$ = 7.0 K. It is found that (Mo$_{0.96}$Ti$_{0.04}$)$_{0.8}$(B$_{1-x}$C$_{x}$)$_{2}$ maintains the AlB$_{2}$-type phase with a uniform elemental distribution for $x$ = 0.12 and 0.16. The substitution of carbon for boron leads to a slight increase in $a$-axis, a remarkable reduction in $c$-axis, the formation of planar defects along the (100) crystallographic planes, and a shift of the B 1$s$ peaks towards higher binding energies. Contrary to (Mo$_{0.96}$Ti$_{0.04}$)$_{0.8}$B$_{2}$, however, no superconductivity is observed down to 1.8 K for the C-doped samples, which is ascribed to the electron filling of boron $\pi$ bands resulting from the carbon doping., Comment: 18 pages, 7 figures

A new medium-entropy diboride (MEDB) (W1/3Re1/3Ru1/3)B2 has been synthesized by spark plasma sintering of elemental powders at 1600 oC. Despite the dissimilar structures of WB2, ReB2 and RuB2, the sintered MEDB consists of a single hexagonal ReB2-type phase (space group P63/mmc) with a relative density of 94.2% and an average grain size of 6.8 $\pm$ 2.2 um. Structural refinement and electron microscopy measurements show that the W, Re, and Ru atoms occupy the same crystallographic site and are distributed uniformly in the lattice. The (W1/3Re1/3Ru1/3)B2 MEDB has Vickers hardnesses of 30.7 GPa at a load of 0.49 N and 20.5 GPa at a load of 9.8 N, which are comparable or higher than those reported for individual binary counterparts., Comment: 16 pages, 6 figures

We report the synthesis and characterization of metal deficient (Ti$_{0.2}$Zr$_{0.2}$Hf$_{0.2}$Nb$_{0.2}$Ta$_{0.2}$)$_{1-\delta}$B$_{2}$ high-entropy diborides (HEBs). A single homogeneous AlB$_{2}$-type phase is successfully obtained over the $\delta$ range of 0.03 $\leq$ $\delta$ $\leq$ 0.18. With increasing $\delta$, the unit-cell volume exhibits a nonmonotonic variation with a maximum at $\delta$ = 0.07. These metal-deficient HEBs possess high Vickers hardness of 16.6-18.9 GPa at a load of 9.8 N and their phase stability is attributed to the increased mixing entropy. Our results not only present the first series of metal-deficient AlB$_{2}$-type HEBs, but also suggest the existence of similar multicomponent diborides., Comment: 7 pages, 4 figures

A series of new Cr$_{5+x}$Mo$_{35-x}$W$_{12}$Re$_{35}$Ru$_{13}$C$_{20}$ high-entropy alloys (HEAs) have been synthesized and characterized by x-ray diffraction, scanning electron microscopy, electrical resistivity, magnetic susceptibility and specific heat measurements. It is found that the HEAs adopt a noncentrosymmetric cubic $\beta$-Mn type structure and exhibit bulk superconductivity for 0 $\leq$ $x$ $\leq$ 9. With increasing $x$, the cubic lattice parameter decreases from 6.7940(3) {\AA} to 6.7516(3) {\AA}. Meanwhile, the superconducting transition temperature $T_{\rm c}$ is suppressed from 5.49 K to 3.35 K due to the magnetic pair breaking caused by Cr moments. For all these noncentrosymmetric HEAs, the zero-temperature upper critical field $B_{\rm c2}$(0) is comparable to Pauli paramagnetic limit $B_{\rm P}$(0) = 1.86$T_{\rm c}$. In particular, the $B_{\rm c2}$(0)/$B_{\rm P}$(0) ratio reaches a maximum of $\sim$1.03 at $x$ = 6, which is among the highest for $\beta$-Mn type superconductors., Comment: 8 pages, 5 figures

A quaternary compound with the composition Mo$_{3}$ReRuC is obtained in a previously unexplored MoReRu-Mo$_{2}$C system. According to x-ray structural analysis, Mo$_{3}$ReRuC crystallizes in the noncentrosymmetric space group $P$4$_{1}$32 (cubic $\beta$-Mn type structure, $a$ = 6.8107(1) {\AA}). Below 7.7 K, Mo$_{3}$ReRuC becomes a bulk type-II superconductor with an upper critical field close to the Pauli paramagnetic limit. The specific heat data gives a large normalized jump $\Delta$$C_{\rm p}$/$\gamma$$T_{\rm c}$ = 2.3 at $T_{\rm c}$, which points to a strongly coupled superconducting state. First principles calculations show that its electronic states at the Fermi level are mainly contributed by Mo, Re and Ru atoms and strongly increased by the spin-orbit coupling. Our finding suggests that the intermediate phase between alloys and carbides may be a good place to look for $\beta$-Mn type noncentrosymmetric superconductors., Comment: 9 pages, 7 figures

We report the synthesis, crystal structure and physical properties of two new high-entropy silicides (HESs), namely (Nb$_{0.1}$Mo$_{0.3}$W$_{0.3}$Re$_{0.2}$Ru$_{0.1}$)$_{5}$Si$_{3}$ and (Nb$_{0.2}$Mo$_{0.3}$W$_{0.3}$Re$_{0.1}$Ru$_{0.1}$)$_{5}$Si$_{3}$. Structural analysis indicates that both HESs consist of a (nearly) single tetragonal W$_{5}$Si$_{3}$-type phase (space group $I$4/$mcm$) with a disordered cation distribution. Electrical resistivity, magnetic susceptibility and specific heat measurements show that (Nb$_{0.1}$Mo$_{0.3}$W$_{0.3}$Re$_{0.2}$Ru$_{0.1}$)$_{5}$Si$_{3}$ and (Nb$_{0.2}$Mo$_{0.3}$W$_{0.3}$Re$_{0.1}$Ru$_{0.1}$)$_{5}$Si$_{3}$ are weakly coupled bulk superconductors, which represent the first superconducting high-entropy nonoxide ceramics. In particular, these HESs have higher $T_{\rm c}$ values (3.2-3.3 K) compared with those of the binary counterparts, and their $B_{\rm c2}$(0)/$T_{\rm c}$ ratios are the largest among superconductors of the same structural type., Comment: 8 pages, 5 figures

Two-photon Hong-Ou-Mandel (HOM) interference is a fundamental quantum effect with no classical counterpart. The exiting researches on two-photon interference were mainly limited in one degree of freedom (DoF), hence it is still a challenge to realize the quantum interference in multiple DoFs. Here we demonstrate the HOM interference between two hyper-entangled photons in two DoFs of polarization and orbital angular momentum (OAM) for all the sixteen hyper-entangled Bell states. We observe hyper-entangled two-photon interference with bunching effect for ten symmetric states (nine Boson-Boson states, one Fermion-Fermion state) and anti-bunching effect for six anti-symmetric states (three Boson-Fermion states, three Fermion-Boson states). More interestingly, expanding the Hilbert space by introducing an extra DoF for two photons enables to transfer the unmeasurable external phase in the initial DoF to a measurable internal phase in the expanded two DoFs. We directly measured the symmetric exchange phases being $0.012 \pm 0.002$, $0.025 \pm 0.002$ and $0.027 \pm 0.002$ in radian for the three Boson states in OAM and the anti-symmetric exchange phase being $0.991 \pi \pm 0.002$ in radian for the other Fermion state, as theoretical predictions. Our work may not only pave the way for more wide applications of quantum interference, but also develop new technologies by expanding Hilbert space in more DoFs., Comment: Accepted by Physical Review Letters

Arsenic doping in silicides has been much less studied compared with phosphorus. In this study, superconductivity is successfully induced by As doping in Mo$_5$Si$_3$. The superconducting transition temperature ($T_c$) reaches 7.7 K, which is higher than those in previously known W$_5$Si$_3$-type superconductors. Mo$_5$Si$_2$As is a type-II BCS superconductor with upper and lower critical fields of 6.65 T and 22.4 mT, respectively. In addition, As atoms are found to selectively take the 8$h$ sites in Mo$_5$Si$_2$As. The emergence of superconductivity is possibly due to the shift of Fermi level as a consequence of As doping, as revealed by the specific heat measurements and first-principles calculations. Our work provides not only another example of As doping, but also a practical strategy to achieve superconductivity in silicides through Fermi level engineering., Comment: Supporting Information available at the corresponding DOI

The recognition in the 1990s that vortex beams (VBs), paraxial light beams with optical vortices, carry orbital angular momentum (OAM), has benefited applications ranging from optical manipulation to high-dimensional classical and quantum information communications. The transverse profiles of common VBs, e.g., Laguerre-Gaussian beam and high-order Bessel beam, are hollow donuts whose radii grow up with OAM inevitably. The inherently unperfect character of the VBs that the radius is always positively correlated with OAM, restricts the application of the VBs in many scenarios like fiber optic data transmission, spatial OAM mode (de)multiplexing communication, and particle manipulation, which call for VBs to have the same scale with distinct OAM or even the small vortex ring for large OAM. Here, we derived a theory based on the most widely used Laguerre-Gaussian beam to generate a brand new type of VB with OAM-independent radii that moves away from the common unperfect constraint, called Laguerre-Gaussian Perfect Vortex Beam (LGPVB). LGPVBs have the self-similar property like common Laguerre-Gaussian beams but can self-heal after suffering disturbance and always remain 'perfection' when propagating. Our Fourier-space design not only allows us to shape the LGPVB's propagating intensity at will, but it also gives LGPVB the fascinating potential to arbitrarily self-accelerate while still perfectly propagating, self-similar, and self-healing. This customizable self-healing LGPVB, whose properties inform our most expectations of VBs, offers a better alternative for application scenarios of common VBs in a wide range of areas., Comment: 20 pages,9 figures. arXiv admin note: text overlap with arXiv:2209.00481

The rapid scale broadening and divergence increasing of vortex beams (VBs) with orbital angular momentum (OAM), e.g., Laguerre-Gaussian beams, severely impede the wide applications of VBs ranging from optical manipulation to high-dimensional quantum information communications, which call for VBs to have the same transverse scale and divergence for distinct OAM or even the small vortex ring for large OAM. Non-diffracting beams, on the other hand, that are capable of overcoming diffraction without divergence, are very evocative and indeed appealing in numerous applications including atom optics and medical imaging. Here, we propose theoretically and demonstrate experimentally a brand new type of VB having OAM-independent radii meanwhile holding propagation-invariant without divergence as well as self-healing properties, named non-diffracting perfect vortex beam (NDPVB). We work out a versatile toolkit based on Fourier-space analysis to multidimensionally customize NDPVBs at will so that it is of propagating intensity and phase controllability with intriguing customizable behaviors of self-accelerating, self-similar, and self-rotating. This goes beyond tailoring the transverse plane to the higher-dimensional propagating characteristics in structured light beams. A deeper insight into the internal flow revealed and confirmed that the multidimensional customization of NDPVBs is dominated by inducing corresponding multidimensional internal flow, facilitating our understanding of how our design scheme of propagating properties manipulates the internal flows, unveiling the nature of structure formation and behavior transformation of structured light beams., Comment: 32 pages,14 figures

By performing P doping on the Si sites in the topological semimetal Mo$_5$Si$_3$, we discover strong-coupling superconductivity in Mo$_5$Si$_{3-x}$P$_x$ (0.5 $\le$ $x$ $\le$ 2.0). Mo$_5$Si$_3$ crystallizes in the W$_5$Si$_3$-type structure with space group of $I4/mcm$ (No. 140), and is not a superconductor itself. Upon P doping, the lattice parameter $a$ decreases while $c$ increases monotonously. Bulk superconductivity is revealed in Mo$_5$Si$_{3-x}$P$_x$ (0.5 $\le$ $x$ $\le$ 2.0) from resistivity, magnetization, and heat capacity measurements. $T_c$ in Mo$_5$Si$_{1.5}$P$_{1.5}$ reaches as high as 10.8 K, setting a new record among the W$_5$Si$_3$-type superconductors. The upper and lower critical fields for Mo$_5$Si$_{1.5}$P$_{1.5}$ are 14.56 T and 105 mT, respectively. Moreover, Mo$_5$Si$_{1.5}$P$_{1.5}$ is found to be a fully gapped superconductor with strong electron-phonon coupling. First-principles calculations suggest that the enhancement of electron-phonon coupling is possibly due to the shift of the Fermi level, which is induced by electron doping. The calculations also reveal the nontrivial band topology in Mo$_5$Si$_3$. The $T_c$ and upper critical field in Mo$_5$Si$_{3-x}$P$_x$ are fairly high among pseudobinary compounds. Both of them are higher than those in NbTi, making future applications promising. Our results suggest that the W$_5$Si$_3$-type compounds are ideal platforms to search for new superconductors. By examinations of their band topologies, more candidates for topological superconductors can be expected in this structural family., Comment: 15 pages, 5 figures. Supplementary Information availabe at the corresponding DOI

Structured optical fields embedded with polarization singularities (PSs) have attracted extensive attention due to their capability to retain topological invariance during propagation. Many advances in PSs research have been made over the past 20 years in the areas of mathematical description, generation and detection technologies, propagation dynamics, and applications. However, one of the most crucial and difficult tasks continues to be manipulating PSs with multiple degrees of freedom, especially in three-dimensional (3D) tailored optical fields. We propose and demonstrate the longitudinal PS lines obtained by superimposing Bessel-like modes with orthogonal polarization states on composite vector optical fields (VOFs). The embedded PSs in the fields can be manipulated to propagate robustly along arbitrary trajectories, or to annihilate, revive, and transform each other at on-demand positions in 3D space, allowing complex PSs topological morphology and intensity pattern to be flexibly customized. Our findings could spur further research into singular optics and help with applications such as micromanipulation, microstructure fabrication, and optical encryption.

Quantum pseudotelepathy is a strong form of nonlocality. Different from the conventional non-local games where quantum strategies win statistically, e.g., the Clauser-Horne-Shimony-Holt game, quantum pseudotelepathy in principle allows quantum players to with probability 1. In this work, we report a faithful experimental demonstration of quantum pseudotelepathy via playing the non-local version of Mermin-Peres magic square game, where Alice and Bob cooperatively fill in a 3 by 3 magic square. We adopt the hyperentanglement scheme and prepare photon pairs entangled in both the polarization and the orbital angular momentum degrees of freedom, such that the experiment is carried out in a resource-efficient manner. Under the locality and fair-sampling assumption, our results show that quantum players can simultaneously win all the queries over any classical strategy., Comment: 6+5 pages; published version

$\beta$-ThRhGe, the high-temperature polymorph of ThRhGe, is isostructural to the well-known ferromagnetic superconductor URhGe. However, contrary to URhGe, $\beta$-ThRhGe is nonmagnetic and undergoes an incomplete structural phase transition at 244 K, followed by a superconducting transition below 3.36 K. Here we show that the isovalent substitution of Ir for Rh leads to a strong enhancement of superconductivity by suppressing the structural transition. At $x$ = 0.5, where the structural transition disappears, $T_{\rm c}$ reaches a maximum of 6.88 K. The enhancement of superconductivity is linked to the proximity to a structural quantum critical point at this Ir concentration, as suggested by the analysis of thermodynamic as well as resistivity data. First principles calculations indicate that the Ir doping has little effect on the electronic band dispersion near the Fermi level. $\beta$-ThRh$_{1-x}$Ir$_{x}$Ge thus provides an excellent platform to study the interplay between superconductivity and structural quantum criticality in actinide-containing compounds., Comment: 14 pages, 10 figures, 1 tables

The quest for quantum materials with diverse symmetry-protected topological states has been the focus of recent research interest, primarily due to their fascinating physical properties and the potential technological utility. In this work, we report on the magnetotransport, de Haas-van Alphen (dHvA) oscillations, and the first-principles calculations of the stannide Cu$_3$Sn that is isostructural with the recently reported topological semimetal Ag$_3$Sn. The magnetoresistance was found to vary quasi-linearly in field. Clear dHvA oscillations were observed under a field as low as 1 Tesla at 2 K, with three major oscillation frequencies $F_{\alpha}$=8.74 T, $F_{\beta}$=150.19 T and $F_{\gamma}$=229.66 T and extremely small effective masses. The analysis of dHvA quantum oscillations revealed a possible nonzero Berry phase, suggestive of the nontrivial band topology. The corroborating evidence for the nontrivial electronic topology also comes from the first-principles calculations which yield a nonzero $\mathbb{Z}_2$ topological index. These results collectively suggest that Cu$_3$Sn, in analogy to its homologue Ag$_3$Sn, may be another intermetallic stannide hosting topological Dirac fermions., Comment: 4 figures, 1 table

Optical orbital angular momentum (OAM), as an important degree of freedom of light, has been attracted extensive attention, due to its intrinsic feature of natural discrete infinite dimension. Manipulation of OAM spectra is crucial for many impressive applications from classical to quantum realms, in particular, nonlinear manipulation of OAM spectra. Here we realized the nonlinear manipulation of OAM spectra by using the simultaneous second- and third-harmonic generation in a single nonlinear crystal of quasi-periodically poled potassium titanyl phosphate, for fundamental waves with a variety of OAM spectra, especially for customized OAM spectra of the second and third harmonics. The experimental results confirmed the theoretical predictions. Our approach not only provides a novel way to manipulate OAM spectra at new shorter wavelengths that are hard to be directly generated, but also may find new applications towards multiplexing in classical optics and high-dimensional information processing in quantum optics., Comment: 5 pages, 4 figures

Nonlinear optical processes of spatially structured light, including optical vortex and vector optical fields, have stimulated a lot of interesting physical effects and found a variety of important applications ranging from optical imaging to quantum information processing. However, high harmonic generation of vector optical fields with space-varying polarization states is still a challenge. Here we demonstrate third harmonic generation of spatially structured light including vector optical fields, in a nonlinear Sagnac interferometer containing a carefully designed quasi-periodically poled potassium titanyl phosphate for the first time. The experimental results are in good agreement with the theoretical predictions. Our results will enable to manipulate spatially structured light or photons at new wavelengths and carrying higher orbital angular momentum. Our approach has the potential applications for the research of optical skyrmions and may open up new opportunities to produce spatially structured entangled photons for quantum communication and computation., Comment: 5 pages, 3 figures

Several recent studies have shown that the anisotropy in the magnetic structure of \ECA\ plays a significant role in stabilizing the Weyl nodes. To investigate the relationship between magnetic anisotropy and Weyl physics, we present a comparative study between EuZn$_2$As$_2$ and EuCd$_2$As$_2$ that are isostructural but with different magnetic anisotropy. We performed structural analysis, electronic transport, and magnetization experiments on millimeter-sized single crystals of EuZn$_2$As$_2$, and compared the results to those of EuCd$_2$As$_2$. By combining the first principle calculations and neutron diffraction experiment, we identify the magnetic ground state of EuZn$_2$As$_2$ as A-type antiferromagnetic order with a transition temperature ($T_\mathrm{N}$ = 19.6 K) twice that of EuCd$_2$As$_2$. Like EuCd$_2$As$_2$, the negative magnetoresistance of EuZn$_2$As$_2$ is observed after suppressing the resistivity peak at $T_\mathrm{N}$ with increasing fields. However, the anisotropy in both transport and magnetization are much reduced in EuZn$_2$As$_2$. The difference could be ascribed to the weaker spin-orbit coupling, more localized $d$-orbitals, and a larger contribution from the Eu $s$-orbitals in the zinc compound, as suggested by the electronic band calculations. The same band structure effect could be also responsible for the observation of a smaller non-linear anomalous Hall effect in EuZn$_2$As$_2$ compared to EuCd$_2$As$_2$.

Magnetic Weyl semimetals (MWSM) have attracted significant attention due to their intriguing physical properties and potential applications in spin-electronic devices. Here we report the characterization of NdAlSi including transport, magnetization, and heat capacity on single crystals, as well as band structure calculation. It is a newly proposed MWSM candidate which breaks both time-reversal and spacial inversion symmetries. A temperature-magnetic field phase diagram is experimentally established. Remarkably, on the angular magnetoresistance (AMR), a two-fold symmetric sharp peak instead of a smooth variation is observed in the field-induced ferrimagnetic phase. We argue that the tunability of both the topological and magnetic properties in NdAlSi is crucial for realizing such a behavior. Our results indicate that 4f-electron-based MWSM can provide a unique platform to explore new and intriguing quantum phenomena arising from the interaction between magnetism and topology., Comment: 24 pages, 12 figures

The interplay between magnetism and the topology of electronic band structure may generate new exotic quantum states. Here we report on a new type of quantum oscillations in the temperature dependent electrical resistivity and specific heat at a constant magnetic field in a polar magnetic Weyl semimetal (WSM) NdAlSi. These novel quantum phenomena arise from the destructive interference between quantum oscillations from the spin-split Fermi surfaces due to the strong Weyl fermions-4f electrons exchange interaction combined with Rashba-Dresselhaus (RD) and Zeeman effects. Our findings pave a way to explore unprecedented quantum phenomena in 4f-electron based magnetic semimetals., Comment: In this version,there are 16 pages, 4 figures in main manuscript

The oscillating temperature technique was successfully employed to grow large and composition homogeneous CaFeAsF single crystals due to the reduction of nuclei number by temperature oscillation. The largest as-grown CaFeAsF single crystal was nearly 8 mm in lateral size and 0.27 mm in thickness which is far larger than previously reported in all dimensions. The full-width-at-half maximum (FWHM) of x-ray rocking curve is as small as 0.163{\deg} indicating the high quality of CaFeAsF single crystals.

We report the synthesis, crystal structure, and superconductivity of Ti$_4$Ir$_2$O. The title compound crystallizes in an $\eta$-carbide type structure of the space group $Fd\overline{3}m$ (No. 227), with lattice parameters $a=b=c=11.6194(1)$ \AA. The superconducting $T_c$ is found to be 5.1 $\sim$ 5.7 K. Most surprisingly, Ti$_4$Ir$_2$O hosts an upper critical field of 16.45 T, which is far beyond the Pauli paramagnetic limit. Strong coupled superconductivity with evidences for multigap is revealed by the measurements of heat capacity and upper critical field. First-principles calculations suggest that the density of states near the Fermi level originates from the hybridization of Ti-3$d$ and Ir-5$d$ orbitals, and the effect of spin-orbit coupling on the Fermi surfaces is prominent. Large values of the Wilson ratio ($R_W$ $\sim$ 3.9), the Kadowaki-Woods ratio ($A/\gamma^2$ $\sim$ 9.0 $\times$ 10$^{-6}$ $\mu\Omega$ cm/(mJ mol$^{-1}$ K$^{-1}$)$^2$), and the Sommerfeld coefficient ($\gamma$ = 33.74 mJ mol$^{-1}$ K$^{-2}$) all suggest strong electron correlations (similar to heavy fermion systems) in Ti$_4$Ir$_2$O. The violation of Pauli limit is possibly due to a combination of strong-coupled superconductivity, large spin-orbit scattering, and electron correlation. With these intriguing behaviors, Ti$_4$Ir$_2$O serves as a candidate for unconventional superconductor., Comment: 8 pages, 4 figures + 5 figures in the Supporting Information

Graph states -- one of the most representative families of multipartite entangled states, are important resources for multiparty quantum communication, quantum error correction, and quantum computation. Device-independent certification of highly entangled graph states plays a prominent role in the quantum information processing tasks. Here we have experimentally demonstrated device-independent certification for multipartite graph states, by adopting the robust self-testing scheme based on scalable Bell inequalities. Specifically, the prepared multi-qubit Greenberger-Horne-Zeilinger (GHZ) states and linear cluster states achieve a high degree of Bell violation, which are beyond the nontrivial bounds of the robust self-testing scheme. Furthermore, our work paves the way to the device-independent certification of complex multipartite quantum states.

We report the Ni-doping effect on magnetism and superconductivity (SC) in an Eu-containing 112-type system Eu(Fe$_{1-x}$Ni$_{x})$As$_{2}$ ($0\leq x\leq 0.15$) by the measurements of resistivity, magnetization, and specific heat. The undoped EuFeAs$_2$ undergoes a spin-density-wave (SDW) transition at $T_\mathrm{SDW}\sim$ 105 K in the Fe sublattice and a magnetic ordering at $T_\mathrm{m}\sim$ 40 K in the Eu sublattice. Complex Eu-spin magnetism is manifested by a spin-glass reentrance at $T_\mathrm{SG}\sim$ 15 K and an additional spin reorientation at $T_\mathrm{SR}\sim$ 7 K. With Ni doping, the SDW order is rapidly suppressed, and SC emerges in the Ni-doping range of 0.01 $\leq x\leq$ 0.1 where a maximum of the superconducting transition temperature $T_\mathrm{c}^{\mathrm{max}}=$ 17.6 K shows up at $x$ = 0.04. On the other hand, $T_\mathrm{m}$ decreases very slowly, yet $T_\mathrm{SG}$ and $T_\mathrm{SR}$ hardly change with the Ni doping. The phase diagram has been established, which suggests a very weak coupling between SC and Eu spins. The complex Eu-spin magnetism is discussed in terms of the Ruderman-Kittel-Kasuya-Yosida interactions mediated by the conduction electrons from both layers of FeAs and As surrounding Eu$^{2+}$ ions., Comment: 10 pages, 7 figures; supplemental materials available on request