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Two-dimensional materials with Janus structure host novel physical properties due to their inversional symmetry breaking. However, it remains elusive to synthesize Janus monolayer crystals with tailored long-range magnetic orders. Here, we have developed a general method to fabricate uniform Janus CrTeSe monolayers by selective selenization of preformed CrTe2 monolayers with molecular beam epitaxy. The uniform Janus structure of CrTeSe with high crystal quality is confirmed by high-resolution scanning transmission electron microscopy. Spin-polarized scanning tunneling microscopy/spectroscopy measurements unveil that the Janus CrTeSe undergoes a charge density wave (CDW) transition and a robust antiferromagnetic order. The magnetic anisotropy of CrTeSe is drastically altered compared to monolayer CrTe2 by the breaking symmetries induced from the Janus structure and the CDW transition, as is substantiated with first principles calculations. Our research achieves the construction of large-area Janus structures, and artificially tailors the electronic and magnetic properties of Janus systems at the two-dimensional limit., Comment: 19 pages, 4 figures

This paper investigates the conformal isometry hypothesis as a potential explanation for hexagonal periodic patterns in grid cell response maps. The hypothesis posits that grid cell activity forms a high-dimensional vector in neural space, encoding the agent's position in 2D physical space. As the agent moves, this vector rotates within a 2D manifold in the neural space, driven by a recurrent neural network. The conformal hypothesis suggests that this neural manifold is a conformally isometric embedding of physical space, where local displacements in neural space are proportional to those in physical space. In this paper, we conduct numerical experiments to show that this hypothesis leads to the hexagon periodic patterns of grid cells, agnostic to the choice of transformation models. Furthermore, we present a theoretical understanding that hexagon patterns emerge by minimizing our loss function because hexagon flat torus exhibits minimal deviation from local conformal isometry. In addition, we propose a conformal modulation of the agent's input velocity, enabling the recurrent neural network of grid cells to satisfy the conformal isometry hypothesis automatically., Comment: arXiv admin note: text overlap with arXiv:2310.19192

Grid cells in the entorhinal cortex of mammalian brains exhibit striking hexagon grid firing patterns in their response maps as the animal (e.g., a rat) navigates in a 2D open environment. In this paper, we study the emergence of the hexagon grid patterns of grid cells based on a general recurrent neural network (RNN) model that captures the navigation process. The responses of grid cells collectively form a high dimensional vector, representing the 2D self-position of the agent. As the agent moves, the vector is transformed by an RNN that takes the velocity of the agent as input. We propose a simple yet general conformal normalization of the input velocity of the RNN, so that the local displacement of the position vector in the high-dimensional neural space is proportional to the local displacement of the agent in the 2D physical space, regardless of the direction of the input velocity. We apply this mechanism to both a linear RNN and nonlinear RNNs. Theoretically, we provide an understanding that explains the connection between conformal normalization and the emergence of hexagon grid patterns. Empirically, we conduct extensive experiments to verify that conformal normalization is crucial for the emergence of hexagon grid patterns, across various types of RNNs. The learned patterns share similar profiles to biological grid cells, and the topological properties of the patterns also align with our theoretical understanding.

Identifying intrinsic noncollinear magnetic order in monolayer van der Waals (vdW) crystals is highly desirable for understanding the delicate magnetic interactions at reduced spatial constraints and miniaturized spintronic applications, but remains elusive in experiments. Here, we achieved spin-resolved imaging of helimagnetism at atomic scale in monolayer NiI2 crystals, that were grown on graphene-covered SiC(0001) substrate, using spin-polarized scanning tunneling microscopy. Our experiments identify the existence of a spin spiral state with canted plane in monolayer NiI2. The spin modulation Q vector of the spin spiral is determined as (0.2203, 0, 0), which is different from its bulk value or its in-plane projection, but agrees well with our first principles calculations. The spin spiral surprisingly indicates collective spin switching behavior under magnetic field, whose origin is ascribed to the incommensurability between the spin spiral and the crystal lattice. Our work unambiguously identifies the helimagnetic state in monolayer NiI2, paving the way for illuminating its expected type-II multiferroic order and developing spintronic devices based on vdW magnets., Comment: 22 pages, 4 figures

The precision of quantum metrology is widely believed to be restricted by the Heisenberg limit, corresponding to a root mean square error that is inversely proportional to the number of independent processes probed in an experiment, N. In the past, some proposals have challenged this belief, for example using non-linear interactions among the probes. However, these proposals turned out to still obey the Heisenberg limit with respect to other relevant resources, such as the total energy of the probes. Here, we present a photonic implementation of a quantum metrology protocol surpassing the Heisenberg limit by probing two groups of independent processes in a superposition of two alternative causal orders. Each process creates a phase space displacement, and our setup is able to estimate a geometric phase associated to two sets of N displacements with an error that falls quadratically with N. Our results only require a single-photon probe with an initial energy that is independent of N. Using a superposition of causal orders outperforms every setup where the displacements are probed in a definite order. Our experiment features the demonstration of indefinite causal order in a continuous-variable system, and opens up the experimental investigation of quantum metrology setups boosted by indefinite causal order.

Gaussian Boson Sampling (GBS) exhibits a unique ability to solve graph problems, such as finding cliques in complex graphs. It is noteworthy that many drug discovery tasks can be viewed as the clique-finding process, making them potentially suitable for quantum computation. However, to perform these tasks in their quantum-enhanced form, a large-scale quantum hardware with universal programmability is essential, which is yet to be achieved even with the most advanced GBS devices. Here, we construct a time-bin encoded GBS photonic quantum processor that is universal, programmable, and software-scalable. Our processor features freely adjustable squeezing parameters and can implement arbitrary unitary operations with a programmable interferometer. Using our processor, we have demonstrated the clique-finding task in a 32-node graph, where we found the maximum weighted clique with approximately twice the probability of success compared to classical sampling. Furthermore, a multifunctional quantum pharmaceutical platform is developed. This GBS processor is successfully used to execute two different drug discovery methods, namely molecular docking and RNA folding prediction. Our work achieves the state-of-the-art in GBS circuitry with its distinctive universal and programmable architecture which advances GBS towards real-world applications., Comment: 11 pages, 3 figures

The activity of the grid cell population in the medial entorhinal cortex (MEC) of the mammalian brain forms a vector representation of the self-position of the animal. Recurrent neural networks have been proposed to explain the properties of the grid cells by updating the neural activity vector based on the velocity input of the animal. In doing so, the grid cell system effectively performs path integration. In this paper, we investigate the algebraic, geometric, and topological properties of grid cells using recurrent network models. Algebraically, we study the Lie group and Lie algebra of the recurrent transformation as a representation of self-motion. Geometrically, we study the conformal isometry of the Lie group representation where the local displacement of the activity vector in the neural space is proportional to the local displacement of the agent in the 2D physical space. Topologically, the compact abelian Lie group representation automatically leads to the torus topology commonly assumed and observed in neuroscience. We then focus on a simple non-linear recurrent model that underlies the continuous attractor neural networks of grid cells. Our numerical experiments show that conformal isometry leads to hexagon periodic patterns in the grid cell responses and our model is capable of accurate path integration. Code is available at \url{https://github.com/DehongXu/grid-cell-rnn}.

Polarons are entities of excess electrons dressed with local response of lattices, whose atomic-scale characterization is essential for understanding the many body physics arising from the electron-lattice entanglement, but yet difficult to achieve. Here, using scanning tunneling microscopy and spectroscopy (STM/STS), we show the visualization and manipulation of single polarons with different origin, i.e., electronic and conventional polarons, in monolayer CoCl2, that are grown on HOPG substrate via molecular beam epitaxy. Four types of polarons are identified, all inducing upward local band bending, but exhibiting distinct appearances, lattice occupations, polaronic states and local lattice distortions. First principles calculations unveil three types of polarons are stabilized by electron-electron interaction. The type-4 polaron, however, are driven by conventional lattice distortions. All the four types of polarons can be created, moved, erased, and moreover interconverted individually by the STM tip, allowing precise control of single polarons unprecedently. This finding identifies the rich category of polarons and their feasibility of manipulation in CoCl2, which can be generalized to other transition metal halides., Comment: 23 pages, 5 figures

Recent advances in deep generative models have led to immense progress in 3D shape synthesis. While existing models are able to synthesize shapes represented as voxels, point-clouds, or implicit functions, these methods only indirectly enforce the plausibility of the final 3D shape surface. Here we present a 3D shape synthesis framework (SurfGen) that directly applies adversarial training to the object surface. Our approach uses a differentiable spherical projection layer to capture and represent the explicit zero isosurface of an implicit 3D generator as functions defined on the unit sphere. By processing the spherical representation of 3D object surfaces with a spherical CNN in an adversarial setting, our generator can better learn the statistics of natural shape surfaces. We evaluate our model on large-scale shape datasets, and demonstrate that the end-to-end trained model is capable of generating high fidelity 3D shapes with diverse topology., Comment: ICCV 2021. Project page: https://github.com/aluo-x/NeuralRaycaster

Genuine multipartite entanglement represents the strongest type of entanglement, which is an essential resource for quantum information processing. Standard methods to detect genuine multipartite entanglement, e.g., entanglement witnesses, state tomography, or quantum state verification, require full knowledge of the Hilbert space dimension and precise calibration of measurement devices, which are usually difficult to acquire in an experiment. The most radical way to overcome these problems is to detect entanglement solely based on the Bell-like correlations of measurement outcomes collected in the experiment, namely, device-independently (DI). However, it is difficult to certify genuine entanglement of practical multipartite states in this way, and even more difficult to quantify it, due to the difficulty to identify optimal multipartite Bell inequalities and protocols tolerant to state impurity. In this work, we explore a general and robust DI method which can be applied to various realistic multipartite quantum state in arbitrary finite dimension, while merely relying on bipartite Bell inequalities. Our method allows us both to certify the presence of genuine multipartite entanglement and to quantify it. Several important classes of entangled states are tested with this method, leading to the detection of genuinely entangled states. We also certify genuine multipartite entanglement in weakly-entangled GHZ states, thus showing that the method applies equally well to less standard states.

Correlated states emerge in low-dimensional systems owing to enhanced Coulomb interactions. Elucidating these states requires atomic scale characterization and delicate control capabilities. In this study, spectroscopic imaging-scanning tunneling microscopy was employed to investigate the correlated states residing in the one-dimensional electrons of the monolayer and bilayer MoSe2 mirror twin boundary (MTB). The Coulomb energies, determined by the wire length, drive the MTB into two types of ground states with distinct respective out-of-phase and in-phase charge orders. The two ground states can be reversibly converted through a metastable zero-energy state with in situ voltage pulses, which tunes the electron filling of the MTB via a polaronic process, as substantiated by first-principles calculations. Our modified Hubbard model reveals the ground states as correlated insulators from an on-site U-originated Coulomb interaction, dubbed Hubbard-type Coulomb blockade effect. Our work sets a foundation for understanding correlated physics in complex systems and for tailoring quantum states for nano-electronics applications., Comment: 4 figures, 19 pages

Mott state in 1T-TaS2 is predicted to host quantum spin liquids (QSL). However, its insulating mechanism is controversial due to complications from interlayer coupling. Here, we study the Mott state in monolayer 1T-NbSe2, an electronic analogy to TaS2 exempt from interlayer coupling, using spectroscopic imaging scanning tunneling microscopy and first principles calculations. Monolayer NbSe2 surprisingly displays two types of Star-of-David (SD) motifs with different Mott gap sizes, that are interconvertible via temperature variation. And, bilayer 1T-NbSe2 shows Mott collapse by interlayer coupling. Our calculation unveils the two types of SDs possess distinct structural distortions, altering the effective Coulomb energies of the central Nb orbital. Our calculation suggests the Mott gap, the same parameter for determining the QSL regime, is tunable with strain. This finding offers a general strategy for manipulating the Mott state in 1T-NbSe2 and related systems via structural distortions, which may be tuned into the potential QSL regime., Comment: 20 pages, 5 figures

In optical metrological protocols to measure physical quantities, it is, in principle, always beneficial to increase photon number to improve measurement precision. However, practical constraints prevent arbitrary increase of n due to the imperfections of a practical detector, especially when the detector response is dominated by saturation effect. In this work, we show that a modified weak measurement protocol, namely, biased weak measurement significantly improves the precision of optical metrology in the presence of saturation effect. This method detects an ultra-small fraction of photons while maintains considerable amount of metrological information. The biased pre-coupling leads to an additional reduction of photons in the post-selection and generates an extinction point in the spectrum distribution, which is extremely sensitive to the estimated parameter and difficult to be saturated. Therefore, the Fisher information can be persistently enhanced by increasing the photon number. In our magnetic-sensing experiment, biased weak measurement achieves precision approximately one order of magnitude better than those of previously used methods. The proposed method can be applied in various optical measurement schemes to circumvent detector saturation effect with low-cost apparatuses.

Exploring new two-dimensional (2D) van der Waals (vdW) systems is at the forefront of materials physics. Here, through molecular beam epitaxy on graphene-covered SiC(0001), we report successful growth of AlSb in the double-layer honeycomb (DLHC) structure, a 2D vdW material which has no direct analogue to its 3D bulk and is predicted kinetically stable when freestanding. The structural morphology and electronic structure of the experimental 2D AlSb are characterized with spectroscopic imaging scanning tunneling microscopy and cross-sectional imaging scanning transmission electron microscopy, which compare well to the proposed DLHC structure. The 2D AlSb exhibits a bandgap of 0.93 eV versus the predicted 1.06 eV, which is substantially smaller than the 1.6 eV of bulk. We also attempt the less-stable InSb DLHC structure; however, it grows into bulk islands instead. The successful growth of a DLHC material here opens the door for the realization of a large family of novel 2D DLHC traditional semiconductors with unique excitonic, topological, and electronic properties., Comment: 21 pages, 6 figures

Intrinsic antiferromagnetism in van der Waals (vdW) monolayer (ML) crystals enriches the understanding regarding two-dimensional (2D) magnetic orders and holds special virtues over ferromagnetism in spintronic applications. However, the studies on intrinsic antiferromagnetism are sparse, owing to the lack of net magnetisation. In this study, by combining spin-polarised scanning tunnelling microscopy and first-principles calculations, we investigate the magnetism of vdW ML CrTe2, which has been successfully grown through molecular beam epitaxy. Surprisingly, we observe a stable antiferromagnetic (AFM) order at the atomic scale in the ML crystal, whose bulk is a strong ferromagnet, and correlate its imaged zigzag spin texture with the atomic lattice structure. The AFM order exhibits an intriguing noncollinear spin-flop transition under magnetic fields, consistent with its calculated moderate magnetic anisotropy. The findings of this study demonstrate the intricacy of 2D vdW magnetic materials and pave the way for their in-depth studies., Comment: 28 pages, 4 figures, Nature Communications, accepted

Quantum state verification provides an efficient approach to characterize the reliability of quantum devices for generating certain target states. The figure of merit of a specific strategy is the estimated infidelity $\epsilon$ of the tested state to the target state, given a certain number of performed measurements n. Entangled measurements constitute the globally optimal strategy and achieve the scaling that \epsilon is inversely proportional to n. Recent advances show that it is possible to achieve the same scaling simply with non-adaptive local measurements, however, the performance is still worse than the globally optimal bound up to a constant factor. In this work, by introducing classical communication, we experimentally implement an adaptive quantum state verification. The constant-factor is minimized from ~2.5 to 1.5 in this experiment, which means that only 60% measurements are required to achieve a certain value of \epsilon compared to optimal non-adaptive local strategy. Our results indicate that classical communication significantly enhances the performance of quantum state verification, and leads to an efficiency that further approaches the globally optimal bound., Comment: arXiv admin note: substantial text overlap with arXiv:1803.10961

We present an experimental approach to construct a dephrasure channel, which contains both dephasing and erasure noises, and can be used as an efficient tool to study the superadditivity of coherent information. By using a three-fold dephrasure channel, the superadditivity of coherent information is observed, and a substantial gap is found between the zero single-letter coherent information and zero quantum capacity. Particularly, we find that when the coherent information of n channel uses is zero, in the case of larger number of channel uses, it will become positive. These phenomena exhibit a more obvious superadditivity of coherent information than previous works, and demonstrate a higher threshold for non-zero quantum capacity. Such novel channels built in our experiment also can provide a useful platform to study the non-additive properties of coherent information and quantum channel capacity.

In one-dimensional (1D) metallic systems, the diverging electron susceptibility and electron-phonon coupling collaboratively drive the electrons into a charge density wave (CDW) state. However, strictly 1D system is unstable against perturbations, whose effect on CDW order requires clarification ideally with altered coupling to surroundings. Here, we fabricate such a system with nanowires of Mo6Se6 bundles, which are either attached to edges of monolayer MoSe2 or isolated freely, by post-annealing the preformed MoSe2. Using scanning tunneling microscopy (STM), we visualized charge modulations and CDW gaps with prominent coherent peaks in the edge-attached nanowires. Astonishingly, the CDW order becomes suppressed in the isolated nanowires, showing CDW correlation gaps without coherent peaks. The contrasting behavior, as revealed with theoretical modeling, is interpreted as the effect of phason-polarons on the 1D CDW state. Our work elucidates a possibly unprecedented many body effect that may be generic to strictly 1D system but undermined in quasi-1D system., Comment: 21 pages, 4 figures

Two-dimensional materials offer opportunities for unravelling unprecedented ordered states at single layer limit. Among such ordered states, Mott phase is rarely explored. Here, we report the Mott phase in van der Waals chromium (II) iodide (CrI2) films. High quality CrI2 films with atomically flat surface and macro size are grown on graphitized 6H-SiC(0001) substrate by molecular beam epitaxy. By in situ low temperature scanning tunneling microscopy and spectroscopy (STM/STS), we reveal that the film has a band gap as large as ~3.2 eV, which is nearly thickness independent. Density functional plus dynamic mean field theory calculations suggest that CrI2 films may be a strong Mott insulator with a ferromagnetically ordered ground state. The Mott phase is corroborated by the spectral band splitting, that is consistent with the extended Hubbard model, and gap reduction at charge dopants. Our study provides a platform for studying correlated electron states at single layer limit., Comment: 18 pages, 4 figures

We investigated the dynamical behaviors of bimodular continuous attractor neural networks, each processing a modality of sensory input and interacting with each other. We found that when bumps coexist in both modules, the position of each bump is shifted towards the other input when the intermodular couplings are excitatory and is shifted away when inhibitory. When one intermodular coupling is excitatory while another is moderately inhibitory, temporally modulated population spikes can be generated. On further increase of the inhibitory coupling, momentary spikes will emerge. In the regime of bump coexistence, bump heights are primarily strengthened by excitatory intermodular couplings, but there is a lesser weakening effect due to a bump being displaced from the direct input. When bimodular networks serve as decoders of multisensory integration, we extend the Bayesian framework to show that excitatory and inhibitory couplings encode attractive and repulsive priors, respectively. At low disparity, the bump positions decode the posterior means in the Bayesian framework, whereas at high disparity, multiple steady states exist. In the regime of multiple steady states, the less stable state can be accessed if the input causing the more stable state arrives after a sufficiently long delay. When one input is moving, the bump in the corresponding module is pinned when the moving stimulus is weak, unpinned at intermediate stimulus strength, and tracks the input at strong stimulus strength, and the stimulus strengths for these transitions increase with the velocity of the moving stimulus. These results are important to understanding multisensory integration of static and dynamic stimuli., Comment: 15 pages, 11 figures, journal paper

Quantum metrology aims to enhance the precision of various measurement tasks by taking advantages of quantum properties. In many scenarios, precision is not the sole target; the acquired information must be protected once it is generated in the sensing process. Considering a remote sensing scenario where a local site performs cooperative sensing with a remote site to collect private information at the remote site, the loss of sensing data inevitably causes private information to be revealed. Quantum key distribution is known to be a reliable solution for secure data transmission, however, it fails if an eavesdropper accesses the sensing data generated at a remote site. In this study, we demonstrate that by sharing entanglement between local and remote sites, secure quantum remote sensing can be realized, and the secure level is characterized by asymmetric Fisher information gain. Concretely, only the local site can acquire the estimated parameter accurately with Fisher information approaching 1. In contrast, the accessible Fisher information for an eavesdropper is nearly zero even if he/she obtains the raw sensing data at the remote site. This achievement is primarily due to the nonlocal calibration and steering of the probe state at the remote site. Our results explore one significant advantage of ``quantumness'' and extend the notion of quantum metrology to the security realm.

The initialization of a quantum system into a certain state is a crucial aspect of quantum information science. While a variety of measurement strategies have been developed to characterize how well the system is initialized, for a given one, there is in general a trade-off between its efficiency and the accessible information of the quantum state. Conventional quantum state tomography can characterize unknown states by reconstructing the density matrix; however, its exponentially expensive postprocessing is likely to produce a deviate result. Alternatively, quantum state verification provides a technique to quantify the prepared state with significantly fewer measurements, especially for quantum entangled states. Here, we experimentally implement an optimal verification of entangled states with local measurements, where the estimated infidelity is inversely proportional to the number of measurements. The utilized strategy is tolerant of the impurity of realistic states, hence being highly robust in a practical sense. Even more valuable, our method only requires local measurements, which incurs only a small constant-factor (<2.5) penalty compared to the globally optimal strategy requiring nonlocal measurements.

It has been suggested that both quantum superpositions and nonlinear interactions are important resources for quantum metrology. However, to date the different roles that these two resources play in the precision enhancement are not well understood. Here, we experimentally demonstrate a Heisenberg-scaling metrology to measure the parameter governing the nonlinear coupling between two different optical modes. The intense mode with n (more than 10^6 in our work) photons manifests its effect through the nonlinear interaction strength which is proportional to its average photon-number. The superposition state of the weak mode, which contains only a single photon, is responsible for both the linear Hamiltonian and the scaling of the measurement precision. By properly preparing the initial state of single photon and making projective photon-counting measurement, the extracted classical Fisher information (FI) can saturate the quantum FI embedded in the combined state after coupling, which is ~ n^2 and leads to a practical precision ~ 1.2/n. Free from the utilization of entanglement, our work paves a way to realize Heisenberg-scaling precision when only a linear Hamiltonian is involved.

Self-testing refers to a method with which a classical user can certify the state and measurements of quantum systems in a device-independent way. Especially, the self-testing of entangled states is of great importance in quantum information process. A comprehensible example is that violating the CHSH inequality maximally necessarily implies the bipartite shares a singlet. One essential question in self-testing is that, when one observes a non-maximum violation, how close is the tested state to the target state (which maximally violates certain Bell inequality)? The answer to this question describes the robustness of the used self-testing criterion, which is highly important in a practical sense. Recently, J. Kaniewski predicts two analytic self-testing bounds for bipartite and tripartite systems. In this work, we experimentally investigate these two bounds with high quality two-qubit and three-qubit entanglement sources. The results show that these bounds are valid for various of entangled states we prepared, and thus, we implement robust self-testing processes which improve the previous results significantly.

Quantum entanglement is the key resource for quantum information processing. Device-independent certification of entangled states is a long standing open question, which arouses the concept of self-testing. The central aim of self-testing is to certify the state and measurements of quantum systems without any knowledge of their inner workings, even when the used devices cannot be trusted. Specifically, utilizing Bell's theorem, it is possible to place a boundary on the singlet fidelity of entangled qubits. Here, beyond this rough estimation, we experimentally demonstrate a complete self-testing process for various pure bipartite entangled states up to four dimensions, by simply inspecting the correlations of the measurement outcomes. We show that this self-testing process can certify the exact form of entangled states with fidelities higher than 99.9% for all the investigated scenarios, which indicates the superior completeness and robustness of this method. Our work promotes self-testing as a practical tool for developing quantum techniques.