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Chi Li

Publications and source records attributed to Chi Li.

At least 73 records · Page 4Linked to original sources
arXiv2020

Algebraic uniqueness of Kähler-Ricci flow limits and optimal degenerations of Fano varieties

We prove that for any $\mathbb{Q}$-Fano variety $X$, the special $\mathbb{R}$-test configuration that minimizes the $H$-functional is unique and has a K-semistable $\mathbb{Q}$-Fano central fibre $(W, ξ)$. Moreover there is a unique K-polystable degeneration of $(W, ξ)$. As an application, we confirm the conjecture of Chen-Sun-Wang about the algebraic-uniqueness for Kähler-Ricci flow limits on Fano manifolds, which implies that the Gromov-Hausdorff limit of the flow does not depend on the choice of initial Kähler metrics. The results are achieved by studying algebraic optimal degeneration problems via new functionals of real valuations, which are analogous to the minimization problem for normalized volumes.

math.AG↗
arXiv2020

Tunable quantum photonics platform based on fiber-cavity enhanced single photon emission from two-dimensional hBN

Realization of quantum photonic devices requires coupling single quantum emitters to the mode of optical resonators. In this work we present a hybrid system consisting of defect centers in few-layer hBN grown by chemical vapor deposition and a fiber-based Fabry-Perot cavity. The sub 10 nm thickness of hBN and its smooth surface enables efficient integration into the cavity mode. We operate our hybrid platform over a broad spectral range larger than 30 nm and use its tuneability to explore different coupling regimes. Consequently, we achieve very large cavity-assisted signal enhancement up to 50-fold and equally strong linewidth narrowing owing to cavity funneling, both records for hBN-cavity systems. Additionally, we implement an excitation and readout scheme for resonant excitation that allows us to establish cavity-assisted PLE spectroscopy. Our work marks an important milestone for the deployment of 2D materials coupled to fiber-based cavities in practical quantum technologies.

physics.app-ph↗
arXiv2020

Self-Representation Based Unsupervised Exemplar Selection in a Union of Subspaces

Finding a small set of representatives from an unlabeled dataset is a core problem in a broad range of applications such as dataset summarization and information extraction. Classical exemplar selection methods such as $k$-medoids work under the assumption that the data points are close to a few cluster centroids, and cannot handle the case where data lie close to a union of subspaces. This paper proposes a new exemplar selection model that searches for a subset that best reconstructs all data points as measured by the $\ell_1$ norm of the representation coefficients. Geometrically, this subset best covers all the data points as measured by the Minkowski functional of the subset. To solve our model efficiently, we introduce a farthest first search algorithm that iteratively selects the worst represented point as an exemplar. When the dataset is drawn from a union of independent subspaces, our method is able to select sufficiently many representatives from each subspace. We further develop an exemplar based subspace clustering method that is robust to imbalanced data and efficient for large scale data. Moreover, we show that a classifier trained on the selected exemplars (when they are labeled) can correctly classify the rest of the data points.

cs.LG↗
arXiv2020

Grain Dependent Growth of Bright Quantum Emitters in Hexagonal Boron Nitride

Point defects in hexagonal boron nitride have emerged as a promising quantum light source due to their bright and photostable room temperature emission. In this work, we study the incorporation of quantum emitters during chemical vapor deposition growth on a nickel substrate. Combining a range of characterization techniques, we demonstrate that the incorporation of quantum emitters is limited to (001) oriented nickel grains. Such emitters display improved emission properties in terms of brightness and stability. We further utilize these emitters and integrate them with a compact optical antenna enhancing light collection from the sources. The hybrid device yields average saturation count rates of ~2.9 x106 cps and an average photon purity of ~90%. Our results advance the controlled generation of spatially distributed quantum emitters in hBN and demonstrate a key step towards on-chip devices with maximum collection efficiency.

physics.app-ph↗
arXiv2020

Optical Thermometry with Quantum Emitters in Hexagonal Boron Nitride

Nanoscale optical thermometry is a promising non-contact route for measuring local temperature with both high sensitivity and spatial resolution. In this work, we present a deterministic optical thermometry technique based on quantum emitters in nanoscale hexagonal boron-nitride. We show that these nanothermometers exhibit better performance than that of homologous, all-optical nanothermometers both in sensitivity and range of working temperature. We demonstrate their effectiveness as nanothermometers by monitoring the local temperature at specific locations in a variety of custom-built micro-circuits. This work opens new avenues for nanoscale temperature measurements and heat flow studies in miniaturized, integrated devices.

physics.app-ph↗
arXiv2019

Second-harmonic generation in multilayer hexagonal boron nitride flakes

We report second-harmonic generation (SHG) from thick hexagonal boron nitride (hBN) flakes with approximately 109-111 layers. The resulting effective second-order susceptibility is similar to previously reported few-layer experiments. This confirms that thick hBN flakes can serve as a platform for nonlinear optics, which is useful because thick flakes are easy to exfoliate while retaining a large flake size. We also show spatial second-harmonic maps revealing that SHG remains a useful tool for the characterization of the layer structure even in the case of a large number of layers.

physics.optics↗
arXiv2019

Near-field energy transfer between a luminescent 2D material and color centers in diamond

Energy transfer between fluorescent probes lies at the heart of many applications ranging from bio-sensing and -imaging to enhanced photo-detection and light harvesting. In this work, we study Förster resonance energy transfer (FRET) between shallow defects in diamond --- nitrogen-vacancy (NV) centers --- and atomically-thin, two-dimensional materials --- tungsten diselenide (WSe$_2$). By means of fluorescence lifetime imaging, we demonstrate the occurrence of FRET in the WSe$_2$/NV system. Further, we show that in the coupled system, NV centers provide an additional excitation pathway for WSe$_2$ photoluminescence. Our results constitute the first step towards the realization of hybrid quantum systems involving single-crystal diamond and two-dimensional materials that may lead to new strategies for studying and controlling spin transfer phenomena and spin valley physics.

quant-ph↗
arXiv2019

On sharp rates and analytic compactifications of asymptotically conical Kähler metrics

Let $X$ be a complex manifold and $S\hookrightarrow X$ be an embedding of complex submanifold. Assuming that the embedding is $(k-1)$-linearizable or $(k-1)$-comfortably embedded, we construct via the deformation to the normal cone a diffeomorphism $F$ from a small neighborhood of the zero section in the normal bundle $N_{S}$ to a small neighborhood of $S$ in $X$ such that $F$ is in a precise sense holomorphic to the $(k-1)$-th order. Using this $F$ we obtain optimal estimates on asymptotical rates for asymptotically conical Calabi-Yau metrics constructed by Tian-Yau. Furthermore, when $S$ is an ample divisor satisfying an appropriate cohomological condition, we relate the order of comfortable embedding to the weight of the deformation of the normal isolated cone singularity arising from the deformation to the normal cone. We also give an example showing that the condition of comfortable embedding depends on the splitting liftings. We then prove an analytic compactification result for the deformation of the complex structure on a complex cone that decays to any positive order at infinity. This can be seen as an analytic counterpart of Pinkham's result on deformations of cone singularities with negative weights.

math.DG↗
arXiv2019

Charge transition levels of quantum emitters in hexagonal boron nitride

Quantum emitters in layered materials are promising candidates for applications in nanophotonics. Here we present a technique based on charge transfer to graphene for measuring the charge transition levels ($\rm E_t$) of fluorescent defects in a wide bandgap 2D material, and apply it to quantum emitters in hexagonal boron nitride (hBN). Our results will aid in identifying the atomic structures of quantum emitters in hBN, as well as practical applications since $\rm E_t$ determines defect charge states and plays a key role in photodynamics.

cond-mat.mtrl-sci↗
arXiv2019

NM-Net: Mining Reliable Neighbors for Robust Feature Correspondences

Feature correspondence selection is pivotal to many feature-matching based tasks in computer vision. Searching for spatially k-nearest neighbors is a common strategy for extracting local information in many previous works. However, there is no guarantee that the spatially k-nearest neighbors of correspondences are consistent because the spatial distribution of false correspondences is often irregular. To address this issue, we present a compatibility-specific mining method to search for consistent neighbors. Moreover, in order to extract and aggregate more reliable features from neighbors, we propose a hierarchical network named NM-Net with a series of convolution layers taking the generated graph as input, which is insensitive to the order of correspondences. Our experimental results have shown the proposed method achieves the state-of-the-art performance on four datasets with various inlier ratios and varying numbers of feature consistencies.

cs.CV↗
arXiv2019

Stability of Valuations: Higher Rational Rank

Given a klt singularity $x\in (X, D)$, we show that a quasi-monomial valuation $v$ with a finitely generated associated graded ring is the minimizer of the normalized volume function $\widehat{\rm vol}_{(X,D),x}$, if and only if $v$ induces a degeneration to a K-semistable log Fano cone singularity. Moreover, such a minimizer is unique among all quasi-monomial valuations up to rescaling. As a consequence, we prove that for a klt singularity $x\in X$ on the Gromov-Hausdorff limit of Kähler-Einstein Fano manifolds, the intermediate K-semistable cone associated to its metric tangent cone is uniquely determined by the algebraic structure of $x\in X$, hence confirming a conjecture by Donaldson-Sun.

math.AG↗
arXiv2019

On the stability of extensions of tangent sheaves on Kähler-Einstein Fano / Calabi-Yau pairs

Let $S$ be a smooth projective variety and $Δ$ a simple normal crossing $\mathbb{Q}$-divisor with coefficients in $(0,1]$. For any ample $\mathbb{Q}$-line bundle $L$ over $S$, we denote by $\mathscr{E}(L)$ the extension sheaf of the orbifold tangent sheaf $T_S(-\log(Δ))$ by the structure sheaf $\mathcal{O}_S$ with the extension class $c_1(L)$. We show the following two results: (i) If $-(K_S+Δ)$ is ample and $(S, Δ)$ is K-semistable, then for any $λ\in \mathbb{Q}_{>0}$, the extension sheaf $\mathscr{E}({λc_1(-(K_S+Δ))})$ is slope semistable with respect to $-(K_S+Δ)$; (ii) If $K_S+Δ\equiv 0$, then for any ample $\mathbb{Q}$-line bundle $L$ over $S$, $\mathscr{E}(L)$ is slope semistable with respect to $L$. These results generalize Tian's result where $-K_S$ is ample and $Δ=\emptyset$. We give two applications of these results. The first is to study a question by Borbon-Spotti about the relationship between local Euler numbers and normalized volumes of log canonical surface singularities. We prove that the two invariants differ only by a factor $4$ when the log canonical pair is an orbifold cone over a marked Riemann surface. The second application is to derive Miyaoka-Yau-type inequalities on K-semistable log-smooth Fano pairs and Calabi-Yau pairs, which generalize some Chern-number inequalities proved by Song-Wang.

math.DG↗
arXiv2019

On the proper moduli spaces of smoothable Kähler-Einstein Fano varieties

In this paper, we investigate the geometry of the orbit space of the closure of the subscheme parametrizing smooth Fano Kähler-Einstein manifolds inside an appropriate Hilbert scheme. In particular, we prove that being K-semistable is a Zariski open condition and establish the uniqueness for the Gromov-Hausdorff limit for a punctured flat family of Fano Kähler-Einstein manifolds. Based on these, we construct a proper scheme parameterizing the S-equivalent classes of $\QQ$-Gorenstein smoothable, K-semistable Fano varieties, and verify various necessary properties to guarantee that it is a good moduli space.

math.AG↗
arXiv2018

Stability of Valuations and Kollár Components

We prove that among all Kollár components obtained by plt blow ups of a klt singularity $o \in (X, D)$, there is at most one that is (log-)K-semistable. We achieve this by showing that if such a Kollár component exists, it uniquely minimizes the normalized volume function introduced in [Li15a] among all divisorial valuations. Conversely, we show any divisorial minimizer of the normalized volume function yields a K-semistable Kollár component. We also prove that for any klt singularity, the infimum of the normalized function is always approximated by the normalized volumes of Kollár components.

math.AG↗
arXiv2018

Study of electron emission from 1D nanomaterials under super high field

Photoemission driven by a strong electric field of near-infrared or visible light, referred to as strong-field photoemission, produces attosecond electron pulses that are synchronized to the waveform of the incident light, and this principle lies at the heart of current attosecond technologies. However, full access to strong-field photoemission regimes at near-infrared wavelengths based on solid-state materials is restricted by space-charge screening and material damage at high optical-field strengths, which significantly hampers the realization of predicted attosecond technologies, such as ultra-sensitive optical phase modulation. Here, we demonstrate a new type of strong-field photoemission behaviour with extreme nonlinearity -- photoemission current scales follow a 40th power law of the optical-field strength, making use of sub-nanometric carbon nanotubes and 800 nm pulses. As a result, the total photoemission current depends on the carrier-envelope phase with a greatly improved photoemission current modulation depth of up to 100%, which has not previously been achieved. Time-dependent density functional calculations reveal the completely new behaviour of the optical-field induced tunnelling emission process directly from the valence band of the carbon nanotubes, which is an indication of full access to a strong-field photoemission regime. Furthermore, the nonlinear dynamics are observed to be tunable by changing the binding energy of the valence-band-maximum, as confirmed by Simpleman model calculations. We believe that such extreme nonlinear photoemission from nanotips offers a new means of producing extreme temporal-spatial resolved electron pulses. These results additionally provide a new design philosophy for attosecond electronics and optics by making use of tunable band structures in nanomaterials.

physics.optics↗
arXiv2018

A Unified Framework for Multi-View Multi-Class Object Pose Estimation

One core challenge in object pose estimation is to ensure accurate and robust performance for large numbers of diverse foreground objects amidst complex background clutter. In this work, we present a scalable framework for accurately inferring six Degree-of-Freedom (6-DoF) pose for a large number of object classes from single or multiple views. To learn discriminative pose features, we integrate three new capabilities into a deep Convolutional Neural Network (CNN): an inference scheme that combines both classification and pose regression based on a uniform tessellation of the Special Euclidean group in three dimensions (SE(3)), the fusion of class priors into the training process via a tiled class map, and an additional regularization using deep supervision with an object mask. Further, an efficient multi-view framework is formulated to address single-view ambiguity. We show that this framework consistently improves the performance of the single-view network. We evaluate our method on three large-scale benchmarks: YCB-Video, JHUScene-50 and ObjectNet-3D. Our approach achieves competitive or superior performance over the current state-of-the-art methods.

cs.CV↗
arXiv2018

Deep Supervision with Intermediate Concepts

Recent data-driven approaches to scene interpretation predominantly pose inference as an end-to-end black-box mapping, commonly performed by a Convolutional Neural Network (CNN). However, decades of work on perceptual organization in both human and machine vision suggests that there are often intermediate representations that are intrinsic to an inference task, and which provide essential structure to improve generalization. In this work, we explore an approach for injecting prior domain structure into neural network training by supervising hidden layers of a CNN with intermediate concepts that normally are not observed in practice. We formulate a probabilistic framework which formalizes these notions and predicts improved generalization via this deep supervision method. One advantage of this approach is that we are able to train only from synthetic CAD renderings of cluttered scenes, where concept values can be extracted, but apply the results to real images. Our implementation achieves the state-of-the-art performance of 2D/3D keypoint localization and image classification on real image benchmarks, including KITTI, PASCAL VOC, PASCAL3D+, IKEA, and CIFAR100. We provide additional evidence that our approach outperforms alternative forms of supervision, such as multi-task networks.

cs.CV↗