arXiv subjects

Li Ge

Publications and source records attributed to Li Ge.

At least 19 recordsLinked to original sources

arXiv2026

Cyclic ladder operators and hidden Weyl-Heisenberg structure in a Floquet system

Ladder operators, found in the quantum harmonic oscillator and other quantized systems, provide an elegant approach to solving or understanding otherwise intricate physics problems. In this Letter, we discuss cyclic ladder operators in both Hermitian and non-Hermitian systems with a finite Hilbert space, with the highest (lowest) level directly descending (ascending) to the lowest (highest) level via a single raising (lowering) operation. We show that an equally spaced energy ladder emerges when these systems have an underlying Weyl-Heisenberg commutation relation, with the cyclic ladder operators and the temporal evolution operator behaving as the generators of the Weyl-Heisenberg group. We further illustrate such a system using a one-dimensional Floquet lattice, where the cyclic ladder operators become diagonal and the temporal evolution simplifies to a permutation matrix after a Floquet period. Our findings reveal a hidden relation between non-trivial dynamics and algebraic principles in Floquet systems, which may exist for other quantum numbers as well besides the energy levels.

quant-ph↗

arXiv2026

Observing complementary Lucas sequences using non-Hermitian zero modes

The Lucas sequences are integers defined by a homogeneous recurrence relation. They include the well-known Fibonacci numbers, which appear abundantly in nature. The complementary Lucas numbers, defined by the same recurrence relation, are less well-known. In this work, we show that such complementary Lucas sequences can be observed simultaneously on the same physical platform, using zero modes in one-dimensional system(s) coupled to a non-Hermitian reservoir. When the latter consists solely of gain and loss modulated non-Hermiticity, the two Lucas sequences can manifest as a linearly localized edge state and a constant-intensity mode, respectively. When the reservoir features asymmetric couplings as well, more general Lucas sequences can be realized either directly on one sublattice in the reservoir or by reconstructing the wave function on both sublattices. Finally, if we allow, in addition, an alternate frequency detuning in the reservoir, all Lucas sequences can be observed in principle, including the Fibonacci and Lucas numbers.

quant-ph↗

arXiv2026

Tight Bounds for Gaussian Mean Estimation under Personalized Differential Privacy

We study mean estimation for Gaussian distributions under \textit{personalized differential privacy} (PDP), where each record has its own privacy budget. PDP is commonly considered in two variants: \textit{bounded} and \textit{unbounded} PDP. In bounded PDP, the privacy budgets are public and neighboring datasets differ by replacing one record. In unbounded PDP, neighboring datasets differ by adding or removing a record; consequently, an algorithm must additionally protect participation information, making both the dataset size and the privacy profile sensitive. Existing works have only studied mean estimation over bounded distributions under bounded PDP. Different from mean estimation for distributions with bounded range, where each element can be treated equally and we only need to consider the privacy diversity of elements, the challenge for Gaussian is that, elements can have very different contributions due to the unbounded support. we need to jointly consider the privacy information and the data values. Such a problem becomes even more challenging under unbounded PDP, where the privacy information is protected and the way to compute the weights becomes unclear. In this paper, we address these challenges by proposing optimal Gaussian mean estimators under both bounded and unbounded PDP, where in each setting we first derive lower bounds for both problems, following PDP mean estimators with the algorithmic upper bounds matching the corresponding lower bounds up to logarithmic factors.

cs.DS↗

arXiv2025

Twisted light from topological chiral exceptional points in a nanolaser array

We propose and experimentally demonstrate an orbital angular momentum (OAM) nanolaser array arranged in a ring geometry on an InP-based photonic crystal membrane. The device realizes a non-Hermitian extension of the Rice-Mele model, featuring alternating coupling strengths and imaginary on-site detunings. This configuration supports a symmetry-protected zero mode stabilized by non-Hermitian particle-hole symmetry, which enforces a uniform $\pi/2$ phase shift between adjacent nanolasers, establishing a coherent phase winding around the array. By adjusting the gain/loss contrast in a parity-time (PT)-like pumping scheme, the system can be tuned to a chiral exceptional point, where energy flows unidirectionally between nanocavities despite their reciprocal coupling. This symmetry-enforced, directional tunneling leads to far-field emission carrying non-zero OAM, providing a direct signature of the phase-structured lasing mode. Our results demonstrate a robust and scalable strategy for engineering compact, phase-locked laser arrays with controllable angular momentum output, and open new avenues for structured light generation in integrated photonic platforms.

physics.optics↗

arXiv2025

ROI-Guided Point Cloud Geometry Compression Towards Human and Machine Vision

Point cloud data is pivotal in applications like autonomous driving, virtual reality, and robotics. However, its substantial volume poses significant challenges in storage and transmission. In order to obtain a high compression ratio, crucial semantic details usually confront severe damage, leading to difficulties in guaranteeing the accuracy of downstream tasks. To tackle this problem, we are the first to introduce a novel Region of Interest (ROI)-guided Point Cloud Geometry Compression (RPCGC) method for human and machine vision. Our framework employs a dual-branch parallel structure, where the base layer encodes and decodes a simplified version of the point cloud, and the enhancement layer refines this by focusing on geometry details. Furthermore, the residual information of the enhancement layer undergoes refinement through an ROI prediction network. This network generates mask information, which is then incorporated into the residuals, serving as a strong supervision signal. Additionally, we intricately apply these mask details in the Rate-Distortion (RD) optimization process, with each point weighted in the distortion calculation. Our loss function includes RD loss and detection loss to better guide point cloud encoding for the machine. Experiment results demonstrate that RPCGC achieves exceptional compression performance and better detection accuracy (10% gain) than some learning-based compression methods at high bitrates in ScanNet and SUN RGB-D datasets.

cs.CV↗

arXiv2025

Skywork R1V: Pioneering Multimodal Reasoning with Chain-of-Thought

We introduce Skywork R1V, a multimodal reasoning model extending the an R1-series Large language models (LLM) to visual modalities via an efficient multimodal transfer method. Leveraging a lightweight visual projector, Skywork R1V facilitates seamless multimodal adaptation without necessitating retraining of either the foundational language model or the vision encoder. To strengthen visual-text alignment, we propose a hybrid optimization strategy that combines Iterative Supervised Fine-Tuning (SFT) with Group Relative Policy Optimization (GRPO), significantly enhancing cross-modal integration efficiency. Additionally, we introduce an adaptive-length Chain-of-Thought distillation approach for reasoning data generation. This approach dynamically optimizes reasoning chain lengths, thereby enhancing inference efficiency and preventing excessive reasoning overthinking. Empirical evaluations demonstrate that Skywork R1V, with only 38B parameters, delivers competitive performance, achieving a score of 69.0 on the MMMU benchmark and 67.5 on MathVista. Meanwhile, it maintains robust textual reasoning performance, evidenced by impressive scores of 72.0 on AIME and 94.0 on MATH500. The Skywork R1V model weights have been publicly released to promote openness and reproducibility.

cs.CV↗

arXiv2024

Non-Hermitian gauged reciprocity and symmetry

The Lorentz reciprocity is a fundamental property in electromagnetism and well known to break down due to an external magnetic field. With a fictitious or imaginary vector potential, however, its behavior is largely unknown. Here we show that in systems with an imaginary vector potential and displaying the non-Hermitian skin effect, the Lorentz reciprocity is broken but still governed by a rigorous mathematical relation, which we term non-Hermitian gauged reciprocity. When mimicking an imaginary vector potential using just linear integrated photonic elements, however, the conditions that lead to the Lorentz reciprocity are still satisfied and hence the latter cannot be broken. Nevertheless, we show that the non-Hermitian gauged reciprocity can still be observed with a proper choice of inputs and outputs, alongside the Lorentz reciprocity. In addition, we also reveal another equal-amplitude response in the same system, which we attribute to a non-Hermitian gauged symmetry. Furthermore, we show that light propagation is not impinged by the non-Hermitian topological funnel effect, highlighting an underappreciated difference between coherently driven and non-driven systems. These findings are confirmed using a tight-binding model and full-wave simulations of coupled optical micro-ring resonators, providing a valuable extension of the Lorentz reciprocity in the non-Hermitian domain.

physics.optics↗

arXiv2024

Detecting and Understanding the Difference between Natural Mediation Effects and Their Randomized Interventional Analogues

In causal mediation analysis, the natural direct and indirect effects (natural effects) are nonparametrically unidentifiable in the presence of treatment-induced confounding, which motivated the development of randomized interventional analogues (RIAs) of the natural effects. Being easier to identify, the RIAs are becoming widely used in practice. However, applied researchers often interpret RIA estimates as if they were the natural effects, even though the RIAs can be poor proxies for the natural effects. This calls for practical and theoretical guidance on when the RIAs differ from or coincide with the natural effects. We develop the first empirical test to detect the divergence between the natural effects and their RIAs under the weak assumptions sufficient for identifying the RIAs and illustrate the test using the Moving to Opportunity Study. We also provide new theoretical insights on the relationship between the natural effects and the RIAs both using a covariance formulation and from a structural equation perspective. This analysis also reveals previously undocumented connections between the natural effects, the RIAs, and estimands in instrumental variable analysis and Wilcoxon-Mann-Whitney tests.

stat.ME↗

arXiv2024

Dual-color Coherent Perfect Absorber

Perfect absorption of light critically affects light-matter interaction for various applications. Coherent perfect absorbers (CPA) gain the unique capability of controlling light with light in a linear fashion. Multi-color CPAs [Phys. Rev. Lett. 107, 033901] are highly desirable for broadband and nonlinear light-to-light coherent control, however, the experimental demonstration has still remained elusive. Here we experimentally observe a dual-color version of CPA (DC-CPA) through a second harmonic generation in a single whispering-gallery-mode microcavity. The DC-CPA enables simultaneous perfect absorption of both the incoming fundamental wave and its second harmonic. Similar to its linear counterpart, coherent control in the DC-CPA can be also realized by tuning the relative phase and intensity between the two-colored waves through nonlinear interference instead of the linear one. This scheme breaks the linear boundary of the traditional CPA into a multi-frequency domain and paves the way toward all-optically signal processing and quantum information.

physics.optics↗

arXiv2024

Non-Hermitian systems with a real spectrum and selective skin effect

In this work we first show a simple approach to constructing non-Hermitian Hamiltonians with a real spectrum, which are \textit{not} obtained by a non-unitary transformation such as the imaginary gauge transformation. They are given, instead, by the product of a Hermitian Hamiltonian $H_0$ and a positive semi-definite matrix $A$. Depending on whether $A$ has zero eigenvalue(s), the resulting $H$ can possess an exceptional point at zero energy. When $A$ is only required to be Hermitian instead, the resulting $H$ is pseudo-Hermitian that can have real and complex conjugate energy levels. In the special case where $A$ is diagonal, we compare our approach to an imaginary gauge transformation, which reveals a selective non-Hermitian skin effect in our approach, i.e., only the zero mode is a skin mode and the non-zero modes reside in the bulk. We further show that this selective non-Hermitian skin mode has a much lower lasing threshold than its counterpart in the standard non-Hermitian skin effect with the same spatial profile, when we pump at the boundary where they are localized. The form of our construction can also be found, for example, in dynamical matrices describing coupled frictionless harmonic oscillators with different masses.

quant-ph↗

arXiv2024

Subwavelength Photorefractive Grating in a Thin-Film Lithium Niobate Microcavity

Subwavelength gratings play a fundamental and pivotal role in numerous science and applications for wave manipulation, exhibiting distinctive features such as filtering, phase manipulation, and anti-reflection. However, conventional fabrication methods for ultrasmall periodic structures are constrained by the fundamental optical diffraction limit, making it challenging to produce subwavelength gratings for optics. Here, we demonstrate a novel technique to build a reconfigurable subwavelength photorefractive grating (SPG) in a thin-film lithium niobate on the platform of an optical microcavity. Such SPGs are optically induced through the photorefractive effect and the subwavelength features originate from the spatial phase modulations of the pump's standing wave. The resulting SPGs lead to the mode splitting of two counter-propagating modes inside the microcavity, exhibiting an Electromagnetically Induced Transparency (EIT)-like transmission spectrum. Moreover, the unique subwavelength characteristic of SPGs enables first-order quasi-phase-matching for backward second-harmonic generation, a long-standing problem in nonlinear optics. Also, free-space-to-chip vertical nonlinear frequency conversion can be achieved in a similar manner. These results provide a flexible approach towards fabricating subwavelength gratings, which holds significant potential in various applications such as nonlinear frequency conversion, optical communication, sensing, and quantum technologies.

physics.optics↗

arXiv2024

Enhanced Frequency Conversion in Parity-Time Symmetry Line

Non-Hermitian degeneracies reveal intriguing and non-trivial behaviors in open physical systems. Examples like Parity-Time (PT) symmetry breaking, topological encircling chirality, and enhanced sensing near an exceptional point (EP) are often associated with the abrupt nature of the phase transition around these degeneracies. Here we experimentally observe a cavity-enhanced second-harmonic frequency (SHG) conversion on a PT symmetry line, i.e. a set consisting of open-ended isofrequency or isoloss lines, both terminated at EPs on the Riemann surface in parameter space. The enhancement factor can reach as high as 300, depending on the crossing point whether in the symmetry or the broken phase of the PT line. Moreover, such enhancement of SHG enables sensitive distance sensing with a nanometer resolution. Our works may pave the way for practical applications in sensing, frequency conversion, and coherent wave control.

physics.optics↗

arXiv2024

Exact Tensor Completion Powered by Slim Transforms

In this work, a tensor completion problem is studied, which aims to perfectly recover the tensor from partial observations. The existing theoretical guarantee requires the involved transform to be orthogonal, which hinders its applications. In this paper, jumping out of the constraints of isotropy and self-adjointness, the theoretical guarantee of exact tensor completion with arbitrary linear transforms is established by directly operating the tensors in the transform domain. With the enriched choices of transforms, a new analysis obtained by the proof discloses why slim transforms outperform their square counterparts from a theoretical level. Our model and proof greatly enhance the flexibility of tensor completion and extensive experiments validate the superiority of the proposed method.

cs.LG↗

arXiv2024

Effective size of a parity-time symmetric dimer

Parity-time (PT) symmetric dimers were introduced to highlight the unusual properties of non-Hermitian systems that are invariant after a combined parity and time reversal operation. They are also the building blocks of a variety of symmetry and topologically protected structures, especially on integrated photonic platforms. As the name suggests, it consists of two coupled oscillators, which can be optical, mechanical, electronic, and so on in nature. In this article, we show that its effective size, defined by the number of lattice sites inversely proportional to the lattice momentum, is surprisingly three instead of two from the perspective of energy quantization. More specifically, we show analytically that the complex energy levels of a one-dimensional concatenated chain with $N$ PT-dimers are determined by a system size of $1+2N$, which reduces to three in the case of a single PT-dimer. We note that while energy quantization conditions were established in various non-Hermitian systems, exact and explicitly quantized complex energies as reported here are still scarce. In connection, we also discuss the other symmetries of a PT-dimer and concatenated PT-dimer chain, including non-Hermitian particle-hole symmetry and chiral symmetry.

physics.optics↗

arXiv2023

Robust zero modes in non-Hermitian systems without global symmetries

We present an approach to achieve zero modes in lattice models that do not rely on any symmetry or topology of the bulk, which are robust against disorder in the bulk of any type and strength. Such symmetry-free zero modes (SFZMs) are formed by attaching a single site or small cluster with zero mode(s) to the bulk, which serves as the "nucleus" that expands to the entire lattice. We identify the requirements on the couplings between this boundary and the bulk, which reveals that this approach is intrinsically non-Hermitian. We then provide several examples with either an arbitrary or structured bulk, forming spectrally embedded zero modes in the bulk continuum, midgap zero modes, and even restoring the "zeroness" of coupling or disorder-shifted topological corner states. Focusing on viable realizations using photonic lattices, we show that the resulting SFZM can be observed as the single lasing mode when optical gain is applied to the boundary.

physics.optics↗

arXiv2023

Non-Hermitian gauged laser arrays with localized excitations: Anomalous threshold and generalized principle of selective pumping

We investigate non-Hermitian skin modes in laser arrays with spatially localized excitation. Intriguingly, we observe an unusual threshold behavior when selectively pumping either the head or the tail of these modes: both cases exhibit the same lasing threshold and hence defy the conventional principle of selective pumping, which aims to maximize the overlap between the pump profile and the target lasing mode. To shed light on this enigma, we reveal a previously overlooked phenomenon, i.e., energy exchange at non-Hermitian coupling junctions with the photonic environment, which does not occur with uniform gain or loss. Utilizing a transfer matrix approach, we elucidate the mechanism of this anomalous threshold behavior, which is determined by the specific physical realization of the non-Hermitian gauge field (i.e., using gain, loss, or their mixture). Finally, we derive a generalized principle of selective pumping in non-Hermitian arrays, which shows that the decisive spatial overlap is given by the tripartite product of the pump, the lasing mode, and its biorthogonal partner. Our study provides a glimpse into how the two forms of non-Hermiticity, i.e., asymmetric couplings and a complex onsite potential, interact synergetically in laser arrays, which may stimulate further explorations of their collective effects in photonics and related fields.

physics.optics↗

arXiv2023

Analysis of Dirac exceptional points and their isospectral Hermitian counterparts

Recently, a Dirac exceptional point (EP) was reported in a non-Hermitian system. Unlike a Dirac point in Hermitian systems, this Dirac EP has coalesced eigenstates in addition to the degenerate energy. Also different from a typical EP, the two energy levels connected at this Dirac EP remain real in its vicinity and display a linear instead of square root dispersion, forming a tilted Dirac cone in the hybrid space consisting of a momentum dimension and a synthetic dimension for the strength of non-Hermiticity. In this report, we first present simple three-band and two-band matrix models with a Dirac EP, where the linear dispersion of the tilted Dirac cone can be expressed analytically. Importantly, our analysis also reveals that there exist Hermitian and non-Hermitian systems that have the same (real-valued) energy spectrum in their entire parameter space, with the exception that one or more degeneracies in the former are replaced by Dirac EPs in the later. Finally, we show the existence of an imaginary Dirac cone with an EP at its center.

quant-ph↗

arXiv2022

Tracking exceptional points above laser threshold

Recent studies on non-Hermitian optical systems having exceptional points (EPs) have revealed a host of unique characteristics associated with these singularities, including unidirectional invisibility, chiral mode switching and laser self-termination, to mention just a few examples. The vast majority of these works focused either on passive systems or active structures where the EPs were accessed below the lasing threshold, i.e. when the system description is inherently linear. In this work, we experimentally demonstrate that EP singularities in coupled semiconductor nanolasers can be accessed and tracked above the lasing threshold, where they become branch points of a nonlinear dynamical system. Contrary to the common belief that unavoidable cavity detuning will impede the formation of an EP, here we demonstrate that this same detuning is necessary for compensating the carrier-induced frequency shift, hence restoring the nonlinear EP in the lasing regime. Furthermore, unlike linear non-Hermitian systems, we find that the spectral location of EPs above laser threshold varies as a function of total pump power and can therefore be continuously tracked. Our work is a first step towards the realization of lasing EPs in more complex laser geometries, and enabling the enhancement of photonic local density of states through non-Hermitian symmetries combined with nonlinear interactions in coupled laser arrays.

physics.optics↗