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Quantum backflow, a counterintuitive interference phenomenon where particles with positive momentum can propagate backward, is important in applications involving light-matter interactions. To date, experimental demonstrations of backflow have been restricted to classical optical systems, where momentum is measured using the slit scanning technique or the Shack-Hartmann wavefront sensor technique. However, these techniques have low spatial resolution due to limitations in slit width and Fourier transform lenslet array density. Here, by adopting the technique of weak measurement, we report an observation of azimuthal backflow both theoretically and experimentally. Our results show that a heralded single photon, prepared in specific superposition states with solely negative orbital angular momentum (OAM), exhibits positive OAM. The effects of mode ratio, propagation distance and OAM index on the azimuthal backflow are systematically investigated. Our method avoids using slits and lenslet arrays, allowing for the accurate extraction of photon momentum at each pixel. This work provides new insights and techniques for observing and manipulating backflow in quantum systems., Comment: 5 pages, 3 figures

We propose a novel method, called the dimension-changing transformation (DCT), to compute one-loop Feynman integrals and recently introduced fixed-branch integrals to arbitrary orders in $\epsilon$. The DCT relates one-loop Feynman integrals or fixed-branch integrals in one spacetime dimension to their corresponding quantities with auxiliary mass in any other dimension, making the expansion to high orders in $\epsilon$ highly efficient. We applied this method to several examples to demonstrate its validity and efficiency. The approach introduced in this work has been implemented in an open-source C++ package, available at \href{https://gitlab.com/multiloop-pku/dct}{https://gitlab.com/multiloop-pku/dct}., Comment: 6 pages, 5 figures

Recent large language models (LLMs) have demonstrated versatile capabilities in long-context scenarios. Although some recent benchmarks have been developed to evaluate the long-context capabilities of LLMs, there is a lack of benchmarks evaluating the mathematical reasoning abilities of LLMs over long contexts, which is crucial for LLMs' application in real-world scenarios. In this paper, we introduce MathHay, an automated benchmark designed to assess the long-context mathematical reasoning capabilities of LLMs. Unlike previous benchmarks like Needle in a Haystack, which focus primarily on information retrieval within long texts, MathHay demands models with both information-seeking and complex mathematical reasoning abilities. We conduct extensive experiments on MathHay to assess the long-context mathematical reasoning abilities of eight top-performing LLMs. Even the best-performing model, Gemini-1.5-Pro-002, still struggles with mathematical reasoning over long contexts, achieving only 51.26% accuracy at 128K tokens. This highlights the significant room for improvement on the MathHay benchmark., Comment: Work-in-Progress

By employing x-Bohm theory and p-Bohm theory, we construct the position and momentum trajectories of single-mode and superposed-mode Laguerre-Gaussian (LG) beams. The dependence of divergence velocity and rotation velocity on the initial position and propagation distance is quantified, indicating that LG beams exhibit subluminal effects, even in free space. Additionally, we clarify the formation of the petal-shaped intensity distribution of the superposed-mode LG beam in terms of motion trajectory, where the particle-like trajectory and wave-like interference are ``simultaneously" observed. Our work provides an intuitive way to visualize the propagation characteristics of LG beams and deepen the comprehension of Bohm-like theory., Comment: 7 pages, 6 figures

This paper introduces a new in-context learning (ICL) mechanism called In-Image Learning (I$^2$L) that combines demonstration examples, visual cues, and chain-of-thought reasoning into an aggregated image to enhance the capabilities of Large Multimodal Models (e.g., GPT-4V) in multimodal reasoning tasks. Unlike previous approaches that rely on converting images to text or incorporating visual input into language models, I$^2$L consolidates all information into an aggregated image and leverages image processing, understanding, and reasoning abilities. This has several advantages: it reduces inaccurate textual descriptions of complex images, provides flexibility in positioning demonstration examples, and avoids multiple input images and lengthy prompts. We also introduce I$^2$L-Hybrid, a method that combines the strengths of I$^2$L with other ICL methods. Specifically, it uses an automatic strategy to select the most suitable method (I$^2$L or another certain ICL method) for a specific task instance. We conduct extensive experiments to assess the effectiveness of I$^2$L and I$^2$L-Hybrid on MathVista, which covers a variety of complex multimodal reasoning tasks. Additionally, we investigate the influence of image resolution, the number of demonstration examples in a single image, and the positions of these demonstrations in the aggregated image on the effectiveness of I$^2$L. Our code is publicly available at https://github.com/AGI-Edgerunners/IIL., Comment: Preprint

Topological excitonic insulators combine topological edge states and spontaneous exciton condensation, with dual functionality of topological insulators and excitonic insulators. Yet, they are very rare and little is known about their formation. In this work, we find that a mechanism dubbed as parity frustration prevents excitonic instability in usual topological insulators, and those whose band inversion is independent of spin-orbit coupling are possible candidates. We verify this by first-principles calculations on monolayer transition-metal carbides (MXenes), which show a robust thermal-equilibrium exciton condensation, being sufficient for topological applications at room temperature. Such a state can be identified by angle-resolved photoemission spectroscopy and transport measurement. Our work provides not only a guide for finding more topological excitonic insulators, but also a new platform for studying the interplay between non-trivial band topology and quantum many-body effects., Comment: Accepted by PRB

Quantum steering is commonly shared among multiple observers by utilizing unsharp measurements. However, their usage is limited to local measurements and is not suitable for nonlocal-measurement-based cases. Here, we present a novel approach in this study, suggesting a highly efficient technique to construct optimal nonlocal measurements by utilizing quantum ellipsoids to share quantum steering. This technique is suitable for any bipartite state and offers benefits even in scenarios with a high number of measurement settings. Using the Greenberger-Horne-Zeilinger state as an illustration, we show that employing unsharp nonlocal product measurements can activate the phenomenon of steering sharing in contrast to using local measurements. Moreover, our findings demonstrate that nonlocal measurements with unequal strength possess a greater activation capability compared to those with equal strength. Our activation method differs from previous ones as it eliminates the need to copy the shared states or diminish other quantum correlations, thus making it convenient for practical experimentation and conservation of resources., Comment: 9 pages, 4 figures

High-precision surface roughness estimation plays an important role in many applications. However, the classical estimating methods are limited by shot noise and only can achieve the precision of 0.1 nm with white light interferometer. Here, we propose two weak measurement schemes to estimate surface roughness through spectrum analysis and intensity analysis. The estimating precision with spectrum analysis is about $10 ^{-5}$ nm by using a currently available spectrometer with the resolution of $\Delta \lambda= 0.04$ pm and the corresponding sensitivity is better than 0.1 THz/nm. And the precision and sensitivity of the light intensity analysis scheme achieve as high as 0.07 nm and 1/nm, respectively. By introducing a modulated phase, we show that the sensitivity and precision achieved in our schemes can be effectively retained in a wider dynamic range. We further provide the experimental design of the surface profiler based on our schemes. It simultaneously meets the requirements of high precision, high sensitivity, and wide measurement range, making it to be a promising practical tool., Comment: 7 pages, 6 figures

Motivated by the recent synthesis of two-dimensional monolayer AlSb, we theoretically investigate its ground state and electronic properties using the first-principles calculations coupled with Bethe-Salpeter equation. An excitonic instability is revealed as a result of larger exciton binding energy than the corresponding one-electron energy gap by $\sim$0.1 eV, which is an indicative of a many-body ground state accompanied by spontaneous exciton generation. Including the spin-orbit coupling is proven to be a must to correctly predict the ground state. At room temperature, the two-dimensional monolayer AlSb is a direct gap semiconductor with phonon-limited electron and hole mobilities both around 1700 cm$^2$/V$\cdot$s. These results show that monolayer AlSb may provide a promising platform for realization of the excitonic insulator and for applications in the next-generation electronic devices.

First-principles density functional theory plus Bethe-Salpeter equation calculations are employed to investigate the electronic and excitonic properties of monolayer titanium trichalcogenide alloys TiS$_{3-x}$Se$_x$ ($x$=1 and 2). It is found that bandgap and exciton binding energy display asymmetric dependence on the substitution of Se for S. While the bandgap can be significantly decreased as compared to that of pristine TiS$_3$, the exciton binding energy just varies a little, regardless of position and concentration of the Se substitution. A negative exciton formation energy is found when the central S atoms are replaced by Se atoms, suggesting a many-body ground state with the spontaneous exciton condensation. Our work thus offers a new insight for engineering an excitonic insulator., Comment: Accepted by PRB