arXiv subjects

Doudou Wang

Publications and source records attributed to Doudou Wang.

4 recordsLinked to original sources

arXiv2026

MathCoPilot: An Interactive System for Human-AI Symbiotic Paradigm of Mathematical Research

Existing LLM-based theorem provers have achieved impressive results on formal mathematics benchmarks, yet they remain confined to acting as autonomous agents that prove a stated proposition. In this paper, we propose MathCoPilot, a human-in-the-loop system that embodies a new human--AI symbiotic paradigm for mathematical research, in which the mathematician steers the high-level mathematical direction while AI agents carry out the detailed formalization and proof work under continuous human guidance. MathCoPilot unifies three core capabilities: (1) an interactive workbench where the mathematician and AI agents collaborate through a living proof blueprint that decomposes a proof into navigable steps the human can directly inspect, direct, and refine; (2) automated proving skill orchestration with adaptive knowledge base search and Lean-integrated iterative verification; and (3) topic-driven paper retrieval and automated formalization into a verified Lean knowledge base. Using MathCoPilot, we systematically compare four state-of-the-art LLMs, including Gemini~3.1~Pro, GPT-5.4, and Claude~Opus~4.7, on a FormalMATH subset and on two real PDE theorems requiring deep domain expertise, evaluating their ability to produce verified Lean~4 proofs and to identify errors in deliberately incorrect proofs. Our results show that while current models can handle undergraduate-level problems with high success rates under favorable autoformalization conditions, substantial challenges remain for domain-specific theorems requiring genuine mathematical understanding.

cs.AI↗

arXiv2026

Optomechanical system with tunable dissipative and dispersive couplings

We demonstrate an optomechanical system with tunable dissipative and dispersive couplings using a Fabry-Perot cavity and a string mechanical resonator. By varying the diameter and material of the mechanical resonator, and the relative location between the mechanical resonator and the cavity, the relative strengths of dissipative and dispersive coupling could be tuned continuously from dissipation-dominated regime to dispersion-dominated regime. In our experiments, the dissipative-to-dispersive coupling ratios of 1.3 and 0.6 are achieved by using two different mechanical resonators, corresponding to a transition from dissipation-dominated to dispersion-dominated optomechanical system. Theoretically, the coupling ratio could be tuned from 25 to 0.02 by optimizing the mechanical resonator, spanning over three orders of magnitude. These two distinct coupling regimes are achieved with the same experimental platform. The capability to freely adjust the coupling ratio provides a versatile platform for exploring quantum effects of massive mechanical resonators and quantum-limited measurements.

quant-ph↗

arXiv2026

Optimized Slice-Phase Control of Mirror Pulse in Cold-Atom Interferometry with Finite Response Time

Atom interferometers require both high efficiency and robust performance in their mirror pulses under experimental inhomogeneities. In this work, we demonstrated that quantum optimal control designed mirror pulse significantly enhance interferometer performance by using novel adaptive sliced structure. Using gradient ascent pulse engineering (GRAPE), optimized mirror pulse for a Mach-Zehnder light-pulse atom interferometer was designed by discretizing the control into non-uniform phase slices. This design broadened the tolerence to experimentally relevant variations in detuning $[-\Omega_0,\Omega_0]$ and Rabi frequency $[0.1\times\Omega_0,1.9\times\Omega_0]$ ($\Omega_0=2\pi\times25$ kHz), while maintaining high transfer efficiency even when the response-time delays up to 1.6 $\rm{\mu s}$. The optimized pulse was found to be robust to coupling inhomogeneity and velocity spread, offering a significant improvement in robustness over conventional pulse. The adaptive pulse slicing method provides a minimalist strategy that reduces experimental complexity while enhancing robustness and scalability, offering an innovative scheme for quantum optimal control in high precision atom interferometry.

quant-ph↗

arXiv2024

Phononically shielded multi-wavelength photonic-crystal membrane for cavity quantum optomechanics

We propose and design a stoichiometric silicon-nitride membrane resonator featuring highly reflective at multi-wavelengths and high mechanical quality factor. The membrane resonator has a thickness of 100 nm and 2D-photonic and phononic crystal patterns. By designing concentric holes of suitable radius on both sides of the membrane, high reflectivity at multi-wavelengths can be achieved. In particularly, the simulation shows that high reflectivity can be realized at telecommunications wavelength and alkaline atoms absorption lines, with reflectivity of 99.76% at 852 nm, and 99.98% at 1054 nm, and 99.96% at 1566 nm, respectively. The designed device can find useful applications in cavity optomechanical system to realize quantum frequency conversion and precise quantum measurement, and other field of quantum information processing tasks.

physics.optics↗