分类： 数学 >> 应用数学 提交时间： 2024-02-22
摘要： 本文研究Heisenberg群上非退化散度型次椭圆方程弱解的正则性。基于系数矩阵更一般的假设，本文针对齐次与非齐次两种情形，建立弱解在Besov空间中的水平Calderon-Zygmund估计。本文的研究将丰富发展Heisenberg群上非线性Calderon-Zygmund正则性理论。
分类： 光学 >> 量子光学 提交时间： 2023-02-19
摘要： Photonic crystal (PhC) membranes patterned with sub-wavelength periods offer a unique combination of high reflectivity, low mass, and high mechanical quality factor. We demonstrate a PhC membrane that we use as one mirror of a Fabry-Perot cavity with finesse as high as $F=35,000(500)$, corresponding to a record high PhC reflectivity of $R=0.999835(6)$. The fundamental mechanical frequency is 426 kHz, more than twice the optical linewidth, placing it firmly in the resolved-sideband regime. The mechanical quality factor in vacuum is $Q=1.1(1)\times 10^6$, allowing us to achieve values of the single-photon cooperativity as high as ${\cal C}_0=6.6\times10^{-3}$. We easily see optomechanical bistability as hysteresis in the cavity transmission. As the input power is raised well beyond the bistability threshold, dynamical backaction induces strong mechanical oscillation above 1~MHz, even in the presence of air damping. This platform will facilitate advances in optomechanics, precision sensing, and applications of optomechanically-induced bistability.
分类： 光学 >> 量子光学 提交时间： 2023-02-19
Yuhan Yao
Yuhe Zhao
Yanxian Wei
Feng Zhou
Daigao Chen
Yuguang Zhang
Xi Xiao
Ming Li
Jianji Dong
Shaohua Yu
Xinliang Zhang
摘要： We demonstrate a fully-integrated multipurpose microwave frequency identification system on silicon-on-insulator platform. Thanks to its multipurpose features, the chip is able to identify different types of microwave signals, including single-frequency, multiple-frequency, chirped and frequency-hopping microwave signals, as well as discriminate instantaneous frequency variation among the frequency-modulated signals. This demonstration exhibits fully integrated solution and fully functional microwave frequency identification, which can meet the requirements in reduction of size, weight and power for future advanced microwave photonic processor.
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