Subjects: Mathematics >> Applied Mathematics submitted time 2024-02-22
Abstract： In this paper, we deal with weak solutions to non-degenerate sub-elliptic equations in the Heisenberg group, and study the regularities of solutions. We establish horizontal Calderon-Zygmund type estimate in Besov spaces with more general assumptions on coefficients for both homogeneous equations and non-homogeneous equations. This study of regularity estimates expands the Calderon-Zygmund theory in the Heisenberg group.
Peer Review Status:
Awaiting Review
Subjects: Optics >> Quantum optics submitted time 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
Abstract： 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.
Peer Review Status:Awaiting Review
Subjects: Optics >> Quantum optics submitted time 2023-02-19
Abstract： 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.
Peer Review Status:Awaiting Review
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