Subjects: Mathematics >> Numerical Analysis submitted time 2024-06-16
Abstract： We introduce a novel random integration algorithm that boasts both high convergence order and polynomial tractability for functions characterized by sparse frequencies or rapidly decaying Fourier coefficients. Specifically, for integration in periodic isotropic Sobolev space and the isotropic Sobolev space with compact support, our approach attains a near-optimal root mean square error. In contrast to previous nearly optimal algorithms, our method exhibits polynomial tractability,ensuring that the number of samples does not scale exponentially with increasing dimensions. Our integration algorithm also enjoys near-optimal bound for weighted Korobov space. Furthermore, the algorithm can be applied without the need for prior knowledge of weights, distinguishing it from component-by-component algorithms. For integration in the Wiener algebra, the sample complexity of our algorithm is independent of the decay rate of Fourier coefficients. The effectiveness of the integration is confirmed through numerical experiments.
Peer Review Status:
Awaiting Review
Subjects: Optics >> Quantum optics submitted time 2023-02-19
Liang Chen
Chang-Jiang Huang
Xin-Biao Xu
Zheng-Tian Lu
Zhu-Bo Wang
Guang-Jie Chen
Ji-Zhe Zhang
Hong X. Tang
Chun-Hua Dong
Wen Liu
Guo-Yong Xiang
Guang-Can Guo
Chang-Ling Zou
Abstract： Abstract The magneto-optical trap (MOT) is an essential tool for collecting and preparing cold atoms with a wide range of applications. We demonstrate a planar-integrated MOT by combining an optical grating chip with a magnetic coil chip. The flat grating chip simplifies the conventional six-beam configuration down to a single laser beam; the flat coil chip replaces the conventional anti-Helmholtz coils of a cylindrical geometry. We trap 10^{4} cold ^{87}\text{Rb} atoms in the planar-integrated MOT, at a point 3-9 mm above the chip surface. This novel configuration effectively reduces the volume, weight, and complexity of the MOT, bringing benefits to applications including gravimeter, clock and quantum memory devices.
Peer Review Status:Awaiting Review
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