分类: 数学 >> 数值分析 提交时间: 2024-06-14
摘要: We introduce a novel random integration algorithm that boasts both high con#2;vergence order and polynomial tractability for functions characterized by sparsefrequencies or rapidly decaying Fourier coefficients. Specifically, for integration inperiodic isotropic Sobolev space and the isotropic Sobolev space with compact sup#2;port, our approach attains a near-optimal root mean square error. In contrast toprevious nearly optimal algorithms, our method exhibits polynomial tractability,ensuring that the number of samples does not scale exponentially with increasingdimensions. Our integration algorithm also enjoys near-optimal bound for weightedKorobov space. Furthermore, the algorithm can be applied without the need forprior knowledge of weights, distinguishing it from component-by-component algo#2;rithms. For integration in the Wiener algebra, the sample complexity of our algo#2;rithm is independent of the decay rate of Fourier coefficients. The effectiveness ofthe integration is confirmed through numerical experiments.
分类: 光学 >> 量子光学 提交时间: 2023-02-19
摘要: 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.