Vortex beams with orbital angular momentum has been attracting tremendous attention due to their considerable applications ranging from optical tweezers to quantum information processing. Metalens, an ultra-compact and multifunctional device, provide
a desired platform for designing vortex beams. A spin-dependent metalens can boost the freedom to further satisfy practical applications. By combining geometric phase and propagation phase, we propose and demonstrate an approach to design a spin-dependent metalens generating dual-focused vortex beams along longitudinal or transverse direction, i.e., metalenses with predesigned spin-dependent phase profiles. Under the illumination of an elliptical polarization incident beam, two spin-dependent focused vortex beams can be observed, and the relative focal intensity of them can be easily adjusted by modulating the ellipticity of the incident beam. Moreover, we also demonstrated that the separate distance between these dual-focused beams and their topological charges could be simultaneously tailored at will, which may have a profound impact on optical trapping and manipulation in photonics.
We present a trajectory dynamically tracing compensation method to smooth the spatial fluctuation of the static magnetic field (C-field) that provides a quantization axis in the fountain clock. The C-field coil current is point-to-point adjusted in a
ccordance to the atoms experienced magnetic field along the flight trajectory. A homogeneous field with a 0.2 nT uncertainty is realized compared to 5 nT under the static magnetic field with constant current during the Ramsey interrogation. The corresponding uncertainty associated with the second-order Zeeman shift that we calculate is improved by one order of magnitude. The technique provides an alternative method to improve the magnetic field uniformity particularly for large-scale equipment that is difficult to machine with magnetic shielding. Our method is simple, robust, and essentially important in frequency evaluations concerning the dominant uncertainty contribution due to the quadratic Zeeman shift.
