Detection-noise-limited all electric feedback cooling of an optically levitated microsphere by a vector-rotation algorithm

Optically levitated microspheres in vacuum has great potentials for a wide range of real-world applications in ultra-sensitive sensors and fundamental physics explorations. A key prerequisite for the levitation experiments is the cooling of the microsphere’s center-of-mass motions. Here we implement an all electrical approach for 3D feedback cooling the center-of-mass motions of an optically levitated microsphere to about 76 mK temperature, which is limited by the current commercial detector electrical noises. The directions of the Coulomb forces are not necessary to be applied along the microsphere’s motion axes, instead, they can be freely rotated as vectors to coincide with the motion axes in numerical algorithm. The method is compact, and beneficial for the space-constrained systems, such as small-scale sensors, in future.