Sensitivity of Displacement Detection for a Particle Levitated in the Doughnut Beam

Displacement detection of a sphere particle in focused laser beams with quadrant photodetector (QPD) provides a fast and high precision way to determine the particle location. In contrast to the traditional Gaussian beams, the sensitivity of displacement detection using various doughnut beams are investigated. The sensitivity improvement for large sphere particles along the longitudinal direction is reported. With appropriate vortex charge $l$ of the doughnut beams, they can outperform the Gaussian beam to get more than one order higher sensitivity and thus have potential applications in various high precision measurement. By using the levitating doughnut beam itself to detect the particle displacement, the result will also facilitate the recent proposal of levitating a particle in doughnut beams to suppress the light absorption.