Detection of Magnetic Field Gradient and Single Spin Using Optically Levitated Nano-Particle in Vacuum

Optically levitated nano-particle with spins is a promising system for high-precision measurement and quantum information processing. We theoretically analyze the ratio between the fluctuation of particle's displacement caused by spins in magnetic field and caused by molecular collisions of the residual air. When the ratio is larger than unity, the displacement fluctuation of spins flipping can be remarkably detected. By theoretical analysis and numerical simulation, we propose and validate a scheme for the detection of gradient of the magnetic field by levitating ferromagnetic nano-particle, and also put forward a realizable detection scheme of the single spin by levitating nano-diamond particle with single nitrogen-vacancy(NV) centers.