Rotation Sensing of a Trapped Nanoparticle Assisted by Magnetic Field Gradient

We propose a rotation sensing scheme based on the Sagnac interferometer for a single trapped particle system. In this scheme, the spin and vibrational states of the particle, prepared in a coherent state, are translated into a Schr\"odinger cat state by applying a strong magnetic field gradient to create the spin-dependent force. By reflecting the phase related to the rotational rate accumulated by the two arms of the interferometer to the spin state, we can obtain the rotational rate of the apparatus by performing spin measurement. The scheme can also be applied to the situation with the vibration state in the thermal state. The sensing sensitivity can reach S=4.47×10^-70.2em0exrad/s0.2em0ex√Hz for a suspended diamond nanoparticle and S=5.65×10^-60.2em0exrad/s0.2em0ex√Hz for a trapped ⁴⁰Ca⁺. Combining with the experimental parameters, our scheme is applied to realize the gyroscope in a trapped single nanoparticle and atomic ion.