In the present paper, we provide a scheme to probe the gradient of gravity at the nanoscale in a levitated nanomechanical resonator coupled to a cavity via two-field optical control. The enhanced sharp peak on the probe spectrum will suffer a distinct shift with the nonuniform force being taken into consideration. The nonlinear optics with very narrow bandwidth $({10}^{-8}\mathrm{Hz})$ resulting from the extremely high-quality factor will lead to a superresolution of ${10}^{-20}\mathrm{N}/\mathrm{m}$ for the measurement of gravity gradient. The improved sensitivity may offer new opportunities for detecting Yukawa moduli forces and Kaluza-Klein gravitons in extra dimensions.

• Received 19 October 2016

DOI:https://doi.org/10.1103/PhysRevD.95.044014