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We show that the gravitational acceleration can be measured with thematter-wave Ramsey interferometry, by using a nitrogen-vacancy center coupledto a nano-mechanical resonator. We propose two experimental methods to realizethe Hamiltonian, by using either a cantilever resonator or a trappednanoparticle. The scheme is robust against the thermal noise, and could berealized at the temperature much higher than the quantum regime one. Theeffects of decoherence on the interferometry fringe visibility is caculated,including the mechanical motional decay and dephasing of the nitrogen-vacancycenter. In addition, we demonstrate that under the various sources of randomand systematic noises, our gravimeter can be made on-chip and achieving a highmeasurement precision. Under experimental feasible parameters, the proposedgravimeter could achieve $10^{-10}$ relative precision.

High-precision gravimeter based on a nano-mechanical resonator hybrid with an electron spin