Mechanical squeezed-Fock gravimeter

Levitated mechanical systems are promising candidates for quantum gravimetry, as gravity couples directly to their center-of-mass motion, enabling the large mass of a mesoscopic particle to serve as a sensing resource. In this paper, we propose a mechanical squeezed-Fock qubit gravimeter using a Duffing oscillator that is driven by a detuned two-phonon pump. In the squeezed-Fock basis, the gravitational force couples to the anti-squeezed quadrature, which enhances the gravity-induced transition rate while preserving the direct mass scaling of the mechanical force coupling. We show that sensitivity improves with reduced effective qubit splitting that is controlled by the squeezing parameter and the Duffing nonlinearity. We further analyze mechanical damping and show that squeezing converts ordinary dissipation into anisotropic qubit noise, setting a practical trade-off between signal amplification and decoherence rate. These results identify the mechanical squeezed-Fock qubit as a new platform for quantum-enhanced gravimetry.