Towards gravimetry enhancement with squeezed states

We investigate the sensitivity of gravitational acceleration estimation using squeezed probe states in a quantum metrology framework. In particular, we analyze how the squeezing phase, beyond its amplitude, affects the attainable precision. We show that probes squeezed along the canonical phase-space quadratures can surpass the shot-noise limit only in specific time regimes, whereas position-momentum correlated input states can consistently overcome this limit across all interaction times. Furthermore, we demonstrate that optimal sensitivity can be achieved by combining projective momentum measurements with a time-dependent adjustment of the squeezing phase. Our results highlight the fundamental role of phase-engineered squeezing in quantum gravimetry protocols and provide new insights into the design of optimized sensing strategies.