Towards gravimetry enhancement with squeezed states

Abstract: We investigate the estimation sensitivity of gravitational acceleration using squeezed probe states within a quantum metrology framework. In particular, we analyze how the squeezing phase, beyond its amplitudes, of the probes affects the attainable precision. We find that probes squeezed along the canonical phase-space quadrature can fail to achieve a quantum Fisher information (QFI) surpassing the shot-noise limit, regardless of the interaction time with the gravitational field. In contrast, position-momentum correlated input states with the squeezing amplitude can overcome this limit. Furthermore, we show that optimal sensitivity is attained through projective momentum measurements combined with a time-dependent adjustment of the squeezing phase. Our results are important to highlight the fundamental role of phase-engineered squeezing in experimental gravimetry protocols.