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.

💡 Research Summary

In this work the authors investigate how squeezed Gaussian probe states can be exploited to improve the precision of gravitational acceleration (g) estimation within the framework of quantum metrology. Starting from a non‑relativistic particle of mass m freely falling in a uniform gravitational potential U(z)=mgz, the initial state is taken to be a squeezed vacuum characterized by a squeezing amplitude r and a squeezing phase θ. The phase determines the orientation of the squeezing ellipse in phase space, thereby controlling both the position uncertainty σ and the position‑momentum correlation γ.

Using the path‑integral formalism the authors derive an exact analytical expression for the quantum Fisher information (QFI) with respect to g, Eq. (2):

F_g(τ,r,θ)=sinh 2(2r) sin 2(2θ)+¼σ₀⁻²