Theoretical Study of the Squeezed-Light-Enhanced Sensitivity to Gravity-Induced Entanglement via Finite-Time Analysis

TL;DR

This study demonstrates that using squeezed input light in optomechanical systems significantly enhances the detection sensitivity of gravity-induced entanglement by reducing optical noise and improving signal-to-noise ratio within finite measurement times.

Contribution

It provides a finite-time Fourier analysis showing how squeezed light improves GIE detection, quantifies error estimates, and compares measurement times with and without squeezing.

Findings

Squeezed input light reduces optical noise in GIE detection.

Measurement time for SNR=1 is shorter with squeezed light (10^6 s) than without (10^6.8 s).

Squeezing significantly enhances the feasibility of observing gravity-induced entanglement.

Abstract

We investigate the advantage of using squeezed input light for generating gravity-induced entanglement (GIE) through Fourier-domain analysis. Based on the findings of Ref.~\cite{Miki2024}, which demonstrated the feasibility of detecting GIE in optomechanical systems under quantum control, we further demonstrate that squeezed input light can reduce the optical noise in the mechanical conditional state and enhance GIE. Furthermore, we estimate the systematic and statistical errors in the measurement of GIE using the Fourier transformation over a finite measurement time. Based on the error estimations using the signal-to-noise ratio (SNR) in GIE detection, we find that a total measurement time of $10^6\,\mathrm{s}$ is required to achieve ${\rm SNR} = 1$ when using squeezed input light, whereas $10^{6.8}\,\mathrm{s}$ is needed without squeezed input light. This result highlights the effectiveness of optomechanical systems and the critical role of squeezed input light in enhancing the detectability of GIE.