Momentum Squeezed State Realized via Optimal Filtering in Optomechanics: Implications for Gravity-Induced Entanglement

TL;DR

This paper demonstrates how optimal filtering in optomechanical systems can produce momentum squeezing beyond the standard quantum limit, enhancing the detection of gravity-induced entanglement.

Contribution

It introduces a method to achieve momentum squeezing via optimal filtering and shows its application in amplifying gravity-induced entanglement signals in optomechanical setups.

Findings

Momentum squeezing beyond the standard quantum limit is achievable with optimal filtering.

Enhanced gravity-induced entanglement signals due to momentum squeezing.

Increased spatial superposition size linked to high-purity momentum-squeezed states.

Abstract

We analyze the conditional quantum state of a mechanical mirror in an optomechanical system subject to continuous measurement, feedback control, and quantum filtering. We identify a parameter regime in which the mirror exhibits momentum squeezing beyond the standard quantum limit, achieved through an appropriate choice of the homodyne detection angle. In this regime, we show that optimal filtering effectively realizes a free-particle-like conditional state. When this mechanism is applied to a configuration consisting of two optomechanical systems, the resulting momentum squeezing significantly enhances the signal of gravity-induced entanglement (GIE). This enhancement arises because the momentum squeezing not only amplifies the distinction between the common and differential modes, but also, in the high-purity regime, increases the position uncertainty in accordance with the uncertainty principle, thereby enlarging the spatial extent of the quantum superposition. Our results provide new insights into experimental strategies for probing the quantum nature of gravity using optomechanical platforms.