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Momentum squeezed state realized via optimal filtering in optomechanics: Implications for gravity-induced entanglement

Ryotaro Fukuzumi1,*, Kosei Hatakeyama1,†, Daisuke Miki2,‡, and Kazuhiro Yamamoto1,3,§

  • *Contact author: fukuzumi.ryotaro.709@s.kyushu-u.ac.jp
  • †Contact author: hatakeyama.kosei.103@s.kyushu-u.ac.jp
  • ‡Contact author: dmiki@caltech.edu
  • §Contact author: yamamoto@phys.kyushu-u.ac.jp
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Phys. Rev. Research 8, 023039 – Published 13 April, 2026

DOI: https://doi.org/10.1103/zrs2-sk28

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. 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 insights into experimental strategies for probing the quantum nature of gravity using optomechanical platforms.

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Phys. Rev. Research 8, 023039– Published 13 April, 2026
  • Received 26 August 2025
  • Accepted 4 March 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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