Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2508.14337 · Physical Review Research

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

Ryotaro Fukuzumi, Kosei Hatakeyama, Daisuke Miki, Kazuhiro Yamamoto

Published Mar 4, 2026• 2 citations
arXivHTMLPDF

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.

DOI
10.1103/zrs2-sk28

Related papers

Feasible generation of gravity-induced entanglement by using optomechanical systems

Daisuke Miki, Akira Matsumura, Kazuhiro Yamamoto

We report the feasibility of detecting the gravity-induced entanglement (GIE) with optomechanical systems, which is the first investigation that clarifies the feasible experimental parameters to achieve a signal-to-noise ratio of $\mathrm{S}/\mathrm{N}=1$. Our proposal focuses on GIE generation between optomechanical mirrors, coupled via gravitational interactions, under continuous measurement, feedback control, and Kalman filtering process, which matured in connection with the field of gravitational wave observations. We solved the Riccati equation to evaluate the time evolution of the conditional covariance matrix for optomechanical mirrors that estimated the minimum variance of the motions. The results demonstrate that GIE is generated faster than a well-known time scale without optomechanical coupling. The fast generation of entanglement is associated with quantum-state squeezing by the Kalman filtering process, which is an advantage of using optomechanical systems to experimentally detect GIE.

arXiv:2406.04361•Physical review. D/Physical review. D.•Jul 23, 2024•12 citations

Generating quantum entanglement between macroscopic objects with continuous measurement and feedback control

Daisuke Miki, Nobuyuki Matsumoto, Akira Matsumura +4 more

This paper is aimed at investigating the feasibility of generating quantum conditional entanglement between macroscopic mechanical mirrors in optomechanical systems while under continuous measurement and feedback control. We consider the squeezing of the states of the mechanical common and the differential motions of the mirrors by the action of measuring the common and the differential output light beams in the Fabry-P\'erot-Michelson interferometer. We carefully derive a covariance matrix for the mechanical mirrors in a steady state, employing the Kalman filtering problem with dissipative cavities. We demonstrate that Gaussian entanglement between the mechanical mirrors is generated when the states of the mechanical common and differential modes of the mirrors are squeezed with high purity in an asymmetric manner. Our results also show that quantum entanglement between 7-mg mirrors is achievable in the short term.

arXiv:2210.13169•Physical Review A•Mar 13, 2023•29 citations

Conditional Motional Squeezing of an Optomechanical Oscillator Approaching the Quantum Regime

Benjamin B. Lane, Junxin Chen, Ronald Pagano +6 more

Squeezed mechanical states are a highly coveted resource for quantum-enhanced sensing and serve as a compelling platform for probing the interplay between gravity and quantum mechanics. It has been predicted that a mechanical oscillator can be prepared into a quantum squeezed state if the applied measurement rate is fast relative to its mechanical resonance frequency. However, the experimental feasibility of this protocol has remained uncertain because of the difficulty in achieving low-frequency oscillators with sufficiently strong read-out. Here, we demonstrate that a careful selection of parameters in an optomechanical system, combined with optimal filtering techniques, enables the preparation of a 50 ng GaAs cantilever in a conditional classical squeezed state, achieving a minimum uncertainty of just 1.07 plus/minus 0.04 times the zero-point fluctuation level. This minimum variance is 3 orders of magnitude smaller than what has been achieved in previous experiments using the same protocol. Although we do not fully achieve the quantum squeezed regime, our demonstration provides definitive evidence that a measurement-based protocol is a practical and effective approach for the real-time preparation of macroscopic oscillators in quantum squeezed states.

arXiv:2410.09208•Oct 11, 2024•0 citations

Theoretical study of the squeezed-light-enhanced sensitivity to gravity-induced entanglement via finite-time analysis

Kosei Hatakeyama, Daisuke Miki, Kazuhiro Yamamoto

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.

arXiv:2508.01397•Physical review. D/Physical review. D.•Dec 5, 2025•3 citations

Amplification and generation bounds of gravity-induced entanglement in pulsed optomechanical systems

Daisuke Miki, Alfred Li, Yanbei Chen

We investigate gravity-induced entanglement between the output optical fields of two red-detuned pulsed optomechanical systems with their masses coupled by mutual gravitational interaction. For each individual system, the optomechanical interaction realizes a beam-splitter state swap between an incident optical pulse and its mechanical mode. Using two rectangular pulses for each system -- the first to imprint a nonclassical state on the mechanical modes and the second to read the gravitationally generated entanglement back onto the outgoing light -- we show that the amount of entanglement can be amplified by preparing the input in a squeezed or Fock state. However, the threshold for entanglement generation is set by the competition between the gravitational coupling and thermal decoherence, $g_G>2γ_m N_{\rm th}$, and cannot be lowered by any choice of input state. We prove this bound for two-mode Gaussian inputs and show that it continues to hold for Fock-state inputs. We further analyze how imperfect detection modifies the threshold and identify the entanglement-annihilating and entanglement-breaking regimes, which are set by the thermal decoherence accumulated over the interaction time, independent of the gravitational coupling.

quant-pharXiv:2605.26240•May 27, 2026•0 citations

Optomechanical Entanglement and Squeezing in Coherent-Feedback-assisted Quadratic Optomechanics

焦亚峰, Ruo-Chen Wang, Jingxue Liu +5 more

Quantum entanglement and squeezing associated with the motions of massive mechanical oscillators play an essential role in both fundamental science and emerging quantum technologies, yet realizing such macroscopic nonclassical states remains a formidable challenge. In this paper, we investigate how to achieve strong optomechanical entanglement and mechanical squeezing in a membrane-embedded cavity optomechanical system incorporating a coherent feedback loop, where the membrane interacts with the cavity mode through both linear and quadratic optomechanical couplings. This hybrid optomechanical architecture offers a flexible tunability of intrinsic system parameters, thereby enabling controlled stiffening or softening of the mechanical mode through adjusting quadratic optomechanical coupling, as well as effective modulation of the cavity decay rate via feedback control. More importantly, the synergistic interplay effect allows for a strategic reconfiguration of the system's stability regime, which in turn permits the presence of significantly enhanced effective optomechanical coupling strengths before entering the unstable regime. Exploiting these unique features, we demonstrate that optomechanical entanglement can be substantially enhanced with positive coupling sign and suitable feedback parameters, while strong mechanical squeezing beyond the 3dB limit is simultaneously achieved over a broad parameter range with negative coupling sign, reaching squeezing degree above 10dB under optimized conditions. Our proposal, establishing an all-optical method for generating highly entangled or squeezed states in cavity optomechanical systems, opens up a new route to explore macroscopic quantum effects and to advance quantum information processing.

•Mar 24, 2026•0 citations
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.
We report the feasibility of detecting the gravity-induced entanglement (GIE) with optomechanical systems, which is the first investigation that clarifies the feasible experimental parameters to achieve a signal-to-noise ratio of S/N=1\mathrm{S}/\mathrm{N}=1S/N=1. Our proposal focuses on GIE generation between optomechanical mirrors, coupled via gravitational interactions, under continuous measurement, feedback control, and Kalman filtering process, which matured in connection with the field of gravitational wave observations. We solved the Riccati equation to evaluate the time evolution of the conditional covariance matrix for optomechanical mirrors that estimated the minimum variance of the motions. The results demonstrate that GIE is generated faster than a well-known time scale without optomechanical coupling. The fast generation of entanglement is associated with quantum-state squeezing by the Kalman filtering process, which is an advantage of using optomechanical systems to experimentally detect GIE.
This paper is aimed at investigating the feasibility of generating quantum conditional entanglement between macroscopic mechanical mirrors in optomechanical systems while under continuous measurement and feedback control. We consider the squeezing of the states of the mechanical common and the differential motions of the mirrors by the action of measuring the common and the differential output light beams in the Fabry-P\'erot-Michelson interferometer. We carefully derive a covariance matrix for the mechanical mirrors in a steady state, employing the Kalman filtering problem with dissipative cavities. We demonstrate that Gaussian entanglement between the mechanical mirrors is generated when the states of the mechanical common and differential modes of the mirrors are squeezed with high purity in an asymmetric manner. Our results also show that quantum entanglement between 7-mg mirrors is achievable in the short term.
Squeezed mechanical states are a highly coveted resource for quantum-enhanced sensing and serve as a compelling platform for probing the interplay between gravity and quantum mechanics. It has been predicted that a mechanical oscillator can be prepared into a quantum squeezed state if the applied measurement rate is fast relative to its mechanical resonance frequency. However, the experimental feasibility of this protocol has remained uncertain because of the difficulty in achieving low-frequency oscillators with sufficiently strong read-out. Here, we demonstrate that a careful selection of parameters in an optomechanical system, combined with optimal filtering techniques, enables the preparation of a 50 ng GaAs cantilever in a conditional classical squeezed state, achieving a minimum uncertainty of just 1.07 plus/minus 0.04 times the zero-point fluctuation level. This minimum variance is 3 orders of magnitude smaller than what has been achieved in previous experiments using the same protocol. Although we do not fully achieve the quantum squeezed regime, our demonstration provides definitive evidence that a measurement-based protocol is a practical and effective approach for the real-time preparation of macroscopic oscillators in quantum squeezed states.
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 106 s10^6\,\mathrm{s}106s is required to achieve SNR=1{\rm SNR} = 1SNR=1 when using squeezed input light, whereas 106.8 s10^{6.8}\,\mathrm{s}106.8s 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.
We investigate gravity-induced entanglement between the output optical fields of two red-detuned pulsed optomechanical systems with their masses coupled by mutual gravitational interaction. For each individual system, the optomechanical interaction realizes a beam-splitter state swap between an incident optical pulse and its mechanical mode. Using two rectangular pulses for each system -- the first to imprint a nonclassical state on the mechanical modes and the second to read the gravitationally generated entanglement back onto the outgoing light -- we show that the amount of entanglement can be amplified by preparing the input in a squeezed or Fock state. However, the threshold for entanglement generation is set by the competition between the gravitational coupling and thermal decoherence, gG>2γmNthg_G>2γ_m N_{\rm th}gG​>2γm​Nth​, and cannot be lowered by any choice of input state. We prove this bound for two-mode Gaussian inputs and show that it continues to hold for Fock-state inputs. We further analyze how imperfect detection modifies the threshold and identify the entanglement-annihilating and entanglement-breaking regimes, which are set by the thermal decoherence accumulated over the interaction time, independent of the gravitational coupling.
Quantum entanglement and squeezing associated with the motions of massive mechanical oscillators play an essential role in both fundamental science and emerging quantum technologies, yet realizing such macroscopic nonclassical states remains a formidable challenge. In this paper, we investigate how to achieve strong optomechanical entanglement and mechanical squeezing in a membrane-embedded cavity optomechanical system incorporating a coherent feedback loop, where the membrane interacts with the cavity mode through both linear and quadratic optomechanical couplings. This hybrid optomechanical architecture offers a flexible tunability of intrinsic system parameters, thereby enabling controlled stiffening or softening of the mechanical mode through adjusting quadratic optomechanical coupling, as well as effective modulation of the cavity decay rate via feedback control. More importantly, the synergistic interplay effect allows for a strategic reconfiguration of the system's stability regime, which in turn permits the presence of significantly enhanced effective optomechanical coupling strengths before entering the unstable regime. Exploiting these unique features, we demonstrate that optomechanical entanglement can be substantially enhanced with positive coupling sign and suitable feedback parameters, while strong mechanical squeezing beyond the 3dB limit is simultaneously achieved over a broad parameter range with negative coupling sign, reaching squeezing degree above 10dB under optimized conditions. Our proposal, establishing an all-optical method for generating highly entangled or squeezed states in cavity optomechanical systems, opens up a new route to explore macroscopic quantum effects and to advance quantum information processing.