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Preparing mechanical squeezing of a macroscopic pendulum near quantum regimes

Nobuyuki Matsumoto, Naoki Yamamoto

Published Aug 25, 2020• 2 citations
OpenAlex

Abstract

We present the mechanical squeezing of a mg-scale suspended mirror (i.e. a pendulum) near quantum regimes through continuous linear position measurement. The experiment involved the pendulum interacting with photon coherent fields in a detuned optical cavity. The position uncertainty in the measured data is reduced and squeezed to $470$ times the zero-point amplitude $x_{\rm zpf}$ with a purity of about 0.0004, by means of optimal state estimation through causal Wiener filtering. The purity of the squeezed state is clearly maximized by the Wiener filter, based on precisely identified optomechanical parameters. This is the first step for measurement-based quantum control of macroscopic pendulums, e.g. generation of an entanglement state between macroscopic pendulums. Such quantum control will provide a direct insight into the quantum to classical transition and will pave the way to test semiclassical gravity and gravity sourced by macroscopic quantum oscillators.

Related papers

Conditional mechanical squeezing of a macroscopic pendulum near quantum regimes

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We present the mechanical squeezing of a mg-scale suspended mirror (i.e. a pendulum) near quantum regimes through continuous linear position measurement. The experiment involved the pendulum interacting with photon coherent fields in a detuned optical cavity. The position uncertainty in the measured data is reduced and squeezed to $470$ times the zero-point amplitude $x_{\rm zpf}$ with a purity of about 0.0004, by means of optimal state estimation through causal Wiener filtering. The purity of the squeezed state is clearly maximized by the Wiener filter, based on precisely identified optomechanical parameters. This is the first step for measurement-based quantum control of macroscopic pendulums, e.g. generation of an entanglement state between macroscopic pendulums. Such quantum control will provide a direct insight into the quantum to classical transition and will pave the way to test semiclassical gravity and gravity sourced by macroscopic quantum oscillators.

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arXiv:2410.09208•Oct 11, 2024•0 citations
We present the mechanical squeezing of a mg-scale suspended mirror (i.e. a pendulum) near quantum regimes through continuous linear position measurement. The experiment involved the pendulum interacting with photon coherent fields in a detuned optical cavity. The position uncertainty in the measured data is reduced and squeezed to 470470470 times the zero-point amplitude xzpfx_{\rm zpf}xzpf​ with a purity of about 0.0004, by means of optimal state estimation through causal Wiener filtering. The purity of the squeezed state is clearly maximized by the Wiener filter, based on precisely identified optomechanical parameters. This is the first step for measurement-based quantum control of macroscopic pendulums, e.g. generation of an entanglement state between macroscopic pendulums. Such quantum control will provide a direct insight into the quantum to classical transition and will pave the way to test semiclassical gravity and gravity sourced by macroscopic quantum oscillators.
We present the mechanical squeezing of a mg-scale suspended mirror (i.e. a pendulum) near quantum regimes through continuous linear position measurement. The experiment involved the pendulum interacting with photon coherent fields in a detuned optical cavity. The position uncertainty in the measured data is reduced and squeezed to 470470470 times the zero-point amplitude xzpfx_{\rm zpf}xzpf​ with a purity of about 0.0004, by means of optimal state estimation through causal Wiener filtering. The purity of the squeezed state is clearly maximized by the Wiener filter, based on precisely identified optomechanical parameters. This is the first step for measurement-based quantum control of macroscopic pendulums, e.g. generation of an entanglement state between macroscopic pendulums. Such quantum control will provide a direct insight into the quantum to classical transition and will pave the way to test semiclassical gravity and gravity sourced by macroscopic quantum oscillators.
In quantum mechanics, measurement can be used to prepare a quantum state. This principle is applicable even for macroscopic objects, which may enable us to see classical-quantum transition. Here, we demonstrate conditional mechanical squeezing of a mg-scale suspended mirror (i.e. the center-of-mass mode of a pendulum) near quantum regimes, through continuous linear position measurement and quantum state prediction. The experiment involved the pendulum interacting with photon coherent fields in a detuned optical cavity, which creates an optical spring. Futhermore, the detuned cavity allows us to perform linear position measurement by direct photo-detection of the reflected light. We experimentally verify the conditional squeezing using the theory combining prediction and retrodiction based on the causal and anti-causal filters. As a result, the standard deviation of position and momentum are respectively given by 36 times the zero-point amplitude of position qzpfq_{\rm zpf}qzpf​ and 89 times the zero-point amplitude of momentum pzpfp_{\rm zpf}pzpf​. The squeezing level achieved is about 5 times closer to the zero-point motion, despite that the mass of the mechanical oscillator is approximately 7 orders of magnitude greater, compared to the previous study. Thus, our demonstration is the first step towards quantum control for massive objects whose mass-scale is high enough to measure gravitational interactions. Such quantum control will pave the way to test quantum mechanics using the center-of-mass mode of massive objects.
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 investigated the quantum state of an optomechanical suspended mirror under continuous measurement and feedback control using Wiener filtering. We focus on the impact of the two-mode theory of suspended mirror on the quantum state, which is described by the pendulum and rotational modes. It is derived from the beam model coupled to the cavity light in the low-frequency regime, including the internal friction of the beam and the finite size effect of the mirror. We constructed a Wiener filter for the two-mode theory and predicted the quantum state by evaluating the conditional covariance matrix using Wiener filter analysis. The results demonstrate that multimode analysis may play an important role in generating the quantum squeezed state. We also point out the possibility that one-mode analysis can be a good approximation by choosing the range of the Fourier space in the Wiener filter analysis.
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.