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 analytically investigate a quantum estimation method for a mechanical oscillator in a detuned cavity system based solely on homodyne measurement records, building on the framework developed by C.Meng et al. (Science Advances 8, 7585 (2022)). Estimation based only on measurement records is important because it enables state verification without assuming knowledge of the true system state. We construct a relative estimate operator from causal and anti-causal quantum Wiener filters and calculate its variance. The deviation from the causal conditional variance is defined as a reconstruction bias, whose magnitude is evaluated analytically. We show that, within experimentally relevant parameter regimes for typical quantum-state preparation, the reconstruction bias is sufficiently small to be neglected. As applications to state verification, we apply the method to proposals for macroscopic quantum entanglement mediated by electromagnetic interactions and for conditional momentum-squeezed states generated by homodyne detection, and clarify the conditions under which the bias remains negligible and when the reconstruction bias becomes significant.

Abstract. In the auroral ionosphere, plasma turbulence acts as an important dissipation mechanism for magnetospheric energy and the primary cause of radio wave scintillation. Characterizing auroral plasma turbulence across its full spatial extent has historically been limited by the narrow bandwidths of individual instruments. Our investigation approaches the problem of obtaining accurate, scale-dependent information using the physics of the Farley-Buneman (FB) instability, a modified two-stream plasma instability. In this study, we construct a composite spatial powerspectrum of plasma turbulence in the auroral electrojets spanning roughly four orders of magnitude in scale (from ~100 km down to ~20 m). This is achieved by combining a recent Monte-Carlo-based method of spatial clustering of very-high-frequency (VHF) radar echoes, with phase screen information derived from global navigation satellite system (GNSS) signals, using ground-based instrumentation in Canada. Through multi-instrument conjunctions with the European Swarm and Japanese Arase missions, we observe that the clustering of electrojet turbulence matches the structuring of field-aligned currents, and correlates with magnetospheric electron fluxes. Statistical analysis of the composite spectra, as well as a very large database of radar clustering spectra only, reveals a consistently steep decay of spectral power in the auroral electrojets, with the most probable spectral index being near −8/3. The observations suggest a continuous, scale-invariant cascade that frequently preserves the spatial signature of its magnetospheric drivers, where we outline a way for Alfvén waves to structure the turbulent E-region. Furthermore, we demonstrate that the plasma structures guilty of causing GPS scintillations (~270 meters in size) were moving at the ion acoustic speed, implying that those structures were, in fact, FB waves, and we thereby establish an observational basis for low-frequency electrojet turbulence. The method that we present, the composite radar-GNSS spectra, will on both counts offer useful empirical constraints for future efforts seeking to simulate the "sub-grid" turbulence that complicates the magnetosphere-ionosphere coupling around aurorae.

We investigate the advantage of using squeezed input light for generating gravity-induced entanglement (2024).], 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 in GIE detection, we find that a total measurement time of 106 s is required to achieve SNR 1/4 1 when using squeezed input light, whereas 106.8 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.

The experimental verification of the quantum nature of gravity represents a milestone in quantum gravity research. Recently, interest has grown for testing it via gravitationally induced entanglement (GIE). Here, we propose a space-based interferometer inspired by the LISA Pathfinder (LPF). Our design employs two kg-scale gold-platinum test masses which, unlike in the LPF, are surrounded by a shield below 1 K and positioned side-by-side with a centimeter-scale separation. This configuration enables the detection of GIE through simultaneous measurements of differential and common-mode motions. To estimate the integration time required for GIE detection, we simulate quantum measurements of these modes, considering noise sources such as gas damping, black-body radiation, and cosmic-ray collisions. Our results show that GIE can be demonstrated with a few modifications to the LPF setup.

We investigate the quantum signature of gravity in optomechanical systems under quantum control. We analyze the gravity-induced entanglement and squeezing in mechanical mirrors in a steady state. The behaviors and the conditions for generating the gravity-induced entanglement and squeezing are identified in the Fourier modes of the mechanical mirrors. The condition of generating the entanglement between the mirrors found in the present paper is more severe than that of the gravity-induced entanglement between output lights. The gravity-induced entanglement in optomechanical systems is an important milestone towards verifying the quantum nature of gravity, which should be verified in the future.

In this study, we investigate the decoherence of a spatially superposed electrically neutral spin-1 2 particle in the presence of a relativistic quantum electromagnetic field in Minkowski spacetime. We demonstrate that decoherence due to the spin-magnetic field coupling can be categorized into two distinct factors: local decoherence, originating from the two-point correlation functions along each branch of the superposed trajectories, and nonlocal decoherence, which arises from the correlation functions between the two superposed trajectories. These effects are linked to phase damping and amplitude damping. We also show that if the quantum field is prepared in a thermal state, decoherence monotonically increases with the field temperature.

We measured the mechanical loss of a dielectric multilayer reflective coating (ion-beam-sputtered SiO2 and Ta2O5) with and without TiO2 on sapphire disks between 6 and 77 K. The measured loss angle exhibited a temperature dependence, and the local maximum was found at approximately 20 K. This maximum was 7.0*10^(-4) (with TiO2) and 7.7*10^(-4) (without TiO2), although the previous measurement for the coating on sapphire disks showed almost no temperature dependence (Phys. Rev. D 74 022002 (2006)). We evaluated the coating thermal noise in KAGRA and discussed future investigation strategies.

We investigate the violation of the Leggett-Garg inequalities for a harmonic oscillator in various quantum states. We focus on the two-time quasi-probability distribution function with a dichotomic variable constructed with the position operator of a harmonic oscillator. First, we developed a new formula to compute the two-time quasi-probability distribution function, whose validity is demonstrated in comparison with the formula developed in the recent paper by Mawby and Halliwell[Phys.Rev.A, 107 032216 (2023)]. Second, we demonstrated the variety of the violation of the two-time Leggett-Garg inequalities assuming various quantum states of a harmonic oscillator including the squeezed coherent state and the thermal squeezed coherent state. Third, we demonstrated that a certain type of extension of the dichotomic variable and the corresponding projection operator can boost violation of the Leggett-Garg inequalities for the ground state and the squeezed state. We also discuss when the Leggett-Garg inequalities are violated in an intuitive manner.

We investigate the violation of the Leggett-Garg inequalities for a quantum field, focusing on the two-time quasi-probability distribution function of the dichotomic variable with a coarse-grained scalar field. The Leggett-Garg inequalities are violated depending on the quantum state of the field and the size of coarse-graining. We also demonstrate that the violation of the Leggett-Garg inequalities appears even for the vacuum state and the squeezed state by properly constructing the dichotomic variable and the projection operator.

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 = 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.

We investigate violations of Leggett-Garg inequalities (LGIs) for a harmonic oscillator and a (1 + 1)dimensional chiral scalar field with coherent-state projectors, which is equivalent to a heterodyne-type measurement scheme. For the harmonic oscillator, we found that the vacuum and thermal states violated the LGIs by evaluating the two-time quasiprobability distribution function. In particular, we demonstrate that the value of the two-time quasiprobability reaches -0.123 for a squeezed coherent-state projector, which is equivalent to 98% of the L & uuml;ders bound corresponding to the maximal violation of the LGIs. We also find a violation of the LGIs for the local mode of a quantum chiral scalar field by constructing a coherent-state projector similar to the harmonic-oscillator case. In contrast with the harmonic oscillator, the periodicity in the time direction of the quasiprobability disappears, which is related to the existence of quantum entanglement between the local mode and its complementary degrees of freedom.

Understanding the phenomenon of quantum superposition of gravitational fields induced by massive quantum particles is an important starting point for quantum gravity. The purpose of this study is to deepen our understanding of the phenomenon of quantum superposition of gravitational fields. To this end, we consider a trade-off relation of entanglement (monogamy relation) in a tripartite system consisting of two massive particles and a gravitational field that may be entangled with each other. Consequently, if two particles cannot exchange information mutually, they are in a separable state, and the particle and gravitational field are always entangled. Furthermore, even when two particles can send information to each other, there is a trade-off between the two particles and the gravitational field. We also investigate the behavior of the quantum superposition of the gravitational field using quantum discord. We find that quantum discord increases depending on the length scale of the particle superposition. Our results may help understand the relationship between the quantization of the gravitational field and the meaning of the quantum superposition of the gravitational field.

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.

KAGRA is the first km-scale gravitational wave detector to be constructed underground and employ cryogenics to cool down its test masses. While the underground location provides a quiet site with low seismic noise, the cooling infrastructure is known to generate large mechanical vibrations due to cryocooler operation and structural resonances of the cryostat. As cooling system components are relatively heavy and in close proximity to the test masses, oscillation of gravity force induced by their vibration, so-called Newtonian noise, could contaminate the detector sensitivity. In this paper, we use the results from vibration analysis of the KAGRA cryostat to estimate cooling system Newtonian noise in the 1-100 Hz frequency band. Our calculations show that, while this noise does not limit the current detector sensitivity or inspiral range, it will be an issue in the future when KAGRA improves its sensitivity. We conclude that KAGRA may need to implement Wiener filters to subtract this noise in the future.

We evaluated the accuracy limit for estimating gravitational potential using optical lattice clocks by utilizing the quantum Cramér--Rao bound. We then compared the results for single-layer and multilayer optical lattice clocks. The results indicate that the lower bound of variance of the estimator of gravitational potential using finite-size optical lattice clocks diverges and recovers repeatedly as a function of time. Namely, the accuracy of the gravitational potential estimation is not a monotonic function of time owing to the effect of gravitational dephasing in finite-size optical lattice clock. Further, this effect creates an estimation accuracy limit when attempting to avoid the divergence of the lower bound. When the number of layers in the optical lattice clock is sufficiently large, the limit is independent of the optical lattice clock details. The time required to reach this limit is calculated to be approximately 33 hours for a three-dimensional optical lattice clock consisting of one million cadmium atoms due to Earth's gravity, and approximately the same for other atoms.

Pendulums have long been used as force sensors due to their ultimately low dissipation (high-quality factor) characteristic. They are widely used in the measurement of the gravitational constant, detection of gravitational waves, and determination of ultralight dark matter. Furthermore, it is expected that the quantum nature of gravity will be demonstrated by performing quantum control for macroscopic pendulums. Recently, we have demonstrated that quantum entanglement between two pendulums can be generated using an optical spring [D. Miki, N. Matsumoto, A. Matsumura, T. Shichijo, Y. Sugiyama, K. Yamamoto, and N. Yamamoto, arXiv:2210.13169 (2022)]; however, we have ignored that an optical spring can reduce the quality factor (Q-factor) by applying normal-mode splitting between the pendulum and rotational modes possessing relatively high dissipation. Herein, we analyze a system composed of a cylinder suspended using a beam (a suspended mirror, i.e., a pendulum) and an optical spring to consider normal-mode splitting. The reduction in Q-factor is determined only by the beam parameters: the ratio of the radius of the mirror to the length of the beam, and the ratio of the frequency of the rotational mode to the pendulum mode in the absence of cavity photons. In our analysis, we find that the reduction factor $4.38$ is reproduced, which is consistent with the experimental result in Matsumoto \textit{et al.} [N. Matsumoto, S. B. Catan$\tilde{\text{o}}$-Lopez, M. Sugawara, S. Suzuki, N. Abe, K. Komori, Y. Michimura, Y. Aso, and K. Edamatsu, Phys. Rev. Lett. 122, 071101 (2019)]. Our analysis shows that low dissipation (high quality) can be reached using an optical spring for the realistic pendulum system considering the rotational degree of freedom.

We study the system of a massive fermion field confined between two parallel plates, where the properties of both plates are discussed under chiral MIT boundary conditions. We investigate the effects of the chiral angle on the Casimir energy for a massive fermion field with the general momentum. We find that the Casimir energy as a function of the chiral angle is generally symmetric, and the attractive Casimir force in the chiral case is stronger than that in the nonchiral case. In addition, we investigate the approximate Casimir energy for light and heavy mass cases. The behavior of the discrete momentum and changes of spin orientation are also discussed.