arXiv subjects

Kouji Nakamura

Publications and source records attributed to Kouji Nakamura.

At least 19 recordsLinked to original sources

arXiv2025

Theoretical Detailed Analyses for DC readout and a Fabri-P\'erot gravitational-wave detector

The quantum expectation value and the stationary noise spectral density for a Fabry-P'erot gravitational-wave detector with a DC readout scheme are discussed in detail only through the quantum electrodynamics of lasers and the Heisenberg equations of mirrors' motion. We demonstrate that the initial conditions of the mirrors' motion concentrate around the fundamental frequency of the pendulum and are not related to the frequency range of our interest. Although, in the ideal case, there is consensus that the shot-noise contribution from the laser to the high-frequency range of the signal-referred noise spectral density decreases as the injected laser power increases, our derived noise spectral density shows that the shot-noise contribution does not decrease. This is due to leakage of classical radiation pressure forces from the carrier field to the output port, and the carrier field is used as the reference in the DC readout scheme. Since classical radiation pressure acts as a constant force, it shifts the pendulum's equilibrium point of the mirrors' motion. To recover the ideal case, we must consider adjusting the interferometer's tuning point to place the mirrors at their equilibrium positions. We investigate the case where the equilibrium tuning is incomplete and show that the behavior of the above shot noise is due to this incompleteness. We also discuss the maximum deviation of the mirror displacements from the equilibrium point during incomplete tuning to recover a near-ideal case.

gr-qc↗

arXiv2024

Comparing a gauge-invariant formulation and a "conventional complete gauge-fixing approach" for $l=0,1$ mode perturbations on the Schwarzschild background spacetime

Comparison of the gauge-invariant formulation for $l=0,1$-mode perturbations on the Schwarzschild background spacetime proposed in [K.~Nakamura, Class. Quantum Grav. {\bf 38} (2021), 145010.] and a ``conventional complete gauge-fixing approach'' in which we use the spherical harmonic functions $Y_{lm}$ as the scalar harmonics from the starting point is discussed. Although it is often said that ``gauge-invariant formulations in general-relativistic perturbations are equivalent to complete gauge-fixing approaches,'' as the result of this comparison, we conclude that the derived solutions through the proposed gauge-invariant formulation and those through a ``conventional complete gauge-fixing approach'' are different. It is pointed out that there is a case where the boundary conditions and initial conditions are restricted in a conventional complete gauge-fixing approach.

gr-qc↗

arXiv2023

ICRC2023 Proceedings: Proposal of a gauge-invariant treatment of $l=0,1$-mode perturbations on the Schwarzschild background spacetime

A gauge-invariant perturbation theory on a generic background spacetime is developing from 2003 and ``zero-mode problem'' for linear metric perturbations was proposed as the essential problem of this theory. In the perturbation theory on the Schwarzschild background spacetime, $l=0,1$ modes correspond to the above ``zero-mode'' and the gauge-invariant treatments of these modes is a famous non-trivial problem in perturbation theories on the Schwarzschild background spacetime. Due to this situation, a gauge-invariant treatment for these $l=0,1$-mode perturbations is proposed. Through this gauge-invariant treatment, the solutions to the linearized Einstein equation for these modes with a generic matter field are derived. In the vacuum case, the linearized version of uniqueness theorem of Kerr spacetime is confirmed in a gauge-invariant manner. In this sense, our proposal is reasonable.

gr-qc↗

arXiv2021

Gauge-invariant perturbation theory on the Schwarzschild background spacetime Part I : -- Formulation and odd-mode perturbations

This is the Part I paper of our series of full papers on a gauge-invariant {\it linear} perturbation theory on the Schwarzschild background spacetime which was briefly reported in our short papers [K.~Nakamura, Class. Quantum Grav. {\bf 38} (2021), 145010; K.~Nakamura, Letters in High Energy Physics {\bf 2021} (2021), 215.]. We first review our general framework of the gauge-invariant perturbation theory, which can be easily extended to the {\it higher-order} perturbation theory. When we apply this general framework to perturbations on the Schwarzschild background spacetime, a gauge-invariant treatments of $l=0,1$ mode perturbations are required. On the other hand, in the current consensus on the perturbations of the Schwarzschild spacetime, gauge-invariant treatments for $l=0,1$ modes are difficult if we keep the reconstruction of the original metric perturbations in our mind. Based on this situation, we propose a strategy of a gauge-invariant treatments of $l=0,1$ mode perturbations through the decomposition of the metric perturbations by singular harmonic functions at once and the regularization of this singularity through the imposition of the boundary conditions to the Einstein equations. Following this proposal, we derive the linearized Einstein equations for any modes of $l\geq 0$ in a gauge-invariant manner. We discuss the solutions to the odd-mode perturbation equations in the linearized Einstein equations and show that these perturbations include the Kerr parameter perturbation in these odd-mode perturbation, which is physically reasonable.

gr-qc↗

arXiv2021

Gauge-invariant perturbation theory on the Schwarzschild background spacetime Part II: -- Even-mode perturbations

This is the Part II paper of our series of papers on a gauge-invariant perturbation theory on the Schwarzschild background spacetime. After reviewing our general framework of the gauge-invariant perturbation theory and the proposal on the gauge-invariant treatments for $l=0,1$ mode perturbations on the Schwarzschild background spacetime in the Part I paper [K.~Nakamura, arXiv:2110.13508 [gr-qc]], we examine the linearized Einstein equations for even-mode perturbations. We discuss the strategy to solve the linearized Einstein equations for these even-mode perturbations including $l=0,1$ modes. Furthermore, we explicitly derive the $l=0,1$ mode solutions to the linearized Einstein equations in both the vacuum and the non-vacuum cases. We show that the solutions for $l=0$ mode perturbations includes the additional Schwarzschild mass parameter perturbation, which is physically reasonable. Then, we conclude that our proposal of the resolution of the $l=0,1$-mode problem is physically reasonable due to the realization of the additional Schwarzschild mass parameter perturbation and the Kerr parameter perturbation in the Part I paper.

gr-qc↗

arXiv2021

Gauge-invariant perturbation theory on the Schwarzschild background spacetime Part III: -- Realization of exact solutions

This is the Part III paper of our series of papers on a gauge-invariant perturbation theory on the Schwarzschild background spacetime. After reviewing our general framework of the gauge-invariant perturbation theory and the proposal on the gauge-invariant treatments for $l=0,1$ mode perturbations on the Schwarzschild background spacetime in [K.~Nakamura, arXiv:2110.13508 [gr-qc]], we examine the problem whether the $l=0,1$ even-mode solutions derived in the Part II paper [K.~Nakamura, arXiv:2110.13512 [gr-qc]] are physically reasonable, or not. We consider the linearized versions of the Lema\^itre-Tolman-Bondi solution and the non-rotating C-metric. As the result, we show that our derived even-mode solutions to the linearized Einstein equations actually realize above two linearized solutions. This fact supports that our derived solutions are physically reasonable, which implies that our proposal on the gauge-invariant treatments for $l=0,1$ mode perturbations are also physically reasonable. We also briefly summarize our conclusions of our series of papers.

gr-qc↗

arXiv2021

Quantum noise and vacuum fluctuations in balanced homodyne detections through ideal multi-mode detectors

The balanced homodyne detection as a readout scheme of gravitational-wave detectors is carefully examined from the quantum field theoretical point of view. The readout scheme in gravitational-wave detectors specifies the directly measured quantum operator in the detection. This specification is necessary when we apply the recently developed quantum measurement theory to gravitational-wave detections. We examine the two models of measurement. One is the model in which the directly measured quantum operator at the photodetector is Glauber's photon number operator, and the other is the model in which the power operator of the optical field is directly measured. These two are regarded as ideal models of photodetectors. We first show these two models yield the same expectation value of the measurement. Since it is consensus in the gravitational-wave community that vacuum fluctuations contribute to the noises in the detectors, we also clarify the contributions of vacuum fluctuations to the quantum noise spectral density without using the two-photon formulation which is used in the gravitational-wave community. We found that the conventional noise spectral density in the two-photon formulation includes vacuum fluctuations from the main interferometer but does not include those from the local oscillator. Although the contribution of vacuum fluctuations from the local oscillator theoretically yields the difference between the above two models in the noise spectral densities, this difference is negligible in realistic situations.

gr-qc↗

arXiv2021

Formal solutions of any-order mass, angular-momentum, dipole perturbations on the Schwarzschild background spacetime

Formal solutions of any-order mass, angular-momentum, dipole perturbations on the Schwarzschild background spacetime are derived in a gauge-invariant manner. Once we accept the proposal in [K. Nakamura, Class. Quantum Grav. {\bf 38} (2021), 145010.], we can extend the gauge-invariant linear perturbation theory on the Schwarzschild background spacetime including the monopole ($l=0$) and dipole ($l=1$) modes to any-order perturbations of the same background spacetime through the arguments in [K. Nakamura, Class. Quantum Grav. {\bf 31} (2014), 135013.]. As a result of this resolution, we reached to a simple derivation of the above formal solutions of any order.

gr-qc↗

arXiv2021

Proposal of a gauge-invariant treatment of l=0,1-mode perturbations on Schwarzschild Background Spacetime

A gauge-invariant treatment of the monopole- ($l=0$) and dipole ($l=1$) modes in linear perturbations of the Schwarzschild background spacetime is proposed. Through this gauge-invariant treatment, we derived the solutions to the linearized Einstein equation for these modes with a generic matter field. In the vacuum case, these solutions include the Kerr parameter perturbations in the $l=1$ odd modes and the additional mass parameter perturbations of the Schwarzschild mass in the $l=0$ even modes. The linearized version of Birkhoff's theorem is also confirmed in a gauge-invariant manner. In this sense, our proposal is reasonable.

gr-qc↗

arXiv2021

Vacuum fluctuations and balanced homodyne detection through ideal multi-mode photon number or power counting detectors

The balanced homodyne detection as a readout scheme of gravitational-wave detectors is carefully examined, which specifies the directly measured quantum operator in the detection. This specification is necessary to apply the quantum measurement theory to gravitational-wave detections. We clarify the contribution of vacuum fluctuations to the noise spectral density without using the two-photon formulation. We found that the noise spectral density in the two-photon formulation includes vacuum fluctuations from the main interferometer but does not includes those from the local oscillator which depends on the directly measured operators.

gr-qc↗

arXiv2020

Current status of space gravitational wave antenna DECIGO and B-DECIGO

Deci-hertz Interferometer Gravitational Wave Observatory (DECIGO) is the future Japanese space mission with a frequency band of 0.1 Hz to 10 Hz. DECIGO aims at the detection of primordial gravitational waves, which could be produced during the inflationary period right after the birth of the universe. There are many other scientific objectives of DECIGO, including the direct measurement of the acceleration of the expansion of the universe, and reliable and accurate predictions of the timing and locations of neutron star/black hole binary coalescences. DECIGO consists of four clusters of observatories placed in the heliocentric orbit. Each cluster consists of three spacecraft, which form three Fabry-Perot Michelson interferometers with an arm length of 1,000 km. Three clusters of DECIGO will be placed far from each other, and the fourth cluster will be placed in the same position as one of the three clusters to obtain the correlation signals for the detection of the primordial gravitational waves. We plan to launch B-DECIGO, which is a scientific pathfinder of DECIGO, before DECIGO in the 2030s to demonstrate the technologies required for DECIGO, as well as to obtain fruitful scientific results to further expand the multi-messenger astronomy.

gr-qc↗

arXiv2020

Second-order Gauge-invariant Cosmological Perturbation Theory: Current Status updated in 2019

The current status of the recent developments of the second-order gauge-invariant cosmological perturbation theory is reviewed. To show the essence of this perturbation theory, we concentrate only on the universe filled with a single scalar field. Through this review, we point out the problems which should be clarified for the further theoretical sophistication of this perturbation theory. This review is an extension of the review paper [K.~Nakamura, "Second-Order Gauge-Invariant Cosmological Perturbation Theory: Current Status", Advances in Astronomy, vol.2010 (2010), 576273.]. We also expect that this theoretical sophistication will be also useful to discuss the future developments in cosmology as a precise science.

gr-qc↗

arXiv2018

Double balanced homodyne detection

In the context of the readout scheme for gravitational-wave detectors, the "double balanced homodyne detection" proposed in [K.~Nakamura and M.-K.~Fujimoto, arXiv:1709.01697.] is discussed in detail. This double balanced homodyne detection enables us to measure the expectation values of the photon creation and annihilation operators. Although it has been said that the operator $\hat{b}_θ:=\cosθ\hat{b}_{1}+\sinθ\hat{b}_{2}$ can be measured through the homodyne detection in literature, we first show that the expectation value of the operator $\hat{b}_θ$ cannot be measured as the linear combination of the upper- and lower-sidebands from the output of the balanced homodyne detection. Here, the operators $\hat{b}_{1}$ and $\hat{b}_{2}$ are the amplitude and phase quadrature in the two-photon formulation, respectively. On the other hand, it is shown that the above double balanced homodyne detection enables us to measure the expectation value of the operator $\hat{b}_θ$ if we can appropriately prepare the complex amplitude of the coherent state from the local oscillator. It is also shown that the interferometer set up of the eight-port homodyne detection realizes our idea of the double balanced homodyne detection. We also evaluate the noise-spectral density of the gravitational-wave detectors when our double balanced homodyne detection is applied as their readout scheme. Some requirements for the coherent state from the local oscillator to realize the double balanced homodyne detection are also discussed.

quant-ph↗

arXiv2018

Extension of the input-output relation for a Michelson interferometer to arbitrary coherent-state light sources: --- Gravitational-wave detector and weak-value amplification ---

An extension of the input-output relation for a conventional Michelson interferometric gravitational-wave detector is carried out to treat an arbitrary coherent state for the injected optical beam. This extension is one of necessary researches toward the clarification of the relation between conventional gravitational-wave detectors and a simple model of a gravitational-wave detector inspired by weak-measurements in [A.~Nishizawa, Phys. Rev. A {\bf 92} (2015), 032123.]. The derived input-output relation describes not only a conventional Michelson-interferometric gravitational-wave detector but also the situation of weak measurements. As a result, we may say that a conventional Michelson gravitational-wave detector already includes the essence of the weak-value amplification as the reduction of the quantum noise from the light source through the measurement at the dark port.

quant-ph↗

arXiv2018

An application of the measurement of expectation values for the photon annihilation and creation operators

Motivated by the readout scheme in interferometric gravitational-wave detectors, we consider the device which measures the expectation value of the photon annihilation and creation operators for output optical field from the main interferometer. As the result, the eight-port homodyne detection is rediscovered as such a device. We evaluate the noise spectral density in this measurement. We also briefly discuss on the application of our results to the readout scheme of gravitational-wave detectors. We call this measurement scheme to measure these expectation values as "double balanced homodyne detection."

quant-ph↗

arXiv2014

Recursive structure in the definitions of gauge-invariant variables for any order perturbations

The construction of gauge-invariant variables for any order perturbations is discussed. Explicit constructions of the gauge-invariant variables for perturbations to 4th order are shown. From these explicit construction, the recursive structure in the definitions of gauge-invariant variables for any order perturbations is found. Through this recursive structure, the correspondence with the fully non-linear exact perturbations is briefly discussed.

gr-qc↗

arXiv2014

Torsion bar antenna in the proper reference frame with rotation

The resultant response of the rotating torsion bar antenna for gravitational waves discussed in [M. Ando et al., Phys. Rev. Lett. {\bf 105} (2010), 161101.] is re-investigate from a general-relativistic point of view. To do this, the equation of motion of a free falling particle in the proper reference frame of a rotating observer is used. As a result, the resultant response derived in the above paper is also valid even when $ω_{g}\simΩ$, where $ω_{g}$ and $Ω$ are the angular frequencies of gravitational waves and the rotation of the antenna, respectively.

gr-qc↗

arXiv2013

Re-interpretations of an experiment on the back-action in a weak measurement

Interpretations of an experiment on the back-action in a weak measurement in [M. Iinuma et al., New J. Phys. vol.13 (2011), 033041] are revisited. We show two different but essentially equivalent interpretations for this experiment along the original scenario of weak measurements proposed by Aharonov, Albert, and Vaidman. To do this, we introduce the notion of extended weak values which is associated not only with the states of the system but also the state of the measuring device. We also evaluate fluctuations in this experiment and found that an optimal measurement strength exists for a fixed polarization angle prepared as an initial state, at which fluctuations in measurement results vanish. The consistency of this evaluation with the experimental results is discussed.

quant-ph↗