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巨視的量子実験のためのミリグラムスケール機械光学系

T. Kawasaki

Published Mar 24, 2022• 0 citations
Publisher

Abstract

Milligram-scale optomechanical systems are unique systems that have the potential to realize macroscopic yet quantum phenomena.To achieve a sensitivity that reaches the dominant region of quantum mechanics, we propose a system in which the optical radiation pressure traps the mirror in the rotational degrees of freedom even in a suspended linear cavity, and a high power laser beam can be coupled to it.An optomechanical system consists of mechanical oscillators and optical fields coupled to it.It is suitable for macroscopic quantum experiments because even a macroscopic oscillator's displacements can be read out with a precision greater than the wavelength of light.As mechanical oscillators, pendulums are often used above the milligram scale since they are resistant to environmental vibrations.However, when a linear cavity is built with a suspended mirror, the rotational motion of the mirrors become unstable due to the optical radiation pressure inside the cavity, a phenomenon known as Sidles-Sigg instability.To avoid the Sidles-Sigg instability, experiments were conducted using triangular cavities or rigid suspensions that reduce the effect of radiation pressure.However, quantum fluctuation was concealed by thermal noise in the complicated part of the system.Linear cavities consisting of only two mirrors are advantageous for high sensitivity reaching the quantum fluctuation.In this research, we find that even in a linear cavity, the Sidles-Sigg instability can be overcome if the masses of the two mirrors are unbalanced and the curvatures of the mirrors are shorter than the cavity length.We succeed in constructing a linear cavity with the smallest suspended mirror with curvature.Our optomechanical system becomes a highly sensitive force sensor by using a tiny 8-mg mirror as a test mass.With this system, we quantitatively evaluate the optical torsional spring effect due to the radiation pressure in the cavity, and validate our configuration.Furthermore, we demonstrate a quantum noise reduction technique by injecting classical intensity noise that imitates quantum noise.Improvements in the sensitivity are observed, and they are consistent with theoretical predictions.In addition, as a prospect for improving the sensitivity of our system towards the quantum regime, we discuss the idea of modifying the simple pendulum to a torsional pendulum, and show its promise.As a consequence, we establish a class of linear cavities, and present that these systems are competent for iii macroscopic quantum experiments.

DOI
10.15083/0002008943

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Milligram-scale optomechanical systems are unique systems that have the potential to realize macroscopic yet quantum phenomena.To achieve a sensitivity that reaches the dominant region of quantum mechanics, we propose a system in which the optical radiation pressure traps the mirror in the rotational degrees of freedom even in a suspended linear cavity, and a high power laser beam can be coupled to it.An optomechanical system consists of mechanical oscillators and optical fields coupled to it.It is suitable for macroscopic quantum experiments because even a macroscopic oscillator's displacements can be read out with a precision greater than the wavelength of light.As mechanical oscillators, pendulums are often used above the milligram scale since they are resistant to environmental vibrations.However, when a linear cavity is built with a suspended mirror, the rotational motion of the mirrors become unstable due to the optical radiation pressure inside the cavity, a phenomenon known as Sidles-Sigg instability.To avoid the Sidles-Sigg instability, experiments were conducted using triangular cavities or rigid suspensions that reduce the effect of radiation pressure.However, quantum fluctuation was concealed by thermal noise in the complicated part of the system.Linear cavities consisting of only two mirrors are advantageous for high sensitivity reaching the quantum fluctuation.In this research, we find that even in a linear cavity, the Sidles-Sigg instability can be overcome if the masses of the two mirrors are unbalanced and the curvatures of the mirrors are shorter than the cavity length.We succeed in constructing a linear cavity with the smallest suspended mirror with curvature.Our optomechanical system becomes a highly sensitive force sensor by using a tiny 8-mg mirror as a test mass.With this system, we quantitatively evaluate the optical torsional spring effect due to the radiation pressure in the cavity, and validate our configuration.Furthermore, we demonstrate a quantum noise reduction technique by injecting classical intensity noise that imitates quantum noise.Improvements in the sensitivity are observed, and they are consistent with theoretical predictions.In addition, as a prospect for improving the sensitivity of our system towards the quantum regime, we discuss the idea of modifying the simple pendulum to a torsional pendulum, and show its promise.As a consequence, we establish a class of linear cavities, and present that these systems are competent for iii macroscopic quantum experiments.
In order to observe quantum radiation pressure noise and reduce it by measuring the ponderomotively squeezed light on a table-top experiment, we are developing a laser interferometer with Fabry-Perot cavities with very small suspended mirrors. As a preliminary setup, we have constructed a Fabry-Perot cavity of finesse 1300 with a suspended mirror of 20 mg. The cavity was locked stably at low laser power for which the classical radiation pressure caused little effect on the dynamics of the small mirror. For the stable operation of this cavity with higher laser power, a technique to control the motion of the small mirror, especially its yaw motion, is necessary. We describe that the motion can be stabilized through the radiation pressure of light inside the cavity, by controlling the motion of the front mirror of a Fabry-Perot cavity properly.
Radiation pressure exerted by light in interferometric measurements is responsible for displacements of mirrors which appear as an additional back-action noise and limit the sensitivity of the measurement. We experimentally study these effects by monitoring in a very high-finesse optical cavity the displacements of a mirror with a sensitivity at the 10-20m/√Hz level. This unique sensitivity is a step towards the first observation of the fundamental quantum effects of radiation pressure and the resulting standard quantum limit in interferometric measurements. Our experiment may become a powerful facility to test quantum noise reduction schemes, and we already have demonstrated radiation-pressure induced correlations between two optical beams sent into the same moving mirror cavity. Our scheme can be extended down to the quantum level and has applications both in high-sensitivity measurements and in quantum optics.
Cavity Optomechanics, that is the study of the interaction between an optical cavity mode and a mechanical degree of freedom, has known impressive evolution over the past decade, to become a new field at the union of condensed matter physics and optics. One of the major goals of this discipline is to test and study quantum mechanics using macroscopic systems. Among the most fundamental problems the community aims to address is the question of the quantum limits in position measurement. Quantum mechanics predicts that any measurement comes along with a backaction, which perturbs the state of the measured system. Moreover, it is expected to be conjugated with the quantum noise of the measurement apparatus (called measurement noise) used to probe the system. The optimal sensitivity is reached whenever both the measurement and the backaction noise are identical, a situation which can be assimilated to the acceptance of Heisenberg's inequality for the measurement apparatus. In cavity optomechanics, the mode of an optical cavity is used as a measurement apparatus of the position of a mechanical resonator which is expected to be responsible for the backaction imprecision. However, this so-called radiation pressure quantum backaction has never been observed to date, while it remains a decisive step towards understanding quantum measurement processes. We describe in this manuscript the study of radiation pressure effects in cavity optomechanics. We introduce the optomechanical system we have developed, which consists in a cm-scale ultra high Q (~ 1 000 000) plano-convex mechanical resonator incorporated into a ultra-high finesse (~ 300 000) Fabry-Prot cavity. We present two important results we obtained with this system. First, we were able to report the first direct observation of radiation pressure in real-time, based on establishing pump-probe correlations. We were also able to demonstrate for the first time nonlinear backaction effects related to substantial improvement of position measurement sensitivity. We explain why demonstrating quantum backaction requires ultra-high stability of the optical mode. We present important changes made to the previous experimental setup, notably on the laser source, on the detection and the stabilization of the experiment. We then describe a new optomechanical detection technique providing an independent measurement of the cavity detuning. Finally, we present a proof-of-principle experiment allowing to extract quantum optomechanical correlations at room temperature.
In the classic Chinese novel Journey to the West, the Monkey King has a special power that enables him to be in two or more places simultaneously. Normally, an amazing thing such as this could never happen in real life. However, in the quantum world, where the motions of objects obey the rules of quantum mechanics, this could happen. These weird quantum rules usually only apply in the microscopic world to atoms and molecules, because quantum properties are generally very fragile in the macroscopic world. However, scientists have recently been making efforts to push macroscopic and mesoscopic mechanical systems into the quantum world, i.e. they are putting conventional mechanical systems into the quantum mechanical regime. Spring oscillators, swings, and pendulum clocks are typical mechanical systems that we often see in daily lives, and they can be described by a basic physical model: the harmonic oscillator. In the quantum regime, harmonic oscillators have some quantum properties, including discrete energy spectra and zero-point motion. To observe these quantum properties, the environmental thermal noise must be suppressed so that the energy of the quantum motion dominates over the energy of the thermal motion. To this end, a generic model of a cavity optomechanical system is used, as shown in Fig. 1. The system consists of an optical cavity with a fixed mirror and a movable mirror, where the latter is attached to a spring and undergoes harmonic oscillation. A laser beam is launched into the cavity and is reflected multiple times between the two mirrors, and the cavity field thus builds up, resulting in a greatly enhanced optical field, which then exerts a considerable force on the movable mirror. The interaction between the optical field and the mechanical motion can reduce the thermal motion noise to enable the fragile quantum properties to be observed. The study of such systems has produced an emerging field called cavity optomechanics [1–3]. The pioneering work was conducted by Braginsky and co-workers in the 1960s [4]. In recent years, various experimental systems have been proposed and investigated, including Fabry–Pérot cavities [by groups including MIT/Caltech LIGO Laboratory, the Mavalvala group at MIT, the Aspelmeyer group at the University of Vienna, the Heidmann group at the University of Pierre and Marie Curie, and the Bouwmeester group at the University of California, Santa Barbara (UCSB)], whispering-gallery cavities (by groups including the Vahala group at Caltech, the Kippenberg group at École Polytechnique Fédérale de Lausanne, the Wang group at the University of Oregon, the Lipson group at Cornell University, the Carmon group at the University of Michigan, the Bowen group at the University of Queensland, and the Xiao group at Peking University), photonic crystal cavities (by groups including the Painter group at Caltech, the Wong group at Columbia University, and the Tang group at Yale University), separated mechanical oscillators inside or near a cavity (by groups including the Harris group at Yale University, the Regal group at Joint Institute for Laboratory Astrophysics (JILA), the Favero group at Paris Diderot University, and the Weig group at the University of Munich), superconducting circuits (by groups including the Schwab group at Caltech, the Lehnert group at JILA, the Cleland group at UCSB, and the Teufel group at National Institute of Science and Technology, Boulder), and cold atoms (by groups including the Kimble group at Caltech, the Stamper-Kurn group at the University of California, Berkeley, and the Treutlein group at the University of Basel). Illustration of a generic cavity optomechanical system. The left mirror is fixed and the right mirror is attached to a spring. Cavity optomechanics has been featured as the most recent milestone in photon history in Nature. The research in cavity optomechanics is important to both fundamental physics studies and the applied sciences. First, cavity optomechanics provides a unique platform for the study of fundamental quantum physics, including macroscopic quantum phenomena, decoherence, and quantum–classical transitions. The field offers the best test bed to study effects like gravity-induced decoherence, which is important to the understanding of macroscopic quantum phenomena. Second, cavity optomechanics is promising for high-precision measurements of small forces, masses, displacements, and accelerations, and is considered to be capable of surpassing the standard quantum limit. Third, cavity optomechanics provides resources for both classical and quantum information processing. For instance, optomechanical devices can serve as information storage devices and act as interfaces between light beams with different wavelengths or even microwaves. In the last few years, researchers have made considerable efforts to put mechanical systems into their quantum ground states [5]. Recent efforts have demonstrated optomechanically induced transparency [6], normal-mode splitting [7], quantum-coherent coupling [8], wavelength conversion [9], and measurements performed below the standard quantum limit [10]. Future developments will aim to integrate different quantum systems to form hybrid quantum devices, e.g. hybrid optomechanical and electromechanical systems. In this way, we can enable phonons, photons, and electrons to work together in the quantum world. Recent years have seen rapidly growing interest in the field of cavity optomechanics. As shown in Fig. 2, the publications and citations in this field have grown exponentially. The now booming development in this field will turn the dream of manipulating macroscopic mechanical systems in a quantum manner into reality. Numbers of publications (a) and citations (b) per year in the period from 2005 to 2013 with the keyword ‘cavity optomechanics’, retrieved from the Web of Science.
The experiments presented in this thesis investigate the interaction between radiation and an optical cavity, in which one mirror of the cavity is mounted on a flexure which could be moved by radiation pressure. The cavity was shown to exhibit non-linear behaviour with high input power. The radiation pressure force was shown to change the mechanical resonance frequency of the moveable mirror. Motion was induced through amplitude modulation of a high power input beam and the extent of this motion measured using the cavity control loop. To demonstrate the way quantum correlations could be used to beat the SQL, the laser light incident on the cavity was prepared, using classical modulation techniques, with classical correlations between the quadratures that cause shot noise and radiation pressure noise. A level of modulation much higher than the quantum level was used to make the cancellation effects more visible. The effect of radiation pressure induced motion was cancelled by the addition of correlated frequency modulation. The input amplitude was then modulated by a white noise source. The resulting noise was partially cancelled when the same white noise source was used to drive the frequency modulator with a dierent phase. This cancellation demonstrably improved the signal to noise ratio of a signal injected into the system.
We have developed an experiment of ultrasensitive interferometric measurement of small displacements based on a high-finesse Fabry-Perot cavity. We have observed the internal thermal noise of mirrors and fully characterized their acoustics modes with a sensitivity of 3 × 10 −20 m/Hz 1/2 . This unique sensitivity is a step towards the first observation of the radiation pressure effects and the resulting standard quantum limit in interferometric measurements. Our experiment may become a powerful facility to test quantum noise reduction schemes such as the use of squeezed light or quantum locking of mirrors. As a first result, we present the observation of a cancellation of radiation pressure effects in our cavity. This back-action noise cancellation was first proposed within the framework of gravitational-wave detection with dual resonators, and may drastically improve the sensitivity of such measurements.