Luận án của Haixing Miao: Cơ học lượng tử lớn trong thiết bị optomechanical

Springer Theses Recognizing Outstanding Ph. Research For further volumes: http://www.com/series/8790 Aims and Scope The series ‘‘Springer Theses’’ brings together a selection of the very best Ph. theses from around the world and across the physical sciences. Nominated and endorsed by two recognized specialists, each published volume has been selected for its scientific excellence and the high impact of its contents for the pertinent field of research.

For greater accessibility to non-specialists, the published versions include an extended introduction, as well as a foreword by the student’s supervisor explaining the special relevance of the work for the field. As a whole, the series will provide a valuable resource both for newcomers to the research fields described, and for other scientists seeking detailed background information on special questions. Finally, it provides an accredited documentation of the valuable contributions made by today’s younger generation of scientists. Theses are accepted into the series by invited nomination only and must fulfill all of the following criteria • They must be written in good English.

• The topic should fall within the confines of Chemistry, Physics and related interdisciplinary fields such as Materials, Nanoscience, Chemical Engineering, Complex Systems and Biophysics. • The work reported in the thesis must represent a significant scientific advance. • If the thesis includes previously published material, permission to reproduce this must be gained from the respective copyright holder. • They must have been examined and passed during the 12 months prior to nomination.

• Each thesis should include a foreword by the supervisor outlining the signifi- cance of its content. • The theses should have a clearly defined structure including an introduction accessible to scientists not expert in that particular field.com Haixing Miao Exploring Macroscopic Quantum Mechanics in Optomechanical Devices Doctoral Thesis accepted by School of Physics, The University of Western Australia 123 www.com Author Supervisors Dr. Haixing Miao Prof. David Blair Theoretical Astrophysics Australian International Gravitational Caltech M350-17 Research Centre (AIGRC) E.

California Blvd 1200 The University of Western Pasadena CA 91125 Australia (M013) USA 35 Stirling Highway Crawley WA 6009 Australia Prof. Yanbei Chen Theoretical Astrophysics Mail Code 350-17 California Institute of Technology Pasadena CA 91125-1700 USA ISSN 2190-5053 e-ISSN 2190-5061 ISBN 978-3-642-25639-4 e-ISBN 978-3-642-25640-0 DOI 10.1007/978-3-642-25640-0 Springer Heidelberg Dordrecht London New York Library of Congress Control Number: 2011944204  Springer-Verlag Berlin Heidelberg 2012 This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer.

Violations are liable to prosecution under the German Copyright Law. The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. Printed on acid-free paper Springer is part of Springer Science+Business Media (www.com Decrease your frequency by expanding your horizon.

Increase your Q by purifying your mind. Eventually, you will achieve inner peace and view the internal harmony of our world. —A lesson from a harmonic oscillator www.com Dedicated to my parents Lanying Zhang and Dehua Miao www.com Parts of this thesis have been published in the following journal articles: 1. Haixing Miao, Chunong Zhao, Li Ju, Slawek Gras, Pablo Barriga, Zhongyang Zhang, and David G.

Blair, Three-mode optoacoustic parametric interactions with a coupled cavity, Phys. Haixing Miao, Chunnong Zhao, Li Ju and David G. Blair, Quantum ground- state cooling and tripartite entanglement with three-mode optoacoustic inter- actions, Phys. Chunnong Zhao, Li Ju, Haixing Miao, Slawomir Gras, Yaohui Fan, and David G.

Blair, Three-Mode Optoacoustic Parametric Amplifier: A Tool for Macro- scopic Quantum Experiments, Phys. Khalili, Haixing Miao, and Yanbei Chen, Increasing the sensitivity of future gravitational-wave detectors with double squeezed-input, Phys. Haixing Miao, Stefan Danilishin, Thomas Corbitt, and Yanbei Chen, Standard Quantum Limit for Probing Mechanical Energy Quantization, Phys. Haixing Miao, Stefan Danilishin, Helge Mueller-Ebhardt, Henning Rehbein, Kentaro Somiya, and Yanbei Chen, Probing macroscopic quantum states with a sub-Heisenberg accuracy, Phys.

Haixing Miao, Stefan Danilishin, and Yanbei Chen, Universal quantum entanglement between an oscillator and continuous fields, Phys. Haixing Miao, Stefan Danilishin, Helge Mueller-Ebhardt, and Yanbei Chen, Achieving ground state and enhancing optomechanical entanglement by recovering information, New Journal of Physics, 12, 083032 (2010). Khalili, Stefan Danilishin, Haixing Miao, Helge Mueller-Ebhardt, Huan Yang, and Yanbei Chen, Preparing a Mechanical Oscillator in Non- Gaussian Quantum States, Phys.com Supervisor’s Foreword Quantum mechanics is a successful and elegant theory for describing the behaviors of both microscopic atoms and macroscopic condensed-matter systems. However, there remains the interesting and fundamental question as to how an apparently macroscopic classical world emerges from the microscopic one described by quantum wave functions.

Recent achievements in high-precision measurement technologies could eventually lead to answering this question through studies of quantum phenomena in the macroscopic regime. By coupling coherent light to mechanical degrees of freedom via radiation pressure, several groups around the world have built state-of-the-art optome- chanical devices that are very sensitive to the tiny motions of mechanical oscil- lators. One prominent example is the laser interferometer gravitational-wave detector, which aims to detect weak gravitational waves from astrophysical sources in the universe. With high-power laser beams, and high mechanical quality test masses, future advanced gravitational-wave detectors will achieve extremely high displacement sensitivity—so high that they will be limited by fundamental noise of quantum origin, and the kilogram-scale test masses will have to be considered quantum mechanically.

This means, on the one hand, that we should manipulate the optomechanical interaction between the optical field and the test masses coherently at the quantum level, in order to further improve the detector sensitivity; and, on the other hand, that advanced gravitational-wave detectors will be ideal platforms for studying the quantum dynamics of kilogram-scale test masses—truly macroscopic objects. These two interesting aspects of advanced gravitational-wave detectors, and of more general optomechanical devices, are the main subjects of this dissertation. The author, Dr. Haixing Miao, starts with a quantum model for the optomechanical device, and studies its various quantum features in detail.

In the first part of the thesis, different approaches are considered for surpassing the quantum limit on the displacement sensitivity of gravitational-wave detectors; in the second part, experimental protocols are considered for probing the quantum behaviors of macroscopic mechanical oscillators with both linear and non-linear optomechan- ical interactions. This thesis has inspired much interesting work within the xi www.com xii Supervisor’s Foreword gravitational-wave community, and has been awarded the prestigious Gravitational Wave International Committee (GWIC) thesis prize in 2011. In addition, the formalism developed here may be equally well applied to general quantum limited measurement devices, which are also of interest to the quantum optics community. Australia, September 2011 Winthrop Professor David Blair Director, Australian International Gravitational Research Centre www.com Preface Recent significant achievements in fabricating low-loss optical and mechanical ele- ments have aroused intensive interest in optomechanical devices which couple optical fields to mechanical oscillators, e., in laser interferometer gravitationalwave (GW) detectors.

Not only can such devices be used as sensitive probes for weak forces and tiny displacements, but they also lead to the possibilities of investigating quantum behaviors of macroscopic mechanical oscillators, both of which are the main topics of this thesis. They can shed light on improving the sensitivity of quantum-limited measurement, and on understanding the quantumto-classical transition. This thesis summarizes and puts into perspective several research projects that I worked on together with the UWA group and the LIGO Macroscopic Quantum Mechanics (MQM) discussion group. In the first part of this thesis, we will discuss different approaches for surpassing the standard quantum limit for the displacement sensitivity of optomechanical devices, mostly in the context of GW detectors.

They include: (1) Modifying the input optics. We consider filtering two frequency-inde- pendent squeezed light beams through a tuned resonant cavity to obtain an appro- priate frequency dependence, which can be used to reduce the measurement noise of the GW detector over the entire detection band; (2) Modifying the output optics. We study a time-domain variational readout scheme which measures the conserved dynamical quantity of a mechanical oscillator: the mechanical quadrature. This evades the measurement-induced back action and achieves a sensitivity limited only by the shot noise.

This scheme is useful for improving the sensitivity of signal- recycled GW detectors, provided the signalrecycling cavity is detuned, and the optical spring effect is strong enough to shift the test-mass pendulum frequency from 1 Hz up to the detection band around 100 Hz; (3) Modifying the dynamics. We explore frequency dependence in double optical springs in order to cancel the positive inertia of the test mass, which can significantly enhance the mechanical response and allow us to surpass the SQL over a broad frequency band. In the second part of this thesis, two essential procedures for an MQM experiment with optomechanical devices are considered: (1) state preparation, in which we prepare a mechanical oscillator in specific quantum states. We study xiii www.com xiv Preface the preparations of both Gaussian and non-Gaussian quantum states, and also the creation of quantum entanglements between the mechanical oscillator and the optical field.

Specifically, for the Gaussian quantum states, e., the quantum ground state, we consider the use of passive cooling and optimal feedback control in cavity-assisted schemes. For non-Gaussian quantum states, we introduce the idea of coherently transferring quantum states from the optical field to the mechanical oscillator. For the quantum entanglement, we consider the entangle- ment between the mechanical oscillator and the finite degrees-of-freedom cavity modes, and also the infinite degrees-of-freedom continuum optical mode. (2) state verification, in which we probe and verify the prepared quantum states.

A similar time-dependent homodyne detection method as discussed in the first part is implemented to evade the back action, which allows us to achieve a verification accuracy that is below the Heisenberg limit. The experimental requirements and feasibilities of these two procedures are considered in both small-scale cavity- assisted optomechanical devices, and in large-scale advanced GW detectors.com Acknowledgments I am very thankful to my supervisors: Chunnong Zhao, David Blair and Ju Li at the University of Western Australia (UWA), and Yanbei Chen at the California Institute of Technology (Caltech). With great patience and enthusiasm, they introduced me to many interesting topics, especially, optomechanical interactions and their classical and quantum theories which make this thesis possible. When- ever I encountered some problems that could not be overcome, their sharp insights and great motivations always lit me up, and helped me to move forward.

I also want to express my thankfulness to Stefan Danilishin, Mihai Bondarescu, Helge Mueller-Ebhardt, Chao Li, Henning Rehbein, Thomas Corbitt, Kentaro Somiya, Farid Khalili, and all the other members in the LIGO-MQM discussion groups. In the two months of visiting the Albert-Einstein Institute (AEI) and MQM telecons, I had intensive discussions with them, which produced many fruitful results in this thesis. I thank especially Stefan who played significant roles in all my work concerning macroscopic quantum mechanics. I am very thankful to Rana Adhikari, Koji Arai, Kiwamu Izumi, Jenne Driggers, David Yeaton-Massey, Aiden Brook and Steve Vass at Caltech, with whom I spent my enjoyable 4 month experimental investigations of an advanced suspension isolation scheme based upon magnetic levitation.

Rana Adhikari and Koji Arai made painstaking efforts in trying to teach me the fundamentals of electronics and feedback control theory. I would like to thank Antoine Heidmann, Pierre-Franùcois Cohadon, and Chiara Molinelli for their friendly hosting of my visit to the Laboratoire Kastler Brossel, and for helping me to understand how to characterize a mechanical oscillator experimentally. I thank all my colleagues at UWA: Yaohui Fan, Zhongyang Zhang, Andrew Sunderland, and Andrew Woolley.