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El. knyga: Quantum Optomechanics and Nanomechanics: Lecture Notes of the Les Houches Summer School: Volume 105, August 2015

Edited by (Director and Head of Theory Division, Max Planck Institute for the Science of Light, Erlangen, Germany-), Edited by (Professor of Physics, Yale University, New Haven, USA), Edited by , Edited by (Associate Professor of Physics, Ecole Normale Supérieure, Paris, France)
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Quantum Optomechanics and Nanomechanics: Lecture Notes of the Les Houches Summer School: Volume 105, August 2015Didesnis paveikslėlis
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The Les Houches Summer School in August 2015 covered the emerging fields of cavity optomechanics and quantum nanomechanics. Optomechanics is flourishing and its concepts and techniques are now applied to a wide range of topics. Modern quantum optomechanics was born in the late 1970s in the framework of gravitational wave interferometry, with an initial focus on the quantum limits of displacement measurements.

Carlton Caves, Vladimir Braginsky, and others realized that the sensitivity of the anticipated large-scale gravitational-wave interferometers (GWI) was fundamentally limited by the quantum fluctuations of the measurement laser beam. After tremendous experimental progress, the sensitivity of the upcoming next generation of GWI will effectively be limited by quantum noise. In this way, quantum-optomechanical effects will directly affect the operation of what is arguably the world's most impressive precision experiment. However, optomechanics has also gained a life of its own with a focus on the quantum aspects of moving mirrors. Laser light can be used to cool mechanical resonators well below the temperature of its environment. After proof-of-principle demonstrations of this cooling in 2006, a number of systems were used as the field gradually merged with its condensed matter cousin (nanomechanical systems) to try to reach the mechanical quantum ground state, eventually demonstrated in 2010 by pure cryogenic techniques and just one year later by a combination of cryogenic and radiation-pressure cooling.

The book covers all aspects -- historical, theoretical, experimental -- of the field, with its applications to quantum measurement, foundations of quantum mechanics and quantum information. It is an essential read for any new researcher in the field.
List of Participants
xix
1 Early History and Fundamentals of Optomechanics
1(40)
Antoine Heidmann
Pierre-Francois Cohadon
1.1 Introduction
3(1)
1.2 Optomechanics at the Classical Level
3(9)
1.3 Optomechanics at the Quantum Level
12(12)
1.4 Quantum Optics with Optomechanics
24(2)
1.5 Control and Cooling of a Mechanical Resonator
26(9)
1.6 Conclusion
35(6)
Bibliography
37(4)
2 Optomechanics for Gravitational Wave Detection: From Resonant Bars to Next Generation Laser Interferometers
41(64)
David Blair
Li Ju
Yiqiu M.A.
2.1 Introduction
43(1)
2.2 The Gravitational Wave Spectrum
44(4)
2.3 Gravitational Wave Detection
48(2)
2.4 Cryogenic Bars and the First Parametric Transducers
50(5)
2.5 Non-contacting Superconducting Microwave Parametric Transducers
55(3)
2.6 Coupling Coefficients, Thermal Noise and Effective Temperature
58(3)
2.7 Impedance Formalism for Transducers
61(2)
2.8 The Quantum Picture For Parametric Transducers
63(3)
2.9 The Impedance Matrix for Parametric Transducers
66(5)
2.10 The Design of NIOBE, a 1.5-tonne Resonant Bar with Superconducting Parametric Transducer
71(8)
2.11 Advanced Laser Interferometer Gravitational Wave Detectors
79(9)
2.12 Three-Mode Interactions and Parametric Instability
88(3)
2.13 White Light Optomechanical Cavities for Broadband Enhancement of Gravitational Wave Detectors
91(8)
2.14 Conclusion
99(6)
Bibliography
100(5)
3 Optomechanical Interactions
105(24)
Ivan Favero
3.1 Optically Induced Forces
107(8)
3.2 Light Influenced by Mechanical Motion
115(4)
3.3 Equations of Optomechanics
119(10)
Bibliography
126(3)
4 Quantum Optomechanics: from Gravitational Wave Detectors to Macroscopic Quantum Mechanics
129(54)
Yanbei Chen
4.1 Overview and Basic Notions
131(8)
4.2 Various Configurations that Circumvent the SQL
139(13)
4.3 A More Systematic Approach toward Further Sensitivity Improvements
152(8)
4.4 Quantum State Preparation and Verification
160(11)
4.5 Testing Quantum Mechanics
171(12)
Bibliography
179(4)
5 Optomechanics and Quantum Measurement
183(54)
Aashish A. Clerk
5.1 Introduction
185(1)
5.2 Basic Quantum Cavity Optomechanics Theory
185(8)
5.3 Quantum Limit on Continuous Position Detection
193(24)
5.4 Back-action Evasion and Conditional Squeezing
217(15)
5.5 Appendix: Derivation of Power Gain Expression
232(5)
Bibliography
235(2)
6 Coupling Superconducting Qubits to Electromagnetic and Piezomechanical Resonators
237(40)
Andrew N. Cleland
6.1 Coupling Qubits to Other Systems
239(1)
6.2 Historical Notes on Piezoelectricity
239(1)
6.3 A Quick Introduction to Solid Continuum Mechanics
240(4)
6.4 Dynamical Equations for a Solid
244(1)
6.5 Piezoelectricity
245(2)
6.6 One-dimensional Model of a Piezoelectric Dilatational Resonator: the Langevin Sandwich Transducer
247(5)
6.7 The Phase Qubit: the Current-biased Josephson Junction
252(4)
6.8 Simple Quantization for the Current-biased Josephson Junction
256(2)
6.9 Coupling to the Phase Qubit
258(2)
6.10 Coupling a Qubit to an Electrical Resonator
260(9)
6.11 Coupling a Qubit to a Mechanical Resonator
269(8)
Bibliography
275(2)
7 Spin-coupled Mechanical Systems
277(30)
Ania Bleszynski Jayich
7.1 Introduction
279(3)
7.2 Nitrogen Vacancy Centres in Diamond
282(8)
7.3 Coupling Mechanics and Spins
290(17)
Bibliography
303(4)
8 Dynamic and Multimode Electromechanics
307(22)
Konrad Wlehnert
8.1 Introduction
309(1)
8.2 Finding Electromechanical Equations of Motion
310(8)
8.3 Dynamical Electromechanics
318(3)
8.4 State Transfer between the Microwave and Optical Domains
321(2)
8.5 State-space Models
323(6)
Bibliography
327(2)
9 Atom Optomechanics
329(40)
Philipp Treutlein
9.1 Introduction
331(1)
9.2 Optical Forces on Atoms
332(6)
9.3 Trapped Atoms as Mechanical Oscillators
338(3)
9.4 Atoms as Optical Elements
341(4)
9.5 Cavity Optomechanics with Atoms
345(4)
9.6 Hybrid Mechanical-atomic Systems: Coupling Mechanisms
349(2)
9.7 Optical Lattice with Vibrating Mirror
351(5)
9.8 Sympathetic Cooling of a Membrane with Ultracold Atoms
356(3)
9.9 Ground-state Cooling, Strong Coupling, Cooperativity
359(3)
9.10 Coupling to the Atomic Internal State
362(7)
Bibliography
364(5)
10 Optically Levitated Nanospheres for Cavity Quantum Optomechanics
369(30)
Oriol Romero-Isart
10.1 Levitated Quantum Optomechanics: Atom vs. Sphere
372(10)
10.2 Decoherence in Levitated Nanospheres
382(10)
10.3 Wave-packet dynamics: Coherence vs. Decoherence
392(7)
Bibliography
397(2)
11 Quantum Optomechanics, Thermodynamics and Heat Engines
399
Pierre Meystre
11.1 Introduction
401(3)
11.2 Quantum Thermodynamics: Work and Heat
404(3)
11.3 Stochastic Quantum Trajectories
407(8)
11.4 Continuous Measurements
415(4)
11.5 Quantum Heat Engines
419(2)
11.6 The Optomechanical Interaction-Polariton Picture
421(5)
11.7 A Quantum Optomechanical Heat Engine
426(6)
11.8 Quantum Fluctuations
432(8)
11.9 Polaritonic Heat Pump
440(5)
11.10 Outlook
445
Bibliography
447
Pierre-Francois Cohadon's current research activity is split in two distinct areas. He works on optomechanics experiments at LKB on micro- or nanomechanical systems, which aim to demonstrate quantum properties of both light (under the effect of the motion of a movable mirror) and of a mechanical resonator (under the effect of radiation pressure of a laser beam). He also works in the Virgo Collaboration on the expected radiation-pressure effects in the gravitational interferometer Advanced Virgo, as well as on the sensitivity gain achieved using squeezed light. Despite orders of magnitude between the characteristics of the different systems under study, both activities are surprisingly related.

Jack Harris studies the quantum aspects of motion in macroscopic objects that combine mechanical, optical, and fluid components. His experiments use ultrasensitive force detectors to measure quantum fluctuations of objects that are visible to the naked eye, to reveal the counterintuitive behavior of apparently simple systems. These experiments are also used to study novel topological features in the dynamics of coupled oscillators.

Florian Marquardt applies tools from condensed matter theory and from quantum optics to a range of questions at the interface of nanophysics and quantum optics, addressing both quantum and classical dynamics, paying particular attention to the direct contact with experiments, down to designing the classical electromagnetic and acoustic properties of specific structures. His current interests include cavity optomechanics and nanomechanics, quantum information processing, quantum many body physics, and machine learning for physics.

Leticia Cugliandolo is Professor at Pierre and Marie Curie University, where she works on statistical physics and field theory with applications to soft and hard condensed matter. She has written more than 130 scientific papers, and has been a coeditor of the Les Houches book series since 2007, when she assumed the directorship of the Les Houches Summer School of Physics.
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