MEASUREMENT THEORY QUANTUM AND ITS APPLICATIONS KURT JACOBS. University of Massachusetts at Boston. fg Cambridge WW UNIVERSITY PRESS

Save this PDF as:
 WORD  PNG  TXT  JPG

Size: px
Start display at page:

Download "MEASUREMENT THEORY QUANTUM AND ITS APPLICATIONS KURT JACOBS. University of Massachusetts at Boston. fg Cambridge WW UNIVERSITY PRESS"

Transcription

1 QUANTUM MEASUREMENT THEORY AND ITS APPLICATIONS KURT JACOBS University of Massachusetts at Boston fg Cambridge WW UNIVERSITY PRESS

2 Contents Preface page xi 1 Quantum measurement theory Introduction and overview Classical measurement theory Understanding Bayes'theorem Multiple measurements and Gaussian distributions Prior states-of-knowledge and invariance Quantum measurement theory The measurement postulate Quantum states-of-knowledge: density matrices Quantum measurements Understanding quantum measurements Relationship to classical measurements Measurements of observables and resolving power A measurement of position The polar decomposition: bare measurements and feedback Describing measurements within unitary evolution Inefficient measurements Measurements on ensembles of states 40 2 Useful concepts from information theory Quantifying information The entropy The mutual information Quantifying uncertainty about a quantum system The von Neumann entropy Majorization and density matrices Ensembles corresponding to a density matrix Quantum measurements and information Information-theoretic properties Quantifying disturbance 72 vii

3 viii Contents 2.4 Distinguishing quantum states Fidelity of quantum operations 82 3 Continuous measurement Continuous measurements with Gaussian noise Classical continuous measurements Gaussian quantum continuous measurements When the SME is the classical Kalman-Bucy filter The power spectrum of the measurement record Solving for the evolution: the linear form of the SME The dynamics of measurement: diffusion gradients Quantum jumps Distinguishing quantum from classical Continuous measurements on ensembles of systems Measurements that count events: detecting photons Homodyning: from counting to Gaussian noise Continuous measurements with more exotic noise? The Heisenberg picture: inputs, outputs, and spectra Heisenberg-picture techniques for linear systems Equations of motion for Gaussian states Calculating the power spectrum of the measurement record Parameter estimation: the hybrid master equation An example: distinguishing two quantum states Statistical mechanics, open systems, and measurement Statistical mechanics Thermodynamic entropy and the Boltzmann distribution Entropy and information: Landauer's erasure principle Thermodynamics with measurements: Maxwell's demon Thermalization I: the origin of irreversibility A new insight: the Boltzmann distribution from typicality Hamiltonian typicality Thermalization II: useful models Weak damping: the Redfield master equation Redfield equation for time-dependent or interacting systems Baths and continuous measurements Wavefunction "Monte Carlo" simulation methods Strong damping: master equations and beyond The quantum-to-classical transition Irreversibility and the quantum measurement problem Quantum feedback control 5.1 Introduction Measurements versus coherent interactions Explicit implementations of continuous-time feedback 239

4 Contents ix Feedback via continuous measurements Coherent feedback via unitary interactions Coherent feedback via one-way fields Mixing one-way fields with unitary interactions: a coherent version of Markovian feedback Feedback control via continuous measurements Rapid purification protocols Control via measurement back-action Near-optimal feedback control for a single qubit? Summary Optimization Bellman's equation and the HJB equation Optimal control for linear quantum systems Optimal control for nonlinear quantum systems Metrology Metrology of single quantities The Cramer-Rao bound Optimizing the Cramer-Rao bound Resources and limits to precision Adaptive measurements Metrology of signals Quantum-mechanics-free subsystems Oscillator-mediated force detection Quantum mesoscopic systems I: circuits and measurements Superconducting circuits Procedure for obtaining the circuit Lagrangian (short method) Resonance and the rotating-wave approximation Superconducting harmonic oscillators Superconducting nonlinear oscillators and qubits The Josephson junction The Cooper-pair box and the transmon Coupling qubits to resonators The RF-SQUID and flux qubits Electromechanical systems Optomechanical systems Measuring mesoscopic systems Amplifiers and continuous measurements Translating between experiment and theory Implementing a continuous measurement Quantum transducers and nonlinear measurements Quantum mesoscopic systems II: measurement and control Open-loop control 383

5 X Contents Fast state-swapping for oscillators Preparing non-classical states Measurement-based feedback control Cooling using linear feedback control Squeezing using linear feedback control Coherent feedback control The "resolved-sideband" cooling method Resolved-sideband cooling via one-way fields Optimal cooling and state-preparation 416 Appendix A The tensor product and partial trace 432 Appendix B A fast-track introduction for experimentalists 441 Appendix C A quick introduction to Ito calculus 448 Appendix D Operators for qubits and modes 451 Appendix E Dictionary ofmeasurements 456 Appendix F Input-output theory 458 FA A mode of an optical or electrical cavity 458 F.2 The traveling-wave fields atx = 0: the input and output signals 462 F.3 The Heisenberg equations of motion for the system 463 FA A weakly damped oscillator 467 F.5 Sign conventionsfor input-output theory 467 F.6 The quantum noise equations for the system: Ito calculus 468 F. 7 Obtaining the Redfield master equation 469 F.8 Spectrum of the measurement signal 470 Appendix G Various formulae and techniques 475 G. I The relationship between Hz and s~], and writing decay rates in Hz 475 G.2 Position representation of a pure Gaussian state 475 G.3 The multivariate Gaussian distribution 476 G.4 The rotating-wave approximation (RWA) 476 G.5 Suppression of off-resonant transitions Ml G.6 Recursion relationsfor time-independent perturbation theory 478 G. 7 Finding operator transformation, reordering, and splitting relations 479 G.8 The Haar measure 484 G.9 Generalform of the Kushner-Stratonovich equation 485 G. 10 Obtaining steady states for linear open systems 486 Appendix H Some proofs and derivations 490 //./ The Schumacher-Westmoreland-Wootters theorem 490 H.2 The operator-sum representation for quantum evolution 492 H.3 Derivation of the Wiseman-Milburn Markovian feedback SME 494 References 498 Index 539

QUANTUM MEASUREMENT THEORY AND ITS APPLICATIONS

QUANTUM MEASUREMENT THEORY AND ITS APPLICATIONS QUANTUM MEASUREMENT THEORY AND ITS APPLICATIONS Recent experimental advances in the control of quantum superconducting circuits, nanomechanical resonators and photonic crystals have meant that quantum

More information

MESOSCOPIC QUANTUM OPTICS

MESOSCOPIC QUANTUM OPTICS MESOSCOPIC QUANTUM OPTICS by Yoshihisa Yamamoto Ata Imamoglu A Wiley-Interscience Publication JOHN WILEY & SONS, INC. New York Chichester Weinheim Brisbane Toronto Singapore Preface xi 1 Basic Concepts

More information

Superconducting Resonators and Their Applications in Quantum Engineering

Superconducting Resonators and Their Applications in Quantum Engineering Superconducting Resonators and Their Applications in Quantum Engineering Nov. 2009 Lin Tian University of California, Merced & KITP Collaborators: Kurt Jacobs (U Mass, Boston) Raymond Simmonds (Boulder)

More information

Quantum measurement theory

Quantum measurement theory 1 Quantum measurement theory 1.1 Introduction and overview Much that is studied in quantum measurement theory, and thus in this book, is very different from that studied in its classical counterpart, Bayesian

More information

Preface. Preface to the Third Edition. Preface to the Second Edition. Preface to the First Edition. 1 Introduction 1

Preface. Preface to the Third Edition. Preface to the Second Edition. Preface to the First Edition. 1 Introduction 1 xi Contents Preface Preface to the Third Edition Preface to the Second Edition Preface to the First Edition v vii viii ix 1 Introduction 1 I GENERAL THEORY OF OPEN QUANTUM SYSTEMS 5 Diverse limited approaches:

More information

Towards quantum metrology with N00N states enabled by ensemble-cavity interaction. Massachusetts Institute of Technology

Towards quantum metrology with N00N states enabled by ensemble-cavity interaction. Massachusetts Institute of Technology Towards quantum metrology with N00N states enabled by ensemble-cavity interaction Hao Zhang Monika Schleier-Smith Robert McConnell Jiazhong Hu Vladan Vuletic Massachusetts Institute of Technology MIT-Harvard

More information

Quantum Reservoir Engineering

Quantum Reservoir Engineering Departments of Physics and Applied Physics, Yale University Quantum Reservoir Engineering Towards Quantum Simulators with Superconducting Qubits SMG Claudia De Grandi (Yale University) Siddiqi Group (Berkeley)

More information

List of Comprehensive Exams Topics

List of Comprehensive Exams Topics List of Comprehensive Exams Topics Mechanics 1. Basic Mechanics Newton s laws and conservation laws, the virial theorem 2. The Lagrangian and Hamiltonian Formalism The Lagrange formalism and the principle

More information

CONTENTS. 2 CLASSICAL DESCRIPTION 2.1 The resonance phenomenon 2.2 The vector picture for pulse EPR experiments 2.3 Relaxation and the Bloch equations

CONTENTS. 2 CLASSICAL DESCRIPTION 2.1 The resonance phenomenon 2.2 The vector picture for pulse EPR experiments 2.3 Relaxation and the Bloch equations CONTENTS Preface Acknowledgements Symbols Abbreviations 1 INTRODUCTION 1.1 Scope of pulse EPR 1.2 A short history of pulse EPR 1.3 Examples of Applications 2 CLASSICAL DESCRIPTION 2.1 The resonance phenomenon

More information

Short Course in Quantum Information Lecture 8 Physical Implementations

Short Course in Quantum Information Lecture 8 Physical Implementations Short Course in Quantum Information Lecture 8 Physical Implementations Course Info All materials downloadable @ website http://info.phys.unm.edu/~deutschgroup/deutschclasses.html Syllabus Lecture : Intro

More information

Dynamically protected cat-qubits: a new paradigm for universal quantum computation

Dynamically protected cat-qubits: a new paradigm for universal quantum computation Home Search Collections Journals About Contact us My IOPscience Dynamically protected cat-qubits: a new paradigm for universal quantum computation This content has been downloaded from IOPscience. Please

More information

arxiv:quant-ph/ v3 25 Jun 2004

arxiv:quant-ph/ v3 25 Jun 2004 Quantum Feedback Control of Atomic Motion in an Optical Cavity LA-UR-03-6826 Daniel A. Steck, 1 Kurt Jacobs, 1,2 Hideo Mabuchi, 3 Tanmoy Bhattacharya, 1 and Salman Habib 1 1 Theoretical Division (T-8),

More information

PHYSICS. Course Syllabus. Section 1: Mathematical Physics. Subject Code: PH. Course Structure. Electromagnetic Theory

PHYSICS. Course Syllabus. Section 1: Mathematical Physics. Subject Code: PH. Course Structure. Electromagnetic Theory PHYSICS Subject Code: PH Course Structure Sections/Units Topics Section 1 Section 2 Section 3 Section 4 Section 5 Section 6 Section 7 Section 8 Mathematical Physics Classical Mechanics Electromagnetic

More information

Information to energy conversion in an electronic Maxwell s demon and thermodynamics of measurements.

Information to energy conversion in an electronic Maxwell s demon and thermodynamics of measurements. Information to energy conversion in an electronic Maxwell s demon and thermodynamics of measurements Stony Brook University, SUNY Dmitri V Averin and iang Deng Low-Temperature Lab, Aalto University Jukka

More information

SUPPLEMENTARY INFORMATION

SUPPLEMENTARY INFORMATION SUPPLEMENTAR NFORMATON doi:10.1038/nature10786 FOUR QUBT DEVCE f 3 V 2 V 1 The cqed device used in this experiment couples four transmon qubits to a superconducting coplanar waveguide microwave cavity

More information

Lessons in Estimation Theory for Signal Processing, Communications, and Control

Lessons in Estimation Theory for Signal Processing, Communications, and Control Lessons in Estimation Theory for Signal Processing, Communications, and Control Jerry M. Mendel Department of Electrical Engineering University of Southern California Los Angeles, California PRENTICE HALL

More information

ELECTRICITY AND MAGNETISM

ELECTRICITY AND MAGNETISM THIRD EDITION ELECTRICITY AND MAGNETISM EDWARD M. PURCELL DAVID J. MORIN Harvard University, Massachusetts Щ CAMBRIDGE Ell UNIVERSITY PRESS Preface to the third edition of Volume 2 XIII CONTENTS Preface

More information

Thermodynamical cost of accuracy and stability of information processing

Thermodynamical cost of accuracy and stability of information processing Thermodynamical cost of accuracy and stability of information processing Robert Alicki Instytut Fizyki Teoretycznej i Astrofizyki Uniwersytet Gdański, Poland e-mail: fizra@univ.gda.pl Fields Institute,

More information

Quantum computation and quantum information

Quantum computation and quantum information Quantum computation and quantum information Chapter 7 - Physical Realizations - Part 2 First: sign up for the lab! do hand-ins and project! Ch. 7 Physical Realizations Deviate from the book 2 lectures,

More information

Quantum Feedback Control How can we control quantum systems without disturbing them?

Quantum Feedback Control How can we control quantum systems without disturbing them? Feedback Control How can we control quantum systems without disturbing them? Salman Habib, Kurt Jacobs, and Hideo Mabuchi The nanomechanical electrometer shown here was built in Michael Roukes group at

More information

Electrical Transport in Nanoscale Systems

Electrical Transport in Nanoscale Systems Electrical Transport in Nanoscale Systems Description This book provides an in-depth description of transport phenomena relevant to systems of nanoscale dimensions. The different viewpoints and theoretical

More information

Final Report. Superconducting Qubits for Quantum Computation Contract MDA C-A821/0000

Final Report. Superconducting Qubits for Quantum Computation Contract MDA C-A821/0000 Final Report Superconducting Qubits for Quantum Computation Contract MDA904-98-C-A821/0000 Project Director: Prof. J. Lukens Co-project Director: Prof. D. Averin Co-project Director: Prof. K. Likharev

More information

INTRODUCTION TO SCA\ \I\G TUNNELING MICROSCOPY

INTRODUCTION TO SCA\ \I\G TUNNELING MICROSCOPY INTRODUCTION TO SCA\ \I\G TUNNELING MICROSCOPY SECOND EDITION C. JULIAN CHEN Department of Applied Physics and Applied Mathematics, Columbia University, New York OXFORD UNIVERSITY PRESS Contents Preface

More information

With Modern Physics For Scientists and Engineers

With Modern Physics For Scientists and Engineers With Modern Physics For Scientists and Engineers Third Edition Richard Wolfson Middlebury College Jay M. Pasachoff Williams College ^ADDISON-WESLEY An imprint of Addison Wesley Longman, Inc. Reading, Massachusetts

More information

State Observers and the Kalman filter

State Observers and the Kalman filter Modelling and Control of Dynamic Systems State Observers and the Kalman filter Prof. Oreste S. Bursi University of Trento Page 1 Feedback System State variable feedback system: Control feedback law:u =

More information

On the Nature of Random System Matrices in Structural Dynamics

On the Nature of Random System Matrices in Structural Dynamics On the Nature of Random System Matrices in Structural Dynamics S. ADHIKARI AND R. S. LANGLEY Cambridge University Engineering Department Cambridge, U.K. Nature of Random System Matrices p.1/20 Outline

More information

Introduction to Superconductivity. Superconductivity was discovered in 1911 by Kamerlingh Onnes. Zero electrical resistance

Introduction to Superconductivity. Superconductivity was discovered in 1911 by Kamerlingh Onnes. Zero electrical resistance Introduction to Superconductivity Superconductivity was discovered in 1911 by Kamerlingh Onnes. Zero electrical resistance Meissner Effect Magnetic field expelled. Superconducting surface current ensures

More information

Multimode Entanglement in. Continuous Variables

Multimode Entanglement in. Continuous Variables Multimode Entanglement in Continuous Variables Entanglement with continuous variables What are we measuring? How are we measuring it? Why are we using the Optical Parametric Oscillator? What do we learn?

More information

Optomechanics: Hybrid Systems and Quantum Effects

Optomechanics: Hybrid Systems and Quantum Effects Centre for Quantum Engineering and Space-Time Research Optomechanics: Hybrid Systems and Quantum Effects Klemens Hammerer Leibniz University Hannover Institute for Theoretical Physics Institute for Gravitational

More information

MOLECULAR SPECTROSCOPY

MOLECULAR SPECTROSCOPY MOLECULAR SPECTROSCOPY First Edition Jeanne L. McHale University of Idaho PRENTICE HALL, Upper Saddle River, New Jersey 07458 CONTENTS PREFACE xiii 1 INTRODUCTION AND REVIEW 1 1.1 Historical Perspective

More information

University of New Mexico

University of New Mexico Quantum State Reconstruction via Continuous Measurement Ivan H. Deutsch, Andrew Silberfarb University of New Mexico Poul Jessen, Greg Smith University of Arizona Information Physics Group http://info.phys.unm.edu

More information

PART I INTRODUCTION The meaning of probability Basic definitions for frequentist statistics and Bayesian inference Bayesian inference Combinatorics

PART I INTRODUCTION The meaning of probability Basic definitions for frequentist statistics and Bayesian inference Bayesian inference Combinatorics Table of Preface page xi PART I INTRODUCTION 1 1 The meaning of probability 3 1.1 Classical definition of probability 3 1.2 Statistical definition of probability 9 1.3 Bayesian understanding of probability

More information

Condensed Table of Contents for Introduction to Stochastic Search and Optimization: Estimation, Simulation, and Control by J. C.

Condensed Table of Contents for Introduction to Stochastic Search and Optimization: Estimation, Simulation, and Control by J. C. Condensed Table of Contents for Introduction to Stochastic Search and Optimization: Estimation, Simulation, and Control by J. C. Spall John Wiley and Sons, Inc., 2003 Preface... xiii 1. Stochastic Search

More information

Quantum Mechanical Foundations of Causal Entropic Forces

Quantum Mechanical Foundations of Causal Entropic Forces Quantum Mechanical Foundations of Causal Entropic Forces Swapnil Shah North Carolina State University, USA snshah4@ncsu.edu Abstract. The theory of Causal Entropic Forces was introduced to explain the

More information

Superconducting Flux Qubits: The state of the field

Superconducting Flux Qubits: The state of the field Superconducting Flux Qubits: The state of the field S. Gildert Condensed Matter Physics Research (Quantum Devices Group) University of Birmingham, UK Outline A brief introduction to the Superconducting

More information

Quantum optics and optomechanics

Quantum optics and optomechanics Quantum optics and optomechanics 740nm optomechanical crystals LIGO mirror AMO: Alligator nanophotonic waveguide quantum electro-mechanics Oskar Painter, Jeff Kimble, Keith Schwab, Rana Adhikari, Yanbei

More information

Superposition of two mesoscopically distinct quantum states: Coupling a Cooper-pair box to a large superconducting island

Superposition of two mesoscopically distinct quantum states: Coupling a Cooper-pair box to a large superconducting island PHYSICAL REVIEW B, VOLUME 63, 054514 Superposition of two mesoscopically distinct quantum states: Coupling a Cooper-pair box to a large superconducting island Florian Marquardt* and C. Bruder Departement

More information

Problem Set # 8 Solutions

Problem Set # 8 Solutions Id: hw.tex,v 1.4 009/0/09 04:31:40 ike Exp 1 MIT.111/8.411/6.898/18.435 Quantum Information Science I Fall, 010 Sam Ocko November 15, 010 Problem Set # 8 Solutions 1. (a) The eigenvectors of S 1 S are

More information

Quantum Noise. Michael A. Nielsen. University of Queensland

Quantum Noise. Michael A. Nielsen. University of Queensland Quantum Noise Michael A. Nielsen University of Queensland Goals: 1. To introduce a tool the density matrix that is used to describe noise in quantum systems, and to give some examples. Density matrices

More information

Cavity QED. Driven Circuit QED System. Circuit QED. decay atom: γ radiation: κ. E. Il ichev et al., PRL 03

Cavity QED. Driven Circuit QED System. Circuit QED. decay atom: γ radiation: κ. E. Il ichev et al., PRL 03 Decoherence and Relaxation in Driven Circuit QED Systems Alexander Shnirman Arkady Fedorov Julian Hauss Valentina Brosco Stefan André Michael Marthaler Gerd Schön experiments Evgeni Il ichev et al. Univ.

More information

Distributed feedback semiconductor lasers

Distributed feedback semiconductor lasers Distributed feedback semiconductor lasers John Carroll, James Whiteaway & Dick Plumb The Institution of Electrical Engineers SPIE Optical Engineering Press 1 Preface Acknowledgments Principal abbreviations

More information

Quantum non-demolition measurement of a superconducting two-level system

Quantum non-demolition measurement of a superconducting two-level system 1 Quantum non-demolition measurement of a superconducting two-level system A. Lupaşcu 1*, S. Saito 1,2, T. Picot 1, P. C. de Groot 1, C. J. P. M. Harmans 1 & J. E. Mooij 1 1 Quantum Transport Group, Kavli

More information

Information in Biology

Information in Biology Information in Biology CRI - Centre de Recherches Interdisciplinaires, Paris May 2012 Information processing is an essential part of Life. Thinking about it in quantitative terms may is useful. 1 Living

More information

Master Thesis. Quantum Memristors. Master Program Theoretical and Mathematical Physics

Master Thesis. Quantum Memristors. Master Program Theoretical and Mathematical Physics Master Thesis Quantum Memristors Author: Paul Pfeiffer Supervisors: Prof. Enrique Solano Prof. Jan von Delft Master Program Theoretical and Mathematical Physics Ludwig-Maximilians-Universität München Technische

More information

Physics Courses. Courses. Physics Courses 1

Physics Courses. Courses. Physics Courses 1 Physics Courses 1 Physics Courses Courses PHYS 1403. General Physics I (C). General Physics I (3-2) A non-calculus treatment of mechanics and heat. Laboratory experience is an essential component of this

More information

John Stewart Bell Prize. Part 1: Michel Devoret, Yale University

John Stewart Bell Prize. Part 1: Michel Devoret, Yale University John Stewart Bell Prize Part 1: Michel Devoret, Yale University SUPERCONDUCTING ARTIFICIAL ATOMS: FROM TESTS OF QUANTUM MECHANICS TO QUANTUM COMPUTERS Part 2: Robert Schoelkopf, Yale University CIRCUIT

More information

Lecture Notes on QUANTUM COMPUTING STEFANO OLIVARES. Dipartimento di Fisica - Università degli Studi di Milano. Ver. 2.0

Lecture Notes on QUANTUM COMPUTING STEFANO OLIVARES. Dipartimento di Fisica - Università degli Studi di Milano. Ver. 2.0 Lecture Notes on QUANTUM COMPUTING STEFANO OLIVARES Dipartimento di Fisica - Università degli Studi di Milano Ver..0 Lecture Notes on Quantum Computing 014, S. Olivares - University of Milan Italy) December,

More information

Quantum Control of Qubits

Quantum Control of Qubits Quantum Control of Qubits K. Birgitta Whaley University of California, Berkeley J. Zhang J. Vala S. Sastry M. Mottonen R. desousa Quantum Circuit model input 1> 6> = 1> 0> H S T H S H x x 7 k = 0 e 3 π

More information

Mesoscopic Nano-Electro-Mechanics of Shuttle Systems

Mesoscopic Nano-Electro-Mechanics of Shuttle Systems * Mesoscopic Nano-Electro-Mechanics of Shuttle Systems Robert Shekhter University of Gothenburg, Sweden Lecture1: Mechanically assisted single-electronics Lecture2: Quantum coherent nano-electro-mechanics

More information

Spontaneous Emission and the Vacuum State of EM Radiation. Miriam Klopotek 10 December 2007

Spontaneous Emission and the Vacuum State of EM Radiation. Miriam Klopotek 10 December 2007 Spontaneous Emission and the Vacuum State of EM Radiation Miriam Klopotek 10 December 2007 Content Introduction Atom inside thermal equilibrium cavity: stimulated emission, absorption and spontaneous decay

More information

Chapter 14: Quantum Information Theory and Photonic Communications

Chapter 14: Quantum Information Theory and Photonic Communications Chapter 14: Quantum Information Theory and Photonic Communications Farhan Rana (MIT) March, 2002 Abstract The fundamental physical limits of optical communications are discussed in the light of the recent

More information

Principles and Applications of Superconducting Quantum Interference Devices (SQUIDs)

Principles and Applications of Superconducting Quantum Interference Devices (SQUIDs) Principles and Applications of Superconducting Quantum Interference Devices (SQUIDs) PHY 300 - Junior Phyics Laboratory Syed Ali Raza Roll no: 2012-10-0124 LUMS School of Science and Engineering Thursday,

More information

Lectures on Quantum Optics and Quantum Information

Lectures on Quantum Optics and Quantum Information Lectures on Quantum Optics and Quantum Information Julien Laurat Laboratoire Kastler Brossel, Paris Université P. et M. Curie Ecole Normale Supérieure and CNRS julien.laurat@upmc.fr Taiwan-France joint

More information

F.G. Major. The Quantum Beat. The Physical Principles of Atomic Clocks. With 230 Illustrations. Springer

F.G. Major. The Quantum Beat. The Physical Principles of Atomic Clocks. With 230 Illustrations. Springer F.G. Major The Quantum Beat The Physical Principles of Atomic Clocks With 230 Illustrations Springer Contents Preface Chapter 1. Celestial and Mechanical Clocks 1 1.1 Cyclic Events in Nature 1 1.2 The

More information

Optimal Control and Viscosity Solutions of Hamilton-Jacobi-Bellman Equations

Optimal Control and Viscosity Solutions of Hamilton-Jacobi-Bellman Equations Martino Bardi Italo Capuzzo-Dolcetta Optimal Control and Viscosity Solutions of Hamilton-Jacobi-Bellman Equations Birkhauser Boston Basel Berlin Contents Preface Basic notations xi xv Chapter I. Outline

More information

Superoperators for NMR Quantum Information Processing. Osama Usman June 15, 2012

Superoperators for NMR Quantum Information Processing. Osama Usman June 15, 2012 Superoperators for NMR Quantum Information Processing Osama Usman June 15, 2012 Outline 1 Prerequisites 2 Relaxation and spin Echo 3 Spherical Tensor Operators 4 Superoperators 5 My research work 6 References.

More information

OPTI 511R: OPTICAL PHYSICS & LASERS

OPTI 511R: OPTICAL PHYSICS & LASERS OPTI 511R: OPTICAL PHYSICS & LASERS Instructor: R. Jason Jones Office Hours: Monday 1-2pm Teaching Assistant: Sam Nerenburg Office Hours: Wed. (TBD) h"p://wp.op)cs.arizona.edu/op)551r/ h"p://wp.op)cs.arizona.edu/op)551r/

More information

arxiv: v1 [quant-ph] 31 May 2010

arxiv: v1 [quant-ph] 31 May 2010 Single-shot qubit readout in circuit Quantum Electrodynamics François 1 Mallet, Florian R. 1 Ong, Agustin 1 Palacios-Laloy, François 1 Nguyen, Patrice 1 Bertet, Denis 1 Vion * and Daniel 1 Esteve 1 Quantronics

More information

Superconductivity at nanoscale

Superconductivity at nanoscale Superconductivity at nanoscale Superconductivity is the result of the formation of a quantum condensate of paired electrons (Cooper pairs). In small particles, the allowed energy levels are quantized and

More information

Strong tunable coupling between a charge and a phase qubit

Strong tunable coupling between a charge and a phase qubit Strong tunable coupling between a charge and a phase qubit Wiebke Guichard Olivier Buisson Frank Hekking Laurent Lévy Bernard Pannetier Aurélien Fay Ioan Pop Florent Lecocq Rapaël Léone Nicolas Didier

More information

Quantum Mechanics: Foundations and Applications

Quantum Mechanics: Foundations and Applications Arno Böhm Quantum Mechanics: Foundations and Applications Third Edition, Revised and Enlarged Prepared with Mark Loewe With 96 Illustrations Springer-Verlag New York Berlin Heidelberg London Paris Tokyo

More information

OPTI 511R: OPTICAL PHYSICS & LASERS

OPTI 511R: OPTICAL PHYSICS & LASERS OPTI 511R: OPTICAL PHYSICS & LASERS Instructor: R. Jason Jones Office Hours: TBD Teaching Assistant: Robert Rockmore Office Hours: Wed. (TBD) h"p://wp.op)cs.arizona.edu/op)511r/ h"p://wp.op)cs.arizona.edu/op)511r/

More information

The Theory of Quantum Information

The Theory of Quantum Information The Theory of Quantum Information John Watrous Institute for Quantum Computing University of Waterloo 2018 John Watrous To be published by Cambridge University Press. Please note that this is a draft,

More information

Foundations of Geomagnetism

Foundations of Geomagnetism Foundations of Geomagnetism GEORGE BACKUS University of California, San Diego ROBERT PARKER University of California, San Diego CATHERINE CONSTABLE University of California, San Diego m.m CAMBRIDGE UNIVERSITY

More information

Chemical Kinetics and Dynamics

Chemical Kinetics and Dynamics Chemical Kinetics and Dynamics Second Edition Jeffrey I. Steinfeld Massachusetts Institute of Technology Joseph S. Francisco Purdue University William L. Hase Wayne State University Prentice Hall Upper

More information

Microscopic derivation of the Jaynes-Cummings model with cavity losses

Microscopic derivation of the Jaynes-Cummings model with cavity losses Microscopic derivation of the Jaynes-Cummings model with cavity losses M. Scala, B. Militello, A. Messina Dipartimento di Scienze Fisiche ed Astronomiche, Università degli Studi di Palermo, Italy J. Piilo,

More information

Circuit QED with electrons on helium:

Circuit QED with electrons on helium: Circuit QED with electrons on helium: What s the sound of one electron clapping? David Schuster Yale (soon to be at U. of Chicago) Yale: Andreas Fragner Rob Schoelkopf Princeton: Steve Lyon Michigan State:

More information

10.6 Propagating quantum microwaves

10.6 Propagating quantum microwaves AS-Chap. 10-1 10.6 Propagating quantum microwaves Propagating quantum microwaves emit Quantum - - Superconducting quantum circuits Artificial quantum matter Confined quantum states of light Does the emitted

More information

QUANTUM TECHNOLOGIES: THE SECOND QUANTUM REVOLUTION* Jonathan P. Dowling

QUANTUM TECHNOLOGIES: THE SECOND QUANTUM REVOLUTION* Jonathan P. Dowling QUANTUM TECHNOLOGIES: THE SECOND QUANTUM REVOLUTION* Jonathan P. Dowling Quantum Science & Technologies Group Hearne Institute for Theoretical Physics Louisiana State University http://quantum.phys.lsu.edu

More information

Optomechanically induced transparency of x-rays via optical control: Supplementary Information

Optomechanically induced transparency of x-rays via optical control: Supplementary Information Optomechanically induced transparency of x-rays via optical control: Supplementary Information Wen-Te Liao 1, and Adriana Pálffy 1 1 Max-Planck-Institut für Kernphysik, Saupfercheckweg 1, 69117 Heidelberg,

More information

BOGOLIUBOV TRANSFORMATIONS AND ENTANGLEMENT OF TWO FERMIONS

BOGOLIUBOV TRANSFORMATIONS AND ENTANGLEMENT OF TWO FERMIONS BOGOLIUBOV TRANSFORMATIONS AND ENTANGLEMENT OF TWO FERMIONS P. Caban, K. Podlaski, J. Rembieliński, K. A. Smoliński and Z. Walczak Department of Theoretical Physics, University of Lodz Pomorska 149/153,

More information

FEYNMAN DIAGRAM TECHNIQUES IN CONDENSED MATTER PHYSICS

FEYNMAN DIAGRAM TECHNIQUES IN CONDENSED MATTER PHYSICS FEYNMAN DIAGRAM TECHNIQUES IN CONDENSED MATTER PHYSICS A concise introduction to Feynman diagram techniques, this book shows how they can be applied to the analysis of complex many-particle systems, and

More information

Quantum thermodynamics

Quantum thermodynamics Quantum thermodynamics a primer for the curious quantum mechanic Lídia del Rio, ETH Zurich QIP 2017 Seattle This talk is licensed under a Creative Commons Attribution 4.0 International License. Why quantum

More information

Dynamic Systems. Simulation of. with MATLAB and Simulink. Harold Klee. Randal Allen SECOND EDITION. CRC Press. Taylor & Francis Group

Dynamic Systems. Simulation of. with MATLAB and Simulink. Harold Klee. Randal Allen SECOND EDITION. CRC Press. Taylor & Francis Group SECOND EDITION Simulation of Dynamic Systems with MATLAB and Simulink Harold Klee Randal Allen CRC Press Taylor & Francis Group Boca Raton London New York CRC Press is an imprint of the Taylor & Francis

More information

Surface Plasmon Amplification by Stimulated Emission of Radiation. By: Jonathan Massey-Allard Graham Zell Justin Lau

Surface Plasmon Amplification by Stimulated Emission of Radiation. By: Jonathan Massey-Allard Graham Zell Justin Lau Surface Plasmon Amplification by Stimulated Emission of Radiation By: Jonathan Massey-Allard Graham Zell Justin Lau Surface Plasmons (SPs) Quanta of electron oscillations in a plasma. o Electron gas in

More information

Room-Temperature Steady-State Entanglement in a Four-Mode Optomechanical System

Room-Temperature Steady-State Entanglement in a Four-Mode Optomechanical System Commun. Theor. Phys. 65 (2016) 596 600 Vol. 65, No. 5, May 1, 2016 Room-Temperature Steady-State Entanglement in a Four-Mode Optomechanical System Tao Wang ( ), 1,2, Rui Zhang ( ), 1 and Xue-Mei Su ( Ö)

More information

Superconducting Quantum Interference Devices for Current Sensing and Thermometry in the Millikelvin Range

Superconducting Quantum Interference Devices for Current Sensing and Thermometry in the Millikelvin Range Cryoconference 2010 Superconducting Quantum Interference Devices for Current Sensing and Thermometry in the Millikelvin Range J.-H. Storm, J. Beyer, D.Drung,Th.Schurig Physikalisch-Technische Bundesanstalt

More information

MOLECULAR LIGHT SCATTERING AND OPTICAL ACTIVITY

MOLECULAR LIGHT SCATTERING AND OPTICAL ACTIVITY MOLECULAR LIGHT SCATTERING AND OPTICAL ACTIVITY Second edition, revised and enlarged LAURENCE D. BARRON, F.R.S.E. Gardiner Professor of Chemistry, University of Glasgow 122. CAMBRIDGE UNIVERSITY PRESS

More information

Quantum Mechanics for Scientists and Engineers

Quantum Mechanics for Scientists and Engineers Quantum Mechanics for Scientists and Engineers Syllabus and Textbook references All the main lessons (e.g., 1.1) and units (e.g., 1.1.1) for this class are listed below. Mostly, there are three lessons

More information

Path integral in quantum mechanics based on S-6 Consider nonrelativistic quantum mechanics of one particle in one dimension with the hamiltonian:

Path integral in quantum mechanics based on S-6 Consider nonrelativistic quantum mechanics of one particle in one dimension with the hamiltonian: Path integral in quantum mechanics based on S-6 Consider nonrelativistic quantum mechanics of one particle in one dimension with the hamiltonian: let s look at one piece first: P and Q obey: Probability

More information

Optical Waveguide Tap with Ideal Photodetectors

Optical Waveguide Tap with Ideal Photodetectors Massachusetts Institute of Technology Department of Electrical Engineering and Computer Science 6.453 Quantum Optical Communication Date: Tuesday, October 18, 2016 Lecture Number 11 Fall 2016 Jeffrey H.

More information

An Introduction to Quantum Computation and Quantum Information

An Introduction to Quantum Computation and Quantum Information An to and Graduate Group in Applied Math University of California, Davis March 13, 009 A bit of history Benioff 198 : First paper published mentioning quantum computing Feynman 198 : Use a quantum computer

More information

Kilogram, Planck Units, and Quantum Hall Effect

Kilogram, Planck Units, and Quantum Hall Effect Kilogram, Planck Units, and Quantum Hall Effect Alexander Penin University of Alberta & TTP Karlsruhe DESY Hamburg, May 2012 Topics Discussed Systems of units and fundamental constants Planck system of

More information

Supplementary information for Quantum delayed-choice experiment with a beam splitter in a quantum superposition

Supplementary information for Quantum delayed-choice experiment with a beam splitter in a quantum superposition Supplementary information for Quantum delayed-choice experiment with a beam splitter in a quantum superposition Shi-Biao Zheng 1, You-Peng Zhong 2, Kai Xu 2, Qi-Jue Wang 2, H. Wang 2, Li-Tuo Shen 1, Chui-Ping

More information

arxiv:quant-ph/ v5 10 Feb 2003

arxiv:quant-ph/ v5 10 Feb 2003 Quantum entanglement of identical particles Yu Shi Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, United Kingdom and Theory of

More information

arxiv: v1 [cond-mat.mes-hall] 16 Oct 2009

arxiv: v1 [cond-mat.mes-hall] 16 Oct 2009 Coherent oscillations between classically separable quantum states of a superconducting loop Vladimir E. Manucharyan, 1 Jens Koch, 1 Markus Brink, 1 Leonid I. Glazman, 1 and Michel H. Devoret 1 1 Departments

More information

Electrical Quantum Engineering with Superconducting Circuits

Electrical Quantum Engineering with Superconducting Circuits 1.0 10 0.8 01 switching probability 0.6 0.4 0.2 00 Electrical Quantum Engineering with Superconducting Circuits R. Heeres & P. Bertet SPEC, CEA Saclay (France), Quantronics group 11 0.0 0 100 200 300 400

More information

B I A S T E E Reducing the Size of the Filtering Hardware. for Josephson Junction Qubit Experiments Using. Iron Powder Inductor Cores.

B I A S T E E Reducing the Size of the Filtering Hardware. for Josephson Junction Qubit Experiments Using. Iron Powder Inductor Cores. B I A S T E E 2. 0 Reducing the Size of the Filtering Hardware for Josephson Junction Qubit Experiments Using Iron Powder Inductor Cores. Daniel Staudigel Table of Contents Bias Tee 2.0 Daniel Staudigel

More information

(DPHY 01) M.Sc. DEGREE EXAMINATION, DECEMBER First Year. Physics. Paper I MATHEMATICAL PHYSICS

(DPHY 01) M.Sc. DEGREE EXAMINATION, DECEMBER First Year. Physics. Paper I MATHEMATICAL PHYSICS (DPHY 01) M.Sc. DEGREE EXAMINATION, DECEMBER 011. First Year Physics Paper I MATHEMATICAL PHYSICS Time : Three hours Maximum : 100 marks Answer any FIVE questions. All questions carry equal marks. 1. (a)

More information

Entropy in Classical and Quantum Information Theory

Entropy in Classical and Quantum Information Theory Entropy in Classical and Quantum Information Theory William Fedus Physics Department, University of California, San Diego. Entropy is a central concept in both classical and quantum information theory,

More information

Information measures, entanglement and quantum evolution

Information measures, entanglement and quantum evolution Information measures, entanglement and quantum evolution Claudia Zander Faculty of Natural & Agricultural Sciences University of Pretoria Pretoria Submitted in partial fulfilment of the requirements for

More information

Laser Physics OXFORD UNIVERSITY PRESS SIMON HOOKER COLIN WEBB. and. Department of Physics, University of Oxford

Laser Physics OXFORD UNIVERSITY PRESS SIMON HOOKER COLIN WEBB. and. Department of Physics, University of Oxford Laser Physics SIMON HOOKER and COLIN WEBB Department of Physics, University of Oxford OXFORD UNIVERSITY PRESS Contents 1 Introduction 1.1 The laser 1.2 Electromagnetic radiation in a closed cavity 1.2.1

More information

Lecture 9 Superconducting qubits Ref: Clarke and Wilhelm, Nature 453, 1031 (2008).

Lecture 9 Superconducting qubits Ref: Clarke and Wilhelm, Nature 453, 1031 (2008). Lecture 9 Superconducting qubits Ref: Clarke and Wilhelm, Nature 453, 1031 (2008). Newcomer in the quantum computation area ( 2000, following experimental demonstration of coherence in charge + flux qubits).

More information

ELECTRODYNAMICS OF CONTINUOUS MEDIA

ELECTRODYNAMICS OF CONTINUOUS MEDIA ELECTRODYNAMICS OF CONTINUOUS MEDIA by L. D. LANDAU and E. M. LIFSHITZ Institute of Physical Problems, USSR Academy of Sciences Volume 8 of Course of Theoretical Physics Translated from the Russian by

More information

Detection and Estimation Theory

Detection and Estimation Theory Detection and Estimation Theory Instructor: Prof. Namrata Vaswani Dept. of Electrical and Computer Engineering Iowa State University http://www.ece.iastate.edu/ namrata Slide 1 What is Estimation and Detection

More information

1. Introduction. 2. New approaches

1. Introduction. 2. New approaches New Approaches To An Indium Ion Optical Frequency Standard Kazuhiro HAYASAKA National Institute of Information and Communications Technology(NICT) e-mail:hayasaka@nict.go.jp ECTI200 . Introduction Outline

More information

Emergent Fluctuation Theorem for Pure Quantum States

Emergent Fluctuation Theorem for Pure Quantum States Emergent Fluctuation Theorem for Pure Quantum States Takahiro Sagawa Department of Applied Physics, The University of Tokyo 16 June 2016, YITP, Kyoto YKIS2016: Quantum Matter, Spacetime and Information

More information

Multiparticle Entanglement and Interference in Cavity Quantum Electrodynamics

Multiparticle Entanglement and Interference in Cavity Quantum Electrodynamics Multiparticle Entanglement and Interference in Cavity Quantum Electrodynamics A THESIS SUBMITTED TO GUJARAT UNIVERSITY for the degree of Doctor of Philosophy in Physics BY Pradyumna Kumar Pathak Quantum

More information

Cavity optomechanics in new regimes and with new devices

Cavity optomechanics in new regimes and with new devices Cavity optomechanics in new regimes and with new devices Andreas Nunnenkamp University of Basel 1. What? Why? How? 2. Single-photon regime 3. Dissipative coupling Introduction Cavity optomechanics radiation

More information

arxiv:quant-ph/ v1 12 Dec 1996

arxiv:quant-ph/ v1 12 Dec 1996 A quantum-mechanical Maxwell s demon arxiv:quant-ph/9612034v1 12 Dec 1996 Seth Lloyd d Arbeloff Laboratory for Information Systems and Technology Department of Mechanical Engineering Massachusetts Institute

More information