Verfügbarkeit: Quantum optics

Quantum optics: including noise reduction, trapped ions, quantum trajectories, and decoherence

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Bibliographische Detailangaben
1. Verfasser:	Orszag, Miguel 1944- (VerfasserIn)
Format:	Buch
Sprache:	English
Veröffentlicht:	Berlin [u.a.] Springer 2008
Ausgabe:	2. ed.
Schlagworte:	Quantum optics Quantenoptik Laser
Online-Zugang:	Inhaltsverzeichnis
Beschreibung:	Literaturangaben
Beschreibung:	XX, 414 S. Ill., graph. Darst.
ISBN:	9783540727064 9783540650089

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Datensatz im Suchindex

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adam_text	Contents Einstein s Theory of Atom—Radiation Interaction ......... 1 1.1 The A and В Coefficients ................................ 1 1.2 Thermal Equilibrium ................................... 3 1.3 Photon Distribution and Fluctuations ..................... 4 1.4 Light Beam Incident on Atoms ........................... 5 1.5 An Elementary Laser Theory ............................ 5 1.5.1 Threshold and Population Inversion ................ 6 1.5.2 Steady State ..................................... 7 1.5.3 Linear Stability Analysis .......................... 8 References ................................................. 9 Further Reading ............................................ 9 Atom—Field Interaction: Semiclassical Approach .......... 11 2.1 Broad-Band Radiation Spectrum ......................... 14 2.2 Rabi Oscillations ....................................... 15 2.3 Bloch s Equations ...................................... 16 2.4 Decay to an Unobserved Level ........................... 17 2.5 Decay Between Levels ................................... 18 2.6 Optical Nutation ....................................... 18 References ................................................. 19 Further Reading ............................................ 19 Quantization of the Electromagnetic Field ................ 21 3.1 Fock States ............................................ 24 3.2 Density of Modes ....................................... 25 3.3 Commutation Relations ................................. 26 Reference .................................................. 28 Further Reading ............................................ 28 States of the Electromagnetic Field I ..................... 31 4.1 Further Properties ...................................... 32 4.1.1 Coherent States are Minimum Uncertainty States .... 32 4.1.2 Coherent States are not Orthogonal ................ 32 4.1.3 Coherent States are Overcomplete .................. 33 4.1.4 The Displacement Operator ....................... 33 XIV Contents 4.1.5 Photon Statistics ................................. 34 4.1.6 Coordinate Representation ........................ 35 4.2 Mixed State: Thermal Radiation ......................... 35 References ................................................. 39 Further Reading ............................................ 39 5 States of the Electromagnetic Field II .................... 41 5.1 Squeezed States: General Properties and Detection ......... 41 5.1.1 The Squeeze Operator and the Squeezed State ....... 43 5.1.2 The Squeezed State is an Eigenstate of A ............ 44 5.1.3 Calculation of Moments with Squeezed States ........ 44 5.1.4 Quadrature Fluctuations .......................... 45 5.1.5 Photon Statistics ................................. 46 5.2 Multimode Squeezed States .............................. 47 5.3 Detection of Squeezed States ............................. 47 5.3.1 Ordinary Homodyne Detection ..................... 48 5.3.2 Balanced Homodyne Detection ..................... 50 5.3.3 Heterodyne Detection ............................. 50 References ................................................. 51 6 Quantum Theory of Coherence ........................... 53 6.1 One-Atom Detector ..................................... 54 6.2 The η -Atom Detector ................................... 57 6.3 General Properties of the Correlation Functions ............ 59 6.4 Young s Interference and First-Order Correlation ........... 60 6.5 Second-Order Correlations: Photon Bunching and Antibunching ...................................... 62 6.5.1 Classical Second-Order Coherence .................. 63 6.5.2 Quantum Theory of Second-Order Coherence ........ 65 6.6 Photon Counting ....................................... 67 6.6.1 Some Simple Examples ............................ 70 6.6.2 Quantum Mechanical Photon Count Distribution ..... 71 6.6.3 Particular Examples .............................. 72 References ................................................. 72 Further Reading ............................................ 72 7 Phase Space Description .................................. 73 7.1 Q-Representation: Antinormal Ordering .................. 73 7.1.1 Normalization .................................... 73 7.1.2 Average of Antinormally Ordered Products .......... 74 7.1.3 Some Examples .................................. 74 7.1.4 The Density Operator in Terms of the Function Q .... 75 7.2 Characteristic Function ................................. 76 7.3 P Representation: Normal Ordering ...................... 76 7.3.1 Normalization .................................... 76 Contents XV 7.3.2 Averages of Normally Ordered Products ............. 77 7.3.3 Some Interesting Properties ........................ 77 7.3.4 Some Examples .................................. 77 7.4 The Wigner Distribution: Symmetric Ordering ............. 79 7.4.1 Moments ........................................ 80 References ................................................. 82 Further Reading ............................................ 82 8 Atom—Field Interaction ................................... 83 8.1 Atom-Field Hamiltonian and the Dipole Approximation ..... 83 8.2 A Two-Level Atom Interacting with a Single Field Mode .... 85 8.3 The Dressed State Picture: Quantum Rabi Oscillations ...... 88 8.4 Collapse and Revivals ................................... 91 References ................................................. 94 Further Reading ............................................ 94 9 System—Reservoir Interactions ............................ 97 9.1 Quantum Theory of Damping ............................ 97 9.2 General Properties ......................................100 9.3 Expectation Values of Relevant Physical Quantities .........101 9.4 Time Evolution of the Density Matrix Elements ............102 9.5 The Glauber- Sudarshan Representation, and the Fokker- Planck Equation .......................................105 9.6 Time-Dependent Solution: The Method of the Eigenfunctions 106 9.6.1 General Solution .................................107 9.7 Langevin s Equations ...................................108 9.7.1 Calculation of the Correlation Function (F(t )F(t )i)B 109 9.7.2 Differential Equation for the Photon Number ........109 9.8 Other Master Equations .................................110 9.8.1 Two-Level Atom in a Thermal Bath ................110 9.8.2 Damped Harmonic Oscillator in a Squeezed Bath ..... Ill 9.8.3 Application: Spontaneous Decay in a Squeezed Vaccum 114 References .................................................116 Further Reading ............................................117 10 Resonance Fluorescence ..................................119 10.1 Background ............................................119 10.2 Heisenberg^ Equations ..................................120 10.3 Spectral Density, and the Wiener-Khinchine Theorem .......124 10.4 Emission Spectra from Strongly Driven Two-Level Atoms ... 126 10.5 Intensity Correlations ...................................129 References .................................................133 Further Reading ............................................134 XVI Contents 11 Quantum Laser Theory: Master Equation Approach ......135 11.1 Heuristic Discussion of Injection Statistics .................136 11.2 Master Equation for Generalized Pump Satistics ...........137 11.3 The Quantum Theory of the Laser: Random Injection (p = 0) 139 11.3.1 Photon Statistics .................................140 11.3.2 The Fokker-Planck Equation: Laser Linewidth .......143 11.3.3 Alternative Derivation of the Laser Linewidth ........144 11.4 Quantum Theory of the Micromaser: Random injection (p = 0)146 11.4.1 Generalities ......................................146 11.4.2 The Micromaser..................................147 11.4.3 Trapping States ..................................149 11.5 Quantum Theory of the Laser and the Micromaser with Pump Statistics (p/0) .................................153 References .................................................157 Further Reading ............................................157 12 Quantum Laser Theory: Langevin Approach ..............159 12.1 Quantum Langevin Equations ............................159 12.1.1 The Generalized Einstein s Relations ................160 12.1.2 The Atomic Noise Moments .......................161 12.2 С -Number Langevin Equations ...........................165 12.2.1 Adiabatic Approximation ..........................166 12.3 Phase and Intensity Fluctuations .........................167 12.4 Discussion .............................................168 References .................................................170 Further Reading ............................................171 13 Quantum Noise Reduction 1..............................173 13.1 Correlated Emission Laser Systems .......................175 13.1.1 The Quantum Beat Laser ......................... 175 13.1.2 Other CEL Systems .............................. 181 References ................................................. 182 Further Reading ............................................ 182 14 Quantum Noise Reduction 2..............................185 14.1 Introduction to Non-Linear Optics ........................ 185 14.1.1 Multiple-Photon Transitions ....................... 185 14.2 Parametric Processes Without Losses ..................... 189 14.3 The Input-Output Theory ............................... 191 14.4 The Degenerate Parametric Oscillator ..................... 195 14.5 Experimental Results ...................................198 References .................................................201 Contents XVII 15 Quantum Phase ..........................................203 15.1 The Dirac Phase.......................................203 15.2 The Louiseil Phase.....................................204 15.3 The Susskind-Glogower Phase...........................204 15.4 The Pegg-Barnett Phase................................208 15.4.1 Applications.....................................211 15.5 Phase Fluctuations in a Laser ............................213 References .................................................217 Further Reading ............................................217 16 Quantum Trajectories ....................................219 16.1 Montecarlo Wavefimction Method........................ 220 16.1.1 The Montecarlo Method is Equivalent, on the Average, to the Master Equation ...................221 16.2 The Stochastic Schrödinger Equation .....................223 16.3 Stochastic Schrödinger Equations and Dissipati ve Systems . .. 225 16.4 Simulation of a Monte Carlo SSE .........................227 16.5 Simulation of the Homodyne SSDE .......................232 16.6 Numerical Results and Localizat .¡on ......................236 16.6.1 Quantum Jumps Evolution ........................236 16.6.2 Diffusion-like Evolution ...........................237 16.6.3 Analytical Proof of Localization ....................239 16.7 Conclusions ............................................242 References .................................................244 Further Reading ............................................245 17 Atom Optics ..............................................247 17.1 Optical Elements .......................................247 17.2 Atomic Diffraction from an Optical Standing Wave .........................................248 17.2.1 Theory ..........................................249 17.2.2 Particular Cases ..................................252 17.3 Atomic Focusing .......................................255 17.3.1 The Model ......................................255 17.3.2 Initial Conditions and Solution .....................257 17.3.3 Quantum and Classical Foci .......................258 17.3.4 Thin Versus Thick Lenses .........................258 17.3.5 The Quantum Focal Curve ........................259 17.3.6 Aberrations ......................................261 References .................................................262 18 Measurements, Quantum Limits and All That ............263 18.1 Quantum Standard Limit ................................263 18.1.1 Quantum Standard Limit for a Free Partido .........263 18.1.2 Standard Quantum Limit for an Oscillator ...........264 XVIII Contents 18.1.3 Thermal Effects ..................................265 18.2 Quantum Non-Demolition (QND) Measurements ...........266 18.2.1 The Pree System .................................266 18.2.2 Monitoring a Classical Force .......................268 18.2.3 Effect of the Measuring Apparatus or Probe .........269 18.3 QND Measurement of the Number of Photons in a Cavity . .. 270 18.3.1 The Model ......................................270 18.3.2 The System-Probe Interaction .....................271 18.3.3 Measuring the Atomic Phase with Ramsey Fields .....272 18.3.4 QND Measurement of the Photon Number ..........275 18.4 Quantum Theory of Continuous Photodetection Process .....278 18.4.1 Introduction .....................................278 18.4.2 Continuous Measurement in a Two-Mode System: Phase Narrowing .................................280 References .................................................284 Further R,eading ............................................285 19 Trapped Ions .............................................287 19.1 Paul Trap .............................................287 19.1.1 General Properties ...............................287 19.1.2 Stability Analysis ................................290 19.2 Trapped Ions ..........................................294 19.2.1 Introduction .....................................294 19.2.2 The Model and Effective Hamiltonian ...............294 19.2.3 The Lamb-Dicke Expansion and Raman Cooling .....299 19.2.4 The Dynamical Evolution .........................300 19.2.5 QND Measurements of Vibrational States ...........303 19.2.6 Generation of Non-Classical Vibrational States .......305 References .................................................309 Further Reading ............................................309 20 Decoherence ..............................................311 20.1 Dynamics of the Correlations ............................314 20.2 How Long Does It Take to Decohere? .....................315 20.3 Decoherence Free Subspaces .............................320 20.3.1 Simple Example: Collective dephasing ...............320 20.3.2 General Treatment ...............................322 20.3.3 Condition for DFS: Hamiltonian Approach ..........323 20.3.4 Condition for DFS: Lindblad Approach .............323 20.3.5 Example: A7 Spins in Boson Bath ...................326 References .................................................327 Further Reading ............................................328 Contents XIX 21 Quantum Bits, Entanglement and Applications...........329 21.1 Qubits and Quantum Gates..............................329 21.2 Entanglement ..........................................333 21.2.1 Pure States......................................333 21.2.2 Mixed states..................................... 339 21.2.3 Bell Inequalities ................................. 341 21.3 Quantum Teleportation................................. 344 References .................................................347 22 Quantum Cloning and Processing .........................349 22.1 The No-Cloning Theorem ...............................349 22.2 The Universal Quantum Copying Machine (UQCM) ........350 22.3 Quantum Copying Machine Implemented by a Circuit .......351 22.3.1 Preparation Stage ................................352 22.3.2 Copying Stage and Output ........................353 22.3.3 Output States ...................................355 22.3.4 Summary and Discussion ..........................356 22.4 Quantum Processors ...................................357 22.4.1 Introduction .....................................357 22.4.2 One Qubit Stochastic Processor ...................359 References .................................................361 A Operator Relations .......................................363 A.I Theorem 1.............................................363 A.2 Theorem 2: The Baker-Campbell- Haussdorf Relation .......364 A.3 Theorem 3: Similarity Transformation .....................365 Reference ..................................................366 В The Method of Characteristics ...........................367 Reference ..................................................369 С Proof .....................................................371 References .................................................372 D Stochastic Processes in a Nutshell ........................373 D.I Introduction ...........................................373 D.2 Probability Concepts ....................................374 D.3 Stochastic Processes ....................................375 D.3.1 The Chapman-Kolmogorov Equation ...............375 D.4 The Fokker-Planck Equation ............................378 D.4.1 The Wiener Process ..............................379 D.4. 2 General Properties of the Fokker-Planck Equation .... 381 D.4.3 Steady-State Solution .............................381 D.5 Stochastic Differential Equations .........................382 D.5.1 Introduction .....................................382 XX Contents D. 5.2 Ito Versus Stratonovich...........................384 D.5.3 Ito s Formula ....................................386 D.6 Approximate Methods ..................................388 References .................................................391 E Derivation of the Homodyne Stochastic Schrödinger Differential Equation .....................................393 F Fluctuations ..............................................397 G The No-Cloning Theorem .................................399 Reference ..................................................399 H The Universal Quantum Cloning Machine ................401 Reference ..................................................402 I Hints to Solve the Problems ..............................403 Index .........................................................409
adam_txt	Contents Einstein's Theory of Atom—Radiation Interaction . 1 1.1 The A and В Coefficients . 1 1.2 Thermal Equilibrium . 3 1.3 Photon Distribution and Fluctuations . 4 1.4 Light Beam Incident on Atoms . 5 1.5 An Elementary Laser Theory . 5 1.5.1 Threshold and Population Inversion . 6 1.5.2 Steady State . 7 1.5.3 Linear Stability Analysis . 8 References . 9 Further Reading . 9 Atom—Field Interaction: Semiclassical Approach . 11 2.1 Broad-Band Radiation Spectrum . 14 2.2 Rabi Oscillations . 15 2.3 Bloch's Equations . 16 2.4 Decay to an Unobserved Level . 17 2.5 Decay Between Levels . 18 2.6 Optical Nutation . 18 References . 19 Further Reading . 19 Quantization of the Electromagnetic Field . 21 3.1 Fock States . 24 3.2 Density of Modes . 25 3.3 Commutation Relations . 26 Reference . 28 Further Reading . 28 States of the Electromagnetic Field I . 31 4.1 Further Properties . 32 4.1.1 Coherent States are Minimum Uncertainty States . 32 4.1.2 Coherent States are not Orthogonal . 32 4.1.3 Coherent States are Overcomplete . 33 4.1.4 The Displacement Operator . 33 XIV Contents 4.1.5 Photon Statistics . 34 4.1.6 Coordinate Representation . 35 4.2 Mixed State: Thermal Radiation . 35 References . 39 Further Reading . 39 5 States of the Electromagnetic Field II . 41 5.1 Squeezed States: General Properties and Detection . 41 5.1.1 The Squeeze Operator and the Squeezed State . 43 5.1.2 The Squeezed State is an Eigenstate of A . 44 5.1.3 Calculation of Moments with Squeezed States . 44 5.1.4 Quadrature Fluctuations . 45 5.1.5 Photon Statistics . 46 5.2 Multimode Squeezed States . 47 5.3 Detection of Squeezed States . 47 5.3.1 Ordinary Homodyne Detection . 48 5.3.2 Balanced Homodyne Detection . 50 5.3.3 Heterodyne Detection . 50 References . 51 6 Quantum Theory of Coherence . 53 6.1 One-Atom Detector . 54 6.2 The η -Atom Detector . 57 6.3 General Properties of the Correlation Functions . 59 6.4 Young's Interference and First-Order Correlation . 60 6.5 Second-Order Correlations: Photon Bunching and Antibunching . 62 6.5.1 Classical Second-Order Coherence . 63 6.5.2 Quantum Theory of Second-Order Coherence . 65 6.6 Photon Counting . 67 6.6.1 Some Simple Examples . 70 6.6.2 Quantum Mechanical Photon Count Distribution . 71 6.6.3 Particular Examples . 72 References . 72 Further Reading . 72 7 Phase Space Description . 73 7.1 Q-Representation: Antinormal Ordering . 73 7.1.1 Normalization . 73 7.1.2 Average of Antinormally Ordered Products . 74 7.1.3 Some Examples . 74 7.1.4 The Density Operator in Terms of the Function Q . 75 7.2 Characteristic Function . 76 7.3 P Representation: Normal Ordering . 76 7.3.1 Normalization . 76 Contents XV 7.3.2 Averages of Normally Ordered Products . 77 7.3.3 Some Interesting Properties . 77 7.3.4 Some Examples . 77 7.4 The Wigner Distribution: Symmetric Ordering . 79 7.4.1 Moments . 80 References . 82 Further Reading . 82 8 Atom—Field Interaction . 83 8.1 Atom-Field Hamiltonian and the Dipole Approximation . 83 8.2 A Two-Level Atom Interacting with a Single Field Mode . 85 8.3 The Dressed State Picture: Quantum Rabi Oscillations . 88 8.4 Collapse and Revivals . 91 References . 94 Further Reading . 94 9 System—Reservoir Interactions . 97 9.1 Quantum Theory of Damping . 97 9.2 General Properties .100 9.3 Expectation Values of Relevant Physical Quantities .101 9.4 Time Evolution of the Density Matrix Elements .102 9.5 The Glauber- Sudarshan Representation, and the Fokker- Planck Equation .105 9.6 Time-Dependent Solution: The Method of the Eigenfunctions 106 9.6.1 General Solution .107 9.7 Langevin's Equations .108 9.7.1 Calculation of the Correlation Function (F(t')F(t")i)B 109 9.7.2 Differential Equation for the Photon Number .109 9.8 Other Master Equations .110 9.8.1 Two-Level Atom in a Thermal Bath .110 9.8.2 Damped Harmonic Oscillator in a Squeezed Bath . Ill 9.8.3 Application: Spontaneous Decay in a Squeezed Vaccum 114 References .116 Further Reading .117 10 Resonance Fluorescence .119 10.1 Background .119 10.2 Heisenberg^ Equations .120 10.3 Spectral Density, and the Wiener-Khinchine Theorem .124 10.4 Emission Spectra from Strongly Driven Two-Level Atoms . 126 10.5 Intensity Correlations .129 References .133 Further Reading .134 XVI Contents 11 Quantum Laser Theory: Master Equation Approach .135 11.1 Heuristic Discussion of Injection Statistics .136 11.2 Master Equation for Generalized Pump Satistics .137 11.3 The Quantum Theory of the Laser: Random Injection (p = 0) 139 11.3.1 Photon Statistics .140 11.3.2 The Fokker-Planck Equation: Laser Linewidth .143 11.3.3 Alternative Derivation of the Laser Linewidth .144 11.4 Quantum Theory of the Micromaser: Random injection (p = 0)146 11.4.1 Generalities .146 11.4.2 The Micromaser.147 11.4.3 Trapping States .149 11.5 Quantum Theory of the Laser and the Micromaser with Pump Statistics (p/0) .153 References .157 Further Reading .157 12 Quantum Laser Theory: Langevin Approach .159 12.1 Quantum Langevin Equations .159 12.1.1 The Generalized Einstein's Relations .160 12.1.2 The Atomic Noise Moments .161 12.2 С -Number Langevin Equations .165 12.2.1 Adiabatic Approximation .166 12.3 Phase and Intensity Fluctuations .167 12.4 Discussion .168 References .170 Further Reading .171 13 Quantum Noise Reduction 1.173 13.1 Correlated Emission Laser Systems .175 13.1.1 The Quantum Beat Laser . 175 13.1.2 Other CEL Systems . 181 References . 182 Further Reading . 182 14 Quantum Noise Reduction 2.185 14.1 Introduction to Non-Linear Optics . 185 14.1.1 Multiple-Photon Transitions . 185 14.2 Parametric Processes Without Losses . 189 14.3 The Input-Output Theory . 191 14.4 The Degenerate Parametric Oscillator . 195 14.5 Experimental Results .198 References .201 Contents XVII 15 Quantum Phase .203 15.1 The Dirac Phase.203 15.2 The Louiseil Phase.204 15.3 The Susskind-Glogower Phase.204 15.4 The Pegg-Barnett Phase.208 15.4.1 Applications.211 15.5 Phase Fluctuations in a Laser .213 References .217 Further Reading .217 16 Quantum Trajectories .219 16.1 Montecarlo Wavefimction Method. 220 16.1.1 The Montecarlo Method is Equivalent, on the Average, to the Master Equation .221 16.2 The Stochastic Schrödinger Equation .223 16.3 Stochastic Schrödinger Equations and Dissipati ve Systems . . 225 16.4 Simulation of a Monte Carlo SSE .227 16.5 Simulation of the Homodyne SSDE .232 16.6 Numerical Results and Localizat .¡on .236 16.6.1 Quantum Jumps Evolution .236 16.6.2 Diffusion-like Evolution .237 16.6.3 Analytical Proof of Localization .239 16.7 Conclusions .242 References .244 Further Reading .245 17 Atom Optics .247 17.1 Optical Elements .247 17.2 Atomic Diffraction from an Optical Standing Wave .248 17.2.1 Theory .249 17.2.2 Particular Cases .252 17.3 Atomic Focusing .255 17.3.1 The Model .255 17.3.2 Initial Conditions and Solution .257 17.3.3 Quantum and Classical Foci .258 17.3.4 Thin Versus Thick Lenses .258 17.3.5 The Quantum Focal Curve .259 17.3.6 Aberrations .261 References .262 18 Measurements, Quantum Limits and All That .263 18.1 Quantum Standard Limit .263 18.1.1 Quantum Standard Limit for a Free Partido .263 18.1.2 Standard Quantum Limit for an Oscillator .264 XVIII Contents 18.1.3 Thermal Effects .265 18.2 Quantum Non-Demolition (QND) Measurements .266 18.2.1 The Pree System .266 18.2.2 Monitoring a Classical Force .268 18.2.3 Effect of the Measuring Apparatus or Probe .269 18.3 QND Measurement of the Number of Photons in a Cavity . . 270 18.3.1 The Model .270 18.3.2 The System-Probe Interaction .271 18.3.3 Measuring the Atomic Phase with Ramsey Fields .272 18.3.4 QND Measurement of the Photon Number .275 18.4 Quantum Theory of Continuous Photodetection Process .278 18.4.1 Introduction .278 18.4.2 Continuous Measurement in a Two-Mode System: Phase Narrowing .280 References .284 Further R,eading .285 19 Trapped Ions .287 19.1 Paul Trap .287 19.1.1 General Properties .287 19.1.2 Stability Analysis .290 19.2 Trapped Ions .294 19.2.1 Introduction .294 19.2.2 The Model and Effective Hamiltonian .294 19.2.3 The Lamb-Dicke Expansion and Raman Cooling .299 19.2.4 The Dynamical Evolution .300 19.2.5 QND Measurements of Vibrational States .303 19.2.6 Generation of Non-Classical Vibrational States .305 References .309 Further Reading .309 20 Decoherence .311 20.1 Dynamics of the Correlations .314 20.2 How Long Does It Take to Decohere? .315 20.3 Decoherence Free Subspaces .320 20.3.1 Simple Example: Collective dephasing .320 20.3.2 General Treatment .322 20.3.3 Condition for DFS: Hamiltonian Approach .323 20.3.4 Condition for DFS: Lindblad Approach .323 20.3.5 Example: A7 Spins in Boson Bath .326 References .327 Further Reading .328 Contents XIX 21 Quantum Bits, Entanglement and Applications.329 21.1 Qubits and Quantum Gates.329 21.2 Entanglement .333 21.2.1 Pure States.333 21.2.2 Mixed states. 339 21.2.3 Bell Inequalities . 341 21.3 Quantum Teleportation. 344 References .347 22 Quantum Cloning and Processing .349 22.1 The No-Cloning Theorem .349 22.2 The Universal Quantum Copying Machine (UQCM) .350 22.3 Quantum Copying Machine Implemented by a Circuit .351 22.3.1 Preparation Stage .352 22.3.2 Copying Stage and Output .353 22.3.3 Output States .355 22.3.4 Summary and Discussion .356 22.4 Quantum Processors .357 22.4.1 Introduction .357 22.4.2 One Qubit Stochastic Processor .359 References .361 A Operator Relations .363 A.I Theorem 1.363 A.2 Theorem 2: The Baker-Campbell- Haussdorf Relation .364 A.3 Theorem 3: Similarity Transformation .365 Reference .366 В The Method of Characteristics .367 Reference .369 С Proof .371 References .372 D Stochastic Processes in a Nutshell .373 D.I Introduction .373 D.2 Probability Concepts .374 D.3 Stochastic Processes .375 D.3.1 The Chapman-Kolmogorov Equation .375 D.4 The Fokker-Planck Equation .378 D.4.1 The Wiener Process .379 D.4. 2 General Properties of the Fokker-Planck Equation . 381 D.4.3 Steady-State Solution .381 D.5 Stochastic Differential Equations .382 D.5.1 Introduction .382 XX Contents D. 5.2 Ito Versus Stratonovich.384 D.5.3 Ito's Formula .386 D.6 Approximate Methods .388 References .391 E Derivation of the Homodyne Stochastic Schrödinger Differential Equation .393 F Fluctuations .397 G The No-Cloning Theorem .399 Reference .399 H The Universal Quantum Cloning Machine .401 Reference .402 I Hints to Solve the Problems .403 Index .409
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institution	BVB
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language	English
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spelling	Orszag, Miguel 1944- Verfasser (DE-588)121053679 aut Quantum optics including noise reduction, trapped ions, quantum trajectories, and decoherence Miguel Orszag 2. ed. Berlin [u.a.] Springer 2008 XX, 414 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Literaturangaben Quantum optics Quantenoptik (DE-588)4047990-0 gnd rswk-swf Laser (DE-588)4034610-9 gnd rswk-swf Quantenoptik (DE-588)4047990-0 s Laser (DE-588)4034610-9 s 1\p DE-604 DE-604 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016405170&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk
spellingShingle	Orszag, Miguel 1944- Quantum optics including noise reduction, trapped ions, quantum trajectories, and decoherence Quantum optics Quantenoptik (DE-588)4047990-0 gnd Laser (DE-588)4034610-9 gnd
subject_GND	(DE-588)4047990-0 (DE-588)4034610-9
title	Quantum optics including noise reduction, trapped ions, quantum trajectories, and decoherence
title_auth	Quantum optics including noise reduction, trapped ions, quantum trajectories, and decoherence
title_exact_search	Quantum optics including noise reduction, trapped ions, quantum trajectories, and decoherence
title_exact_search_txtP	Quantum optics including noise reduction, trapped ions, quantum trajectories, and decoherence
title_full	Quantum optics including noise reduction, trapped ions, quantum trajectories, and decoherence Miguel Orszag
title_fullStr	Quantum optics including noise reduction, trapped ions, quantum trajectories, and decoherence Miguel Orszag
title_full_unstemmed	Quantum optics including noise reduction, trapped ions, quantum trajectories, and decoherence Miguel Orszag
title_short	Quantum optics
title_sort	quantum optics including noise reduction trapped ions quantum trajectories and decoherence
title_sub	including noise reduction, trapped ions, quantum trajectories, and decoherence
topic	Quantum optics Quantenoptik (DE-588)4047990-0 gnd Laser (DE-588)4034610-9 gnd
topic_facet	Quantum optics Quantenoptik Laser
url	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016405170&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
work_keys_str_mv	AT orszagmiguel quantumopticsincludingnoisereductiontrappedionsquantumtrajectoriesanddecoherence

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