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Main Authors:	Walls, Daniel F. 1942-1999 (Author), Milburn, Gerard J. 1958- (Author)
Format:	Book
Language:	English
Published:	Berlin ; Heidelberg Springer 2008
Edition:	2nd edition
Subjects:	Quantenoptik Quantum optics Lehrbuch
Online Access:	Inhaltsverzeichnis
Physical Description:	xii, 425 Seiten Illustrationen, Diagramme
ISBN:	3540285733 9783540285731

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adam_text	Contents Introduction ................................................... 1 Quantisation of the Electromagnetic Field ........................ 7 2.1 Field Quantisation .......................................... 7 2.2 Fock or Number States ...................................... 10 2.3 Coherent States ............................................ 12 2.4 Squeezed States ............................................ 15 2.5 Two-Photon Coherent States ................................. 18 2.6 Variance in the Electric Field ................................. 20 2.7 Multimode Squeezed States .................................. 22 2.8 Phase Properties of the Field ................................. 23 Exercises ...................................................... 26 References ..................................................... 26 Further Reading ................................................ 27 Coherence Properties of the Electromagnetic Field ................. 29 3.1 Field-Correlation Functions .................................. 29 3.2 Properties of the Correlation Functions ........................ 31 3.3 Correlation Functions and Optical Coherence ................... 32 3.4 First-Order Optical Coherence ................................ 34 3.5 Coherent Field ............................................. 37 3.6 Photon Correlation Measurements ............................ 38 3.7 Quantum Mechanical Fields .................................. 41 3.7.1 Squeezed State ...................................... 42 3.7.2 Squeezed Vacuum ................................... 44 3.8 Phase-Dependent Correlation Functions ........................ 44 3.9 Photon Counting Measurements .............................. 46 3.9.1 Classical Theory ..................................... 46 3.9.2 Constant Intensity .................................... 48 3.9.3 Fluctuating Intensity-Short-Time Limit ................. 48 Contents 3.10 Quantum Mechanical Photon Count Distribution................ 50 3.10.1 Coherent Light...................................... 51 3.10.2 Chaotic Light....................................... 51 3.10.3 Photo-Electron Current Fluctuations .................... 52 Exercises ...................................................... 54 References ..................................................... 55 Further Reading ................................................ 55 Representations of the Electromagnetic Field ...................... 57 4.1 Expansion in Number States ................................. 57 4.2 Expansion in Coherent States ................................. 58 4.2.1 Ρ Representation ..................................... 58 4.2.2 Wigner s Phase-Space Density ......................... 62 4.2.3 Q Function ......................................... 65 4.2.4 R Representation .................................... 67 4.2.5 Generalized P Representations ......................... 68 4.2.6 Positive P Representation ............................. 71 Exercises ...................................................... 72 References ..................................................... 72 Quantum Phenomena in Simple Systems in Nonlinear Optics ....... 73 5.1 Single-Mode Quantum Statistics .............................. 73 5.1.1 Degenerate Parametric Amplifier ....................... 73 5.1.2 Photon Statistics ..................................... 75 5.1.3 Wigner Function ..................................... 76 5.2 Two-Mode Quantum Correlations ............................. 77 5.2.1 Non-degenerate Parametric Amplifier ................... 77 5.2.2 Squeezing .......................................... 80 5.2.3 Quadrature Correlations and the Einstein-Podolsky-Rosen Paradox ............................................ 82 5.2.4 Wigner Function ..................................... 83 5.2.5 Reduced Density Operator ............................ 84 5.3 Quantum Limits to Amplification ............................. 86 5.4 Amplitude Squeezed State with Poisson Photon Number Statistics . 88 Exercises ...................................................... 91 References ..................................................... 91 Stochastic Methods ............................................. 93 6.1 Master Equation ........................................... 93 6.2 Equivalent с -Number Equations .............................. 99 6.2.1 Photon Number Representation ........................ 99 6.2.2 P Representation ..................................... 100 6.2.3 Properties of Fokker— Planck Equations .................. 102 6.2.4 Steady State Solutions - Potential Conditions ............. 103 6.2.5 Time Dependent Solution ............................. 104 Contents 6.2.6 Q Representation ....................................105 6.2.7 Wigner Function .....................................107 6.2.8 Generalized P Representation ..........................109 6.3 Stochastic Differential Equations .............................112 6.3.1 Use of the Positive P Representation ....................115 6.4 Linear Processes with Constant Diffusion ......................116 6.5 Two Time Correlation Functions in Quantum Markov Processes ... 117 6.5.1 Quantum Regression Theorem .........................118 6.6 Application to Systems with a P Representation .................118 6.7 Stochastic Unravellings .....................................119 6.7.1 Simulating Quantum Trajectories .......................123 Exercises ......................................................124 References .....................................................125 Further Reading ................................................125 Input-Output Formulation of Optical Cavities ....................127 7.1 Cavity Modes ..............................................127 7.2 Linear Systems ............................................131 7.3 Two-Sided Cavity ..........................................132 7.4 Two Time Correlation Functions ..............................133 7.5 Spectrum of Squeezing ......................................135 7.6 Parametric Oscillator .......................................136 7.7 Squeezing in the Total Field ..................................138 7.8 Fokker-Planck Equation .....................................138 Exercises ......................................................141 References .....................................................141 Further Reading ................................................141 Generation and Applications of Squeezed Light ...................143 8.1 Parametric Oscillation and Second Harmonic Generation .........143 8.1.1 Semi-Classical Steady States and Stability Analysis .......145 8.1.2 Parametric Oscillation ................................146 8.1.3 Second Harmonic Generation ..........................146 8.1.4 Squeezing Spectrum ..................................147 8.1.5 Parametric Oscillation ................................148 8.1.6 Experiments ........................................149 8.2 Twin Beam Generation and Intensity Correlations ...............151 8.2.1 Second Harmonic Generation ..........................156 8.2.2 Experiments ........................................157 8.3 Applications of Squeezed Light ...............................158 8.3.1 Interferometric Detection of Gravitational Radiation .......158 8.3.2 Sub-Shot-Noise Phase Measurements ...................171 8.3.3 Quantum Information .................................173 Exercises ......................................................174 χ Contents References .....................................................174 Further Reading ................................................175 9 Nonlinear Quantum Dissipative Systems ..........................177 9.1 Optical Parametric Oscillator: Complex Ρ Function ..............177 9.2 Optical Parametric Oscillator: Positive Ρ Function ...............181 9.3 Quantum Tunnelling Time ...................................186 9.4 Dispersive Optical Bistability ................................190 9.5 Comment on the Use of the Q and Wigner Representations ........192 Exercises ......................................................192 9.A Appendix .................................................193 9.A. 1 Evaluation of Moments for the Complex P function for Parametric Oscillation (9.17) .......................193 9.A.2 Evaluation of the Moments for the Complex P Function for Optical Bistability (9.48)...........................194 References .....................................................195 Further Reading ................................................195 10 Interaction of Radiation with Atoms .............................197 10.1 Quantization of the Many-Electron System .....................197 10.2 Interaction of a Single Two-Level Atom with a Single Mode Field .. 201 10.3 Spontaneous Emission from a Two-Level Atom .................203 10.4 Phase Decay in a Two-Level System ...........................204 10.5 Resonance Fluorescence .....................................205 Exercises ......................................................210 References .....................................................210 Further Reading ................................................211 11 CQED ........................................................213 11.1 Cavity QED ...............................................213 11.1.1 Vacuum Rabi Splitting ................................217 11.1.2 Single Photon Sources ................................218 11.1.3 Cavity QED with N Atoms ............................221 11.2 Circuit QED ...............................................225 Exercises ......................................................227 References .....................................................228 Further Reading ................................................229 12 Quantum Theory of the Laser ...................................231 12.1 Master Equation ...........................................231 12.2 Photon Statistics ...........................................233 12.2.1 Spectrum of Intensity Fluctuations ......................234 12.3 Laser Linewidth ............................................237 12.4 Regularly Pumped Laser ....................................238 12.A Appendix: Derivation of the Single-Atom Increment .............242 Contents xi Exercises ......................................................245 References .....................................................245 13 Bells Inequalities in Quantum Optics .............................247 13.1 The Einstein-Podolsky-Rosen (EPR) Argument .................247 13.2 Bell Inequalities and the Aspect Experiment ....................248 13.3 Violations of Bell s Inequalities Using a Parametric Amplifier Source ....................................................254 13.4 One-Photon Interference .....................................259 Exercises ......................................................264 References .....................................................264 14 Quantum Nondemolition Measurements ..........................267 14.1 Concept of a QND Measurement ..............................268 14.2 Back Action Evasion ........................................270 14.3 Criteria for a QND Measurement .............................270 14.4 The Beam Splitter ..........................................273 14.5 Ideal Quadrature QND Measurements .........................276 14.6 Experimental Realisation ....................................277 14.7 A Photon Number QND Scheme ..............................279 Exercises ......................................................281 References .....................................................282 15 Quantum Coherence and Measurement Theory ...................283 15.1 Quantum Coherence ........................................283 15.2 The Effect of Dissipation ....................................288 15.2.1 Experimental Observation of Coherence Decay ...........291 15.3 Quantum Measurement Theory ...............................293 15.3.1 General Measurement Theory ..........................294 15.3.2 The Pointer Basis ....................................296 15.4 Examples of Pointer Observables .............................299 15.5 Model of a Measurement ....................................299 15.6 Conditional States and Quantum Trajectories ...................302 15.6.1 Homodyne Measurement of a Cavity Field ...............303 Exercises ......................................................305 References .....................................................306 16 Quantum Information ..........................................307 16.1 Introduction ...............................................307 16.1.1 The Qubit ..........................................308 16.1.2 Entanglement .......................................310 16.2 Quantum Key Distribution ...................................312 16.3 Quantum Teleportation ......................................318 16.4 Quantum Computation ......................................324 16.4.1 Linear Optical Quantum Gates .........................327 16.4.2 Single Photon Sources ................................336 Exercises ......................................................343 xii Contents References .....................................................344 Further Reading ................................................346 17 Ion Traps .....................................................347 17.1 Introduction ...............................................347 17.2 Trapping and Cooling .......................................347 17.3 Novel Quantum States ......................................353 17.4 Trapping Multiple Ions ......................................356 17.5 Ion Trap Quantum Information Processing .....................359 Exercises ......................................................362 References .....................................................363 18 Light Forces ...................................................365 18.1 Radiative Forces in the Semiclassical Limit ....................366 18.2 Mean Force for a Two-Level Atom Initially at Rest ..............368 18.3 Friction Force for a Moving Atom ............................371 18.3.1 Laser Standing Wave— Doppler Cooling .................372 18.4 Dressed State Description of the Dipole Force ..................374 18.5 Atomic Diffraction by a Standing Wave ........................377 18.6 Optical Stern-Gerlach Effect .................................381 18.7 Quantum Chaos ............................................385 18.7.1 Dynamical Tunnelling ................................387 18.7.2 Dynamical Localisation ...............................389 18.8 The Effect of Spontaneous Emission ..........................390 References .....................................................394 Further Reading ................................................395 19 Bose-Einstein Condensation .....................................397 19.1 Hamiltonian: Binary Collision Model ..........................398 19.2 Mean-Field Theory — Gross-Pitaevskii Equation ..............399 19.3 Single Mode Approximation ................................400 19.4 Quantum State of the Condensate ............................401 19.5 Quantum Phase Diffusion: Collapses and Revivals of the Condensate Phase .........................401 19.6 Interference of Two Bose-Einstein Condensates and Measurement-Induced Phase .............................405 19.6.1 Interference of Two Condensates Initially in Number States .............................................405 19.7 Quantum Tunneling of a Two Component Condensate ............409 19.7.1 Semiclassical Dynamics ..............................411 19.7.2 Quantum Dynamics ..................................414 19.8 Coherence Properties of Bose-Einstein Condensates .............416 19.8.1 1st Order Coherence ..................................416 19.8.2 Higher Order Coherence ..............................417 Exercises ......................................................419 References .....................................................419 Further Reading ................................................420 Index .421
adam_txt	Contents Introduction . 1 Quantisation of the Electromagnetic Field . 7 2.1 Field Quantisation . 7 2.2 Fock or Number States . 10 2.3 Coherent States . 12 2.4 Squeezed States . 15 2.5 Two-Photon Coherent States . 18 2.6 Variance in the Electric Field . 20 2.7 Multimode Squeezed States . 22 2.8 Phase Properties of the Field . 23 Exercises . 26 References . 26 Further Reading . 27 Coherence Properties of the Electromagnetic Field . 29 3.1 Field-Correlation Functions . 29 3.2 Properties of the Correlation Functions . 31 3.3 Correlation Functions and Optical Coherence . 32 3.4 First-Order Optical Coherence . 34 3.5 Coherent Field . 37 3.6 Photon Correlation Measurements . 38 3.7 Quantum Mechanical Fields . 41 3.7.1 Squeezed State . 42 3.7.2 Squeezed Vacuum . 44 3.8 Phase-Dependent Correlation Functions . 44 3.9 Photon Counting Measurements . 46 3.9.1 Classical Theory . 46 3.9.2 Constant Intensity . 48 3.9.3 Fluctuating Intensity-Short-Time Limit . 48 Contents 3.10 Quantum Mechanical Photon Count Distribution. 50 3.10.1 Coherent Light. 51 3.10.2 Chaotic Light. 51 3.10.3 Photo-Electron Current Fluctuations . 52 Exercises . 54 References . 55 Further Reading . 55 Representations of the Electromagnetic Field . 57 4.1 Expansion in Number States . 57 4.2 Expansion in Coherent States . 58 4.2.1 Ρ Representation . 58 4.2.2 Wigner's Phase-Space Density . 62 4.2.3 Q Function . 65 4.2.4 R Representation . 67 4.2.5 Generalized P Representations . 68 4.2.6 Positive P Representation . 71 Exercises . 72 References . 72 Quantum Phenomena in Simple Systems in Nonlinear Optics . 73 5.1 Single-Mode Quantum Statistics . 73 5.1.1 Degenerate Parametric Amplifier . 73 5.1.2 Photon Statistics . 75 5.1.3 Wigner Function . 76 5.2 Two-Mode Quantum Correlations . 77 5.2.1 Non-degenerate Parametric Amplifier . 77 5.2.2 Squeezing . 80 5.2.3 Quadrature Correlations and the Einstein-Podolsky-Rosen Paradox . 82 5.2.4 Wigner Function . 83 5.2.5 Reduced Density Operator . 84 5.3 Quantum Limits to Amplification . 86 5.4 Amplitude Squeezed State with Poisson Photon Number Statistics . 88 Exercises . 91 References . 91 Stochastic Methods . 93 6.1 Master Equation . 93 6.2 Equivalent с -Number Equations . 99 6.2.1 Photon Number Representation . 99 6.2.2 P Representation . 100 6.2.3 Properties of Fokker— Planck Equations . 102 6.2.4 Steady State Solutions - Potential Conditions . 103 6.2.5 Time Dependent Solution . 104 Contents 6.2.6 Q Representation .105 6.2.7 Wigner Function .107 6.2.8 Generalized P Representation .109 6.3 Stochastic Differential Equations .112 6.3.1 Use of the Positive P Representation .115 6.4 Linear Processes with Constant Diffusion .116 6.5 Two Time Correlation Functions in Quantum Markov Processes . 117 6.5.1 Quantum Regression Theorem .118 6.6 Application to Systems with a P Representation .118 6.7 Stochastic Unravellings .119 6.7.1 Simulating Quantum Trajectories .123 Exercises .124 References .125 Further Reading .125 Input-Output Formulation of Optical Cavities .127 7.1 Cavity Modes .127 7.2 Linear Systems .131 7.3 Two-Sided Cavity .132 7.4 Two Time Correlation Functions .133 7.5 Spectrum of Squeezing .135 7.6 Parametric Oscillator .136 7.7 Squeezing in the Total Field .138 7.8 Fokker-Planck Equation .138 Exercises .141 References .141 Further Reading .141 Generation and Applications of Squeezed Light .143 8.1 Parametric Oscillation and Second Harmonic Generation .143 8.1.1 Semi-Classical Steady States and Stability Analysis .145 8.1.2 Parametric Oscillation .146 8.1.3 Second Harmonic Generation .146 8.1.4 Squeezing Spectrum .147 8.1.5 Parametric Oscillation .148 8.1.6 Experiments .149 8.2 Twin Beam Generation and Intensity Correlations .151 8.2.1 Second Harmonic Generation .156 8.2.2 Experiments .157 8.3 Applications of Squeezed Light .158 8.3.1 Interferometric Detection of Gravitational Radiation .158 8.3.2 Sub-Shot-Noise Phase Measurements .171 8.3.3 Quantum Information .173 Exercises .174 χ Contents References .174 Further Reading .175 9 Nonlinear Quantum Dissipative Systems .177 9.1 Optical Parametric Oscillator: Complex Ρ Function .177 9.2 Optical Parametric Oscillator: Positive Ρ Function .181 9.3 Quantum Tunnelling Time .186 9.4 Dispersive Optical Bistability .190 9.5 Comment on the Use of the Q and Wigner Representations .192 Exercises .192 9.A Appendix .193 9.A. 1 Evaluation of Moments for the Complex P function for Parametric Oscillation (9.17) .193 9.A.2 Evaluation of the Moments for the Complex P Function for Optical Bistability (9.48).194 References .195 Further Reading .195 10 Interaction of Radiation with Atoms .197 10.1 Quantization of the Many-Electron System .197 10.2 Interaction of a Single Two-Level Atom with a Single Mode Field . 201 10.3 Spontaneous Emission from a Two-Level Atom .203 10.4 Phase Decay in a Two-Level System .204 10.5 Resonance Fluorescence .205 Exercises .210 References .210 Further Reading .211 11 CQED .213 11.1 Cavity QED .213 11.1.1 Vacuum Rabi Splitting .217 11.1.2 Single Photon Sources .218 11.1.3 Cavity QED with N Atoms .221 11.2 Circuit QED .225 Exercises .227 References .228 Further Reading .229 12 Quantum Theory of the Laser .231 12.1 Master Equation .231 12.2 Photon Statistics .233 12.2.1 Spectrum of Intensity Fluctuations .234 12.3 Laser Linewidth .237 12.4 Regularly Pumped Laser .238 12.A Appendix: Derivation of the Single-Atom Increment .242 Contents xi Exercises .245 References .245 13 Bells Inequalities in Quantum Optics .247 13.1 The Einstein-Podolsky-Rosen (EPR) Argument .247 13.2 Bell Inequalities and the Aspect Experiment .248 13.3 Violations of Bell's Inequalities Using a Parametric Amplifier Source .254 13.4 One-Photon Interference .259 Exercises .264 References .264 14 Quantum Nondemolition Measurements .267 14.1 Concept of a QND Measurement .268 14.2 Back Action Evasion .270 14.3 Criteria for a QND Measurement .270 14.4 The Beam Splitter .273 14.5 Ideal Quadrature QND Measurements .276 14.6 Experimental Realisation .277 14.7 A Photon Number QND Scheme .279 Exercises .281 References .282 15 Quantum Coherence and Measurement Theory .283 15.1 Quantum Coherence .283 15.2 The Effect of Dissipation .288 15.2.1 Experimental Observation of Coherence Decay .291 15.3 Quantum Measurement Theory .293 15.3.1 General Measurement Theory .294 15.3.2 The Pointer Basis .296 15.4 Examples of Pointer Observables .299 15.5 Model of a Measurement .299 15.6 Conditional States and Quantum Trajectories .302 15.6.1 Homodyne Measurement of a Cavity Field .303 Exercises .305 References .306 16 Quantum Information .307 16.1 Introduction .307 16.1.1 The Qubit .308 16.1.2 Entanglement .310 16.2 Quantum Key Distribution .312 16.3 Quantum Teleportation .318 16.4 Quantum Computation .324 16.4.1 Linear Optical Quantum Gates .327 16.4.2 Single Photon Sources .336 Exercises .343 xii Contents References .344 Further Reading .346 17 Ion Traps .347 17.1 Introduction .347 17.2 Trapping and Cooling .347 17.3 Novel Quantum States .353 17.4 Trapping Multiple Ions .356 17.5 Ion Trap Quantum Information Processing .359 Exercises .362 References .363 18 Light Forces .365 18.1 Radiative Forces in the Semiclassical Limit .366 18.2 Mean Force for a Two-Level Atom Initially at Rest .368 18.3 Friction Force for a Moving Atom .371 18.3.1 Laser Standing Wave— Doppler Cooling .372 18.4 Dressed State Description of the Dipole Force .374 18.5 Atomic Diffraction by a Standing Wave .377 18.6 Optical Stern-Gerlach Effect .381 18.7 Quantum Chaos .385 18.7.1 Dynamical Tunnelling .387 18.7.2 Dynamical Localisation .389 18.8 The Effect of Spontaneous Emission .390 References .394 Further Reading .395 19 Bose-Einstein Condensation .397 19.1 Hamiltonian: Binary Collision Model .398 19.2 Mean-Field Theory — Gross-Pitaevskii Equation .399 19.3 Single Mode Approximation .400 19.4 Quantum State of the Condensate .401 19.5 Quantum Phase Diffusion: Collapses and Revivals of the Condensate Phase .401 19.6 Interference of Two Bose-Einstein Condensates and Measurement-Induced Phase .405 19.6.1 Interference of Two Condensates Initially in Number States .405 19.7 Quantum Tunneling of a Two Component Condensate .409 19.7.1 Semiclassical Dynamics .411 19.7.2 Quantum Dynamics .414 19.8 Coherence Properties of Bose-Einstein Condensates .416 19.8.1 1st Order Coherence .416 19.8.2 Higher Order Coherence .417 Exercises .419 References .419 Further Reading .420 Index .421
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id	DE-604.BV021738741
illustrated	Illustrated
index_date	2024-07-02T15:28:43Z
indexdate	2024-07-09T20:42:54Z
institution	BVB
isbn	3540285733 9783540285731
language	English
oai_aleph_id	oai:aleph.bib-bvb.de:BVB01-014952139
oclc_num	254897076
open_access_boolean
owner	DE-20 DE-19 DE-BY-UBM DE-29T DE-703 DE-355 DE-BY-UBR DE-92 DE-83 DE-91G DE-BY-TUM DE-11 DE-634 DE-188 DE-384
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physical	xii, 425 Seiten Illustrationen, Diagramme
publishDate	2008
publishDateSearch	2008
publishDateSort	2008
publisher	Springer
record_format	marc
spelling	Walls, Daniel F. 1942-1999 Verfasser (DE-588)133792021 aut Quantum optics D. F. Walls ; Gerard J. Milburn 2nd edition Berlin ; Heidelberg Springer 2008 xii, 425 Seiten Illustrationen, Diagramme txt rdacontent n rdamedia nc rdacarrier Quantenoptik Quantum optics Quantenoptik (DE-588)4047990-0 gnd rswk-swf (DE-588)4123623-3 Lehrbuch gnd-content Quantenoptik (DE-588)4047990-0 s DE-604 Milburn, Gerard J. 1958- Verfasser (DE-588)11374806X aut Erscheint auch als Online-Ausgabe 978-3-540-28574-8 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014952139&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis
spellingShingle	Walls, Daniel F. 1942-1999 Milburn, Gerard J. 1958- Quantum optics Quantenoptik Quantum optics Quantenoptik (DE-588)4047990-0 gnd
subject_GND	(DE-588)4047990-0 (DE-588)4123623-3
title	Quantum optics
title_auth	Quantum optics
title_exact_search	Quantum optics
title_exact_search_txtP	Quantum optics
title_full	Quantum optics D. F. Walls ; Gerard J. Milburn
title_fullStr	Quantum optics D. F. Walls ; Gerard J. Milburn
title_full_unstemmed	Quantum optics D. F. Walls ; Gerard J. Milburn
title_short	Quantum optics
title_sort	quantum optics
topic	Quantenoptik Quantum optics Quantenoptik (DE-588)4047990-0 gnd
topic_facet	Quantenoptik Quantum optics Lehrbuch
url	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014952139&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
work_keys_str_mv	AT wallsdanielf quantumoptics AT milburngerardj quantumoptics

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