Availability: Electromagnetic noise and quantum optical measurements

Electromagnetic noise and quantum optical measurements: with 117 problems ; with 41 selected solutions

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Bibliographic Details
Main Author:	Haus, Hermann A. 1925- (Author)
Format:	Book
Language:	English
Published:	Berlin [u.a.] Springer 2000
Series:	Advanced texts in physics Physics and astronomy online library
Subjects:	Optoelektronik - Rauschen Quantenoptik - Rauschen Electromagnetic noise > Measurement Electronic circuits > Noise Interference (Light) Optoelectronic devices > Noise Quantum optics > Measurement Optische Messung Optoelektronik Quantenoptik Elektromagnetische Strahlung Rauschen
Links:	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008866909&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
Physical Description:	XV, 562 S. Ill., graph. Darst.
ISBN:	3540652728

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Record in the Search Index

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adam_text	CONTENTS INTRODUCTION :::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 1 1. MAXWELLS EQUATIONS, POWER, AND ENERGY ::::::::::::::::: 11 1.1 MAXWELLS FIELD EQUATIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 1.2 POYNTINGS THEOREM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 1.3 ENERGY AND POWER RELATIONS AND SYMMETRY OF THE TENSOR . 17 1.4 UNIQUENESS THEOREM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 1.5 THE COMPLEX MAXWELLS EQUATIONS . . . . . . . . . . . . . . . . . . . . . . . 23 1.6 OPERATIONS WITH COMPLEX VECTORS . . . . . . . . . . . . . . . . . . . . . . . 25 1.7 THE COMPLEX POYNTING THEOREM . . . . . . . . . . . . . . . . . . . . . . . . 28 1.8 THE RECIPROCITY THEOREM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 1.9 SUMMARY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 PROBLEMS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 SOLUTIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 2. WAVEGUIDES AND RESONATORS :::::::::::::::::::::::::::::: 39 2.1 THE FUNDAMENTAL EQUATIONS OF HOMOGENEOUS ISOTROPIC WAVEGUIDES . . . . . . . . . . . . . . . . . . . . 39 2.2 TRANSVERSE ELECTROMAGNETIC WAVES . . . . . . . . . . . . . . . . . . . . . . . 44 2.3 TRANSVERSE MAGNETIC WAVES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 2.4 TRANSVERSE ELECTRIC WAVES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 2.4.1 MODE EXPANSIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56 2.5 ENERGY, POWER, AND ENERGY VELOCITY . . . . . . . . . . . . . . . . . . . . . . 59 2.5.1 THE ENERGY THEOREM . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 2.5.2 ENERGY VELOCITY AND GROUP VELOCITY . . . . . . . . . . . . . . . 60 2.5.3 ENERGY RELATIONS FOR WAVEGUIDE MODES . . . . . . . . . . . . . 61 2.5.4 A PERTURBATION EXAMPLE . . . . . . . . . . . . . . . . . . . . . . . . . 62 2.6 THE MODES OF A CLOSED CAVITY . . . . . . . . . . . . . . . . . . . . . . . . . . . 64 2.7 REAL CHARACTER OF EIGENVALUES AND ORTHOGONALITY OF MODES . 67 2.8 ELECTROMAGNETIC FIELD INSIDE A CLOSED CAVITY WITH SOURCES . . 72 2.9 ANALYSIS OF OPEN CAVITY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74 2.10 OPEN CAVITY WITH SINGLE INPUT . . . . . . . . . . . . . . . . . . . . . . . . . . 77 2.10.1 THE RESONATOR AND THE ENERGY THEOREM. . . . . . . . . . . . 78 VI CONTENTS 2.10.2 PERTURBATION THEORY AND THE GENERIC FORM OF THE IMPEDANCE EXPRESSION . . . . . . . . . . . . . . . . . . . . . . 79 2.11 RECIPROCAL MULTIPORTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83 2.12 SIMPLE MODEL OF RESONATOR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84 2.13 COUPLING BETWEEN TWO RESONATORS . . . . . . . . . . . . . . . . . . . . . . . 88 2.14 SUMMARY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91 PROBLEMS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92 SOLUTIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95 3. DIRACTION, DIELECTRIC WAVEGUIDES, OPTICAL FIBERS, AND THE KERR EECT ::::::::::::::::::::::::::::::::::::::: 99 3.1 FREE-SPACE PROPAGATION AND DIRACTION. . . . . . . . . . . . . . . . . . . 100 3.2 MODES IN A CYLINDRICAL PIECEWISE UNIFORM DIELECTRIC . . . . . . . 106 3.3 APPROXIMATE APPROACH . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109 3.4 PERTURBATION THEORY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113 3.5 PROPAGATION ALONG A DISPERSIVE FIBER . . . . . . . . . . . . . . . . . . . . 113 3.6 SOLUTION OF THE DISPERSION EQUATION FOR A GAUSSIAN PULSE . . . 115 3.7 PROPAGATION OF A POLARIZED WAVE IN AN ISOTROPIC KERR MEDIUM . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117 3.7.1 CIRCULAR POLARIZATION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119 3.8 SUMMARY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120 PROBLEMS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120 SOLUTIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123 4. SHOT NOISE AND THERMAL NOISE :::::::::::::::::::::::::::: 127 4.1 THE SPECTRUM OF SHOT NOISE . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128 4.2 THE PROBABILITY DISTRIBUTION OF SHOT NOISE EVENTS . . . . . . . . . 134 4.3 THERMAL NOISE IN WAVEGUIDES AND TRANSMISSION LINES . . . . . . 136 4.4 THE NOISE OF A LOSSLESS RESONATOR . . . . . . . . . . . . . . . . . . . . . . . 140 4.5 THE NOISE OF A LOSSY RESONATOR . . . . . . . . . . . . . . . . . . . . . . . . . 143 4.6 LANGEVIN SOURCES IN A WAVEGUIDE WITH LOSS . . . . . . . . . . . . . . . 144 4.7 LOSSY LINEAR MULTIPORTS AT THERMAL EQUILIBRIUM . . . . . . . . . . 146 4.8 THE PROBABILITY DISTRIBUTION OF PHOTONS AT THERMAL EQUILIBRIUM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150 4.9 GAUSSIAN AMPLITUDE DISTRIBUTION OF THERMAL EXCITATIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152 4.10 SUMMARY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154 PROBLEMS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155 SOLUTIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 156 5. LINEAR NOISY MULTIPORTS :::::::::::::::::::::::::::::::::: 157 5.1 AVAILABLE AND EXCHANGEABLE POWER FROM A SOURCE . . . . . . . . . . 159 5.2 THE STATIONARY VALUES OF THE POWER DELIVERED BY A NOISY MULTIPORT AND THE CHARACTERISTIC NOISE MATRIX . . 160 CONTENTS VII 5.3 THE CHARACTERISTIC NOISE MATRIX IN THE ADMITTANCE REPRESENTATION APPLIED TO A FIELD EECT TRANSISTOR . . . . . . . . . . . . . . . . . . . . . . 166 5.4 TRANSFORMATIONS OF THE CHARACTERISTIC NOISE MATRIX . . . . . . . . 168 5.5 SIMPLIED GENERIC FORMS OF THE CHARACTERISTIC NOISE MATRIX. 172 5.6 NOISE MEASURE OF AN AMPLIER . . . . . . . . . . . . . . . . . . . . . . . . . . . 175 5.6.1 EXCHANGEABLE POWER . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175 5.6.2 NOISE FIGURE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 176 5.6.3 EXCHANGEABLE POWER GAIN . . . . . . . . . . . . . . . . . . . . . . . . 177 5.6.4 THE NOISE MEASURE AND ITS OPTIMUM VALUE . . . . . . . . . 179 5.7 THE NOISE MEASURE IN TERMS OF INCIDENT AND REFLECTED WAVES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181 5.7.1 THE EXCHANGEABLE POWER GAIN . . . . . . . . . . . . . . . . . . . . 183 5.7.2 EXCESS NOISE FIGURE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 184 5.8 REALIZATION OF OPTIMUM NOISE PERFORMANCE . . . . . . . . . . . . . . . 185 5.9 CASCADING OF AMPLIERS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 189 5.10 SUMMARY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 190 PROBLEMS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192 SOLUTIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193 6. QUANTUM THEORY OF WAVEGUIDES AND RESONATORS :::::::::: 197 6.1 QUANTUM THEORY OF THE HARMONIC OSCILLATOR . . . . . . . . . . . . . . 198 6.2 ANNIHILATION AND CREATION OPERATORS . . . . . . . . . . . . . . . . . . . . . 203 6.3 COHERENT STATES OF THE ELECTRIC FIELD . . . . . . . . . . . . . . . . . . . . . 205 6.4 COMMUTATOR BRACKETS, HEISENBERGS UNCERTAINTY PRINCIPLE AND NOISE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 209 6.5 QUANTUM THEORY OF AN OPEN RESONATOR . . . . . . . . . . . . . . . . . . 211 6.6 QUANTIZATION OF EXCITATIONS ON A SINGLE-MODE WAVEGUIDE . . . 215 6.7 QUANTUM THEORY OF WAVEGUIDES WITH LOSS . . . . . . . . . . . . . . . . 217 6.8 THE QUANTUM NOISE OF AN AMPLIER WITH A PERFECTLY INVERTED MEDIUM . . . . . . . . . . . . . . . . . . . . . . . 220 6.9 THE QUANTUM NOISE OF AN IMPERFECTLY INVERTED AMPLIER MEDIUM . . . . . . . . . . . . . . 223 6.10 NOISE IN A FIBER WITH LOSS COMPENSATED BY GAIN . . . . . . . . . . 226 6.11 THE LOSSY RESONATOR AND THE LASER BELOW THRESHOLD . . . . . . . 229 6.12 SUMMARY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 237 PROBLEMS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 238 SOLUTIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 239 7. CLASSICAL AND QUANTUM ANALYSIS OF PHASE-INSENSITIVE SYSTEMS :::::::::::::::::::::::::::::: 241 7.1 RENORMALIZATION OF THE CREATION AND ANNIHILATION OPERATORS 242 7.2 LINEAR LOSSLESS MULTIPORTS IN THE CLASSICAL AND QUANTUM DOMAINS . . . . . . . . . . . . . . . . . . . 243 VIII CONTENTS 7.3 COMPARISON OF THE SCHR¨ ODINGER AND HEISENBERG FORMULATIONS OF LOSSLESS LINEAR MULTIPORTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . 248 7.4 THE SCHR¨ ODINGER FORMULATION AND ENTANGLED STATES . . . . . . . . 251 7.5 TRANSFORMATION OF COHERENT STATES . . . . . . . . . . . . . . . . . . . . . . . 254 7.6 CHARACTERISTIC FUNCTIONS AND PROBABILITY DISTRIBUTIONS . . . . . 256 7.6.1 COHERENT STATE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 256 7.6.2 BOSE{EINSTEIN DISTRIBUTION. . . . . . . . . . . . . . . . . . . . . . . . 258 7.7 TWO-DIMENSIONAL CHARACTERISTIC FUNCTIONS AND THE WIGNER DISTRIBUTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . 259 7.8 THE SCHR¨ ODINGER CAT STATE AND ITS WIGNER DISTRIBUTION . . . . 263 7.9 PASSIVE AND ACTIVE MULTIPORTS . . . . . . . . . . . . . . . . . . . . . . . . . . . 267 7.10 OPTIMUM NOISE MEASURE OF A QUANTUM NETWORK . . . . . . . . . . . 272 7.11 SUMMARY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 276 PROBLEMS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 277 SOLUTIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 278 8. DETECTION ::::::::::::::::::::::::::::::::::::::::::::::::: 281 8.1 CLASSICAL DESCRIPTION OF SHOT NOISE AND HETERODYNE DETECTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 282 8.2 BALANCED DETECTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 285 8.3 QUANTUM DESCRIPTION OF DIRECT DETECTION . . . . . . . . . . . . . . . . . 288 8.4 QUANTUM THEORY OF BALANCED HETERODYNE DETECTION . . . . . . . 290 8.5 LINEARIZED ANALYSIS OF HETERODYNE DETECTION . . . . . . . . . . . . . . 292 8.6 HETERODYNE DETECTION OF A MULTIMODAL SIGNAL . . . . . . . . . . . . . 295 8.7 HETERODYNE DETECTION WITH FINITE RESPONSE TIME OF DETECTOR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 296 8.8 THE NOISE PENALTY OF A SIMULTANEOUS MEASUREMENT OF TWO NONCOMMUTING OBSERVABLES . . . . . . . . . . . . . . . . . . . . . . 298 8.9 SUMMARY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 300 PROBLEMS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 301 SOLUTIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 302 9. PHOTON PROBABILITY DISTRIBUTIONS AND BIT-ERROR RATE OF A CHANNEL WITH OPTICAL PREAMPLICATION ::::::::::::::: 305 9.1 MOMENT GENERATING FUNCTIONS . . . . . . . . . . . . . . . . . . . . . . . . . . 305 9.1.1 POISSON DISTRIBUTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 308 9.1.2 BOSE{EINSTEIN DISTRIBUTION. . . . . . . . . . . . . . . . . . . . . . . . 308 9.1.3 COMPOSITE PROCESSES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 309 9.2 STATISTICS OF ATTENUATION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 311 9.3 STATISTICS OF OPTICAL PREAMPLICATION WITH PERFECT INVERSION . 314 9.4 STATISTICS OF OPTICAL PREAMPLICATION WITH INCOMPLETE INVERSION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 320 9.5 BIT-ERROR RATE WITH OPTICAL PREAMPLICATION . . . . . . . . . . . . . . 324 9.5.1 NARROW-BAND FILTER, POLARIZED SIGNAL, AND NOISE . . . . . 324 9.5.2 BROADBAND FILTER, UNPOLARIZED SIGNAL . . . . . . . . . . . . . . 327 CONTENTS IX 9.6 NEGENTROPY AND INFORMATION . . . . . . . . . . . . . . . . . . . . . . . . . . . . 330 9.7 THE NOISE FIGURE OF OPTICAL AMPLIERS . . . . . . . . . . . . . . . . . . . 333 9.8 SUMMARY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 339 PROBLEMS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 340 SOLUTIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 342 10. SOLITONS AND LONG-DISTANCE FIBER COMMUNICATIONS ::::::: 345 10.1 THE NONLINEAR SCHR¨ ODINGER EQUATION . . . . . . . . . . . . . . . . . . . . . 346 10.2 THE FIRST-ORDER SOLITON . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 348 10.3 PROPERTIES OF SOLITONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 352 10.4 PERTURBATION THEORY OF SOLITONS . . . . . . . . . . . . . . . . . . . . . . . . . 354 10.5 AMPLIER NOISE AND THE GORDON{HAUS EECT . . . . . . . . . . . . . . 357 10.6 CONTROL FILTERS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 361 10.7 ERBIUM-DOPED FIBER AMPLIERS AND THE EECT OF LUMPED GAIN . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 365 10.8 POLARIZATION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 367 10.9 CONTINUUM GENERATION BY SOLITON PERTURBATION . . . . . . . . . . . . 370 10.10 SUMMARY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 374 PROBLEMS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 376 SOLUTIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 377 11. PHASE-SENSITIVE AMPLICATION AND SQUEEZING ::::::::::::: 379 11.1 CLASSICAL ANALYSIS OF PARAMETRIC AMPLICATION. . . . . . . . . . . . . 380 11.2 QUANTUM ANALYSIS OF PARAMETRIC AMPLICATION . . . . . . . . . . . . 383 11.3 THE NONDEGENERATE PARAMETRIC AMPLIER AS A MODEL OF A LINEAR PHASE-INSENSITIVE AMPLIER . . . . . . . . . . . . . . . . . . . 386 11.4 CLASSICAL ANALYSIS OF DEGENERATE PARAMETRIC AMPLIER . . . . . . . . . . . . . . . . . . . . . . 387 11.5 QUANTUM ANALYSIS OF DEGENERATE PARAMETRIC AMPLIER . . . . . . . . . . . . . . . . . . . . . . 390 11.6 SQUEEZED VACUUM AND ITS HOMODYNE DETECTION . . . . . . . . . . . 393 11.7 PHASE MEASUREMENT WITH SQUEEZED VACUUM . . . . . . . . . . . . . . . 395 11.8 THE LASER RESONATOR ABOVE THRESHOLD . . . . . . . . . . . . . . . . . . . 398 11.9 THE FLUCTUATIONS OF THE PHOTON NUMBER . . . . . . . . . . . . . . . . . . 403 11.10 THE SCHAWLOW{TOWNES LINEWIDTH . . . . . . . . . . . . . . . . . . . . . . . . 406 11.11 SQUEEZED RADIATION FROM AN IDEAL LASER . . . . . . . . . . . . . . . . . . 408 11.12 SUMMARY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 412 PROBLEMS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 413 SOLUTIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 414 12. SQUEEZING IN FIBERS ::::::::::::::::::::::::::::::::::::::: 417 12.1 QUANTIZATION OF NONLINEAR WAVEGUIDE . . . . . . . . . . . . . . . . . . . . 418 12.2 THE X REPRESENTATION OF OPERATORS . . . . . . . . . . . . . . . . . . . . . . 420 12.3 THE QUANTIZED EQUATION OF MOTION OF THE KERR EECT IN THE X REPRESENTATION. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 422 X CONTENTS 12.4 SQUEEZING . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 424 12.5 GENERATION OF SQUEEZED VACUUM WITH A NONLINEAR INTERFEROMETER . . . . . . . . . . . . . . . . . . . . . . . . . 427 12.6 SQUEEZING EXPERIMENT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 432 12.7 GUIDED-ACOUSTIC-WAVE BRILLOUIN SCATTERING . . . . . . . . . . . . . . . 434 12.8 PHASE MEASUREMENT BELOW THE SHOT NOISE LEVEL . . . . . . . . . . . 436 12.9 GENERATION OF SCHR¨ ODINGER CAT STATE VIA KERR EECT . . . . . . . 440 12.10 SUMMARY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 442 PROBLEMS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 442 SOLUTIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 443 13. QUANTUM THEORY OF SOLITONS AND SQUEEZING ::::::::::::::: 445 13.1 THE HAMILTONIAN AND EQUATIONS OF MOTION OF A DISPERSIVE WAVEGUIDE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 446 13.2 THE QUANTIZED NONLINEAR SCHR¨ ODINGER EQUATION AND ITS LINEARIZATION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 449 13.3 SOLITON PERTURBATIONS PROJECTED BY THE ADJOINT . . . . . . . . . . . . 453 13.4 RENORMALIZATION OF THE SOLITON OPERATORS . . . . . . . . . . . . . . . . . 457 13.5 MEASUREMENT OF OPERATORS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 461 13.6 PHASE MEASUREMENT WITH SOLITON-LIKE PULSES. . . . . . . . . . . . . . . 462 13.7 SOLITON SQUEEZING IN A FIBER . . . . . . . . . . . . . . . . . . . . . . . . . . . . 465 13.8 SUMMARY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 469 PROBLEMS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 471 SOLUTIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 472 14. QUANTUM NONDEMOLITION MEASUREMENTS AND THE COLLAPSE OF THE WAVE FUNCTION ::::::::::::::::::::::::::::::::::::: 473 14.1 GENERAL PROPERTIES OF A QND MEASUREMENT . . . . . . . . . . . . . . . 475 14.2 A QND MEASUREMENT OF PHOTON NUMBER . . . . . . . . . . . . . . . . . 475 14.3 WHICH PATH EXPERIMENT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 481 14.4 THE COLLAPSE OF THE DENSITY MATRIX . . . . . . . . . . . . . . . . . . . . 484 14.5 TWO QUANTUM NONDEMOLITION MEASUREMENTS IN CASCADE . . . . 490 14.6 THE SCHR¨ ODINGER CAT THOUGHT EXPERIMENT . . . . . . . . . . . . . . . . 493 14.7 SUMMARY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 497 PROBLEMS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 498 SOLUTIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 499 EPILOGUE :::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 503 APPENDICES :::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 505 A.1 PHASE VELOCITY AND GROUP VELOCITY OF A GAUSSIAN BEAM . . . . 505 A.2 THE HERMITE GAUSSIANS AND THEIR DENING EQUATION . . . . . . . 506 A.2.1 THE DENING EQUATION OF HERMITE GAUSSIANS . . . . . . . . 506 A.2.2 ORTHOGONALITY PROPERTY OF HERMITE GAUSSIAN MODES. . 507 CONTENTS XI A.2.3 THE GENERATING FUNCTION AND CONVOLUTIONS OF HERMITE GAUSSIANS . . . . . . . . . . . . . . . . . . . . . . . . . . . . 508 A.3 RECURSION RELATIONS OF BESSEL FUNCTIONS . . . . . . . . . . . . . . . . . . 512 A.4 BRIEF REVIEW OF STATISTICAL FUNCTION THEORY . . . . . . . . . . . . . . . 513 A.5 THE DIERENT NORMALIZATIONS OF FIELD AMPLITUDES AND OF ANNIHILATION OPERATORS . . . . . . . . . . . . . . . . . . . . . . . . . . . 515 A.5.1 NORMALIZATION OF CLASSICAL FIELD AMPLITUDES . . . . . . . . 515 A.5.2 NORMALIZATION OF QUANTUM OPERATORS . . . . . . . . . . . . . . 516 A.6 TWO ALTERNATIVE EXPRESSIONS FOR THE NYQUIST SOURCE . . . . . . . 517 A.7 WAVE FUNCTIONS AND OPERATORS IN THE N REPRESENTATION . . . . . 518 A.8 HEISENBERGS UNCERTAINTY PRINCIPLE . . . . . . . . . . . . . . . . . . . . . . . 523 A.9 THE QUANTIZED OPEN-RESONATOR EQUATIONS . . . . . . . . . . . . . . . . 524 A.10 DENSITY MATRIX AND CHARACTERISTIC FUNCTIONS . . . . . . . . . . . . . . 527 A.10.1 EXAMPLE 1. DENSITY MATRIX OF BOSE{EINSTEIN STATE . . . 528 A.10.2 EXAMPLE 2. DENSITY MATRIX OF COHERENT STATE . . . . . . . 528 A.11 PHOTON STATES AND BEAM SPLITTERS . . . . . . . . . . . . . . . . . . . . . . . 529 A.12 THE BAKER{HAUSDOR THEOREM . . . . . . . . . . . . . . . . . . . . . . . . . . 530 A.12.1 THEOREM 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 530 A.12.2 THEOREM 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 531 A.12.3 MATRIX FORM OF THEOREM 1 . . . . . . . . . . . . . . . . . . . . . . . 531 A.12.4 MATRIX FORM OF THEOREM 2 . . . . . . . . . . . . . . . . . . . . . . . 532 A.13 THE WIGNER FUNCTION OF POSITION AND MOMENTUM . . . . . . . . . . 533 A.14 THE SPECTRUM OF NON-RETURN-TO-ZERO MESSAGES . . . . . . . . . . . . 535 A.15 VARIOUS TRANSFORMS OF HYPERBOLIC SECANTS . . . . . . . . . . . . . . . . 538 A.16 THE NOISE SOURCES DERIVED FROM A LOSSLESS MULTIPORT WITH SUPPRESSED TERMINALS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 541 A.17 THE NOISE SOURCES OF AN ACTIVE SYSTEM DERIVED FROM SUPPRESSION OF PORTS . . . . . . . . . . . . . . . . . . . . . . . 542 A.18 THE TRANSLATION OPERATOR AND THE TRANSFORMATION OF COHERENT STATES FROM THE * REPRESENTATION TO THE X REPRESENTATION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 543 A.19 THE HEISENBERG EQUATION IN THE PRESENCE OF DISPERSION . . . . . 544 A.20 GAUSSIAN DISTRIBUTIONS AND THEIR E * 1 = 2 LOCI . . . . . . . . . . . . . . 544 REFERENCES :::::::::::::::::::::::::::::::::::::::::::::::::::: 549 INDEX ::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 555
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author	Haus, Hermann A. 1925-
author_GND	(DE-588)121645495
author_facet	Haus, Hermann A. 1925-
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series2	Advanced texts in physics Physics and astronomy online library
spellingShingle	Haus, Hermann A. 1925- Electromagnetic noise and quantum optical measurements with 117 problems ; with 41 selected solutions Optoelektronik - Rauschen Quantenoptik - Rauschen Electromagnetic noise Measurement Electronic circuits Noise Interference (Light) Optoelectronic devices Noise Quantum optics Measurement Optische Messung (DE-588)4121429-8 gnd Optoelektronik (DE-588)4043687-1 gnd Quantenoptik (DE-588)4047990-0 gnd Elektromagnetische Strahlung (DE-588)4014297-8 gnd Rauschen (DE-588)4048606-0 gnd
subject_GND	(DE-588)4121429-8 (DE-588)4043687-1 (DE-588)4047990-0 (DE-588)4014297-8 (DE-588)4048606-0
title	Electromagnetic noise and quantum optical measurements with 117 problems ; with 41 selected solutions
title_auth	Electromagnetic noise and quantum optical measurements with 117 problems ; with 41 selected solutions
title_exact_search	Electromagnetic noise and quantum optical measurements with 117 problems ; with 41 selected solutions
title_full	Electromagnetic noise and quantum optical measurements with 117 problems ; with 41 selected solutions Hermann A. Haus
title_fullStr	Electromagnetic noise and quantum optical measurements with 117 problems ; with 41 selected solutions Hermann A. Haus
title_full_unstemmed	Electromagnetic noise and quantum optical measurements with 117 problems ; with 41 selected solutions Hermann A. Haus
title_short	Electromagnetic noise and quantum optical measurements
title_sort	electromagnetic noise and quantum optical measurements with 117 problems with 41 selected solutions
title_sub	with 117 problems ; with 41 selected solutions
topic	Optoelektronik - Rauschen Quantenoptik - Rauschen Electromagnetic noise Measurement Electronic circuits Noise Interference (Light) Optoelectronic devices Noise Quantum optics Measurement Optische Messung (DE-588)4121429-8 gnd Optoelektronik (DE-588)4043687-1 gnd Quantenoptik (DE-588)4047990-0 gnd Elektromagnetische Strahlung (DE-588)4014297-8 gnd Rauschen (DE-588)4048606-0 gnd
topic_facet	Optoelektronik - Rauschen Quantenoptik - Rauschen Electromagnetic noise Measurement Electronic circuits Noise Interference (Light) Optoelectronic devices Noise Quantum optics Measurement Optische Messung Optoelektronik Quantenoptik Elektromagnetische Strahlung Rauschen
url	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008866909&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
work_keys_str_mv	AT haushermanna electromagneticnoiseandquantumopticalmeasurementswith117problemswith41selectedsolutions

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