Quantum optics in phase space:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin [u.a.]
Wiley-VCH
2001
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| Ausgabe: | 1. ed. |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XX, 695 S. Ill., graph. Darst. |
| ISBN: | 352729435X 9783527294350 |
Internformat
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| 100 | 1 | |a Schleich, Wolfgang |d 1957- |e Verfasser |0 (DE-588)123022126 |4 aut | |
| 245 | 1 | 0 | |a Quantum optics in phase space |c Wolfgang P. Schleich |
| 250 | |a 1. ed. | ||
| 264 | 1 | |a Berlin [u.a.] |b Wiley-VCH |c 2001 | |
| 300 | |a XX, 695 S. |b Ill., graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 650 | 4 | |a Espace des phases (Physique statistique) | |
| 650 | 4 | |a Optique quantique | |
| 650 | 4 | |a Phase space (Statistical physics) | |
| 650 | 4 | |a Quantum optics | |
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Datensatz im Suchindex
| _version_ | 1804126095385034752 |
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| adam_text | WOLFGANG P. SCHLEICH QUANTUM OPTICS IN PHASE SPACE )WILEY-VCH BERLIN *
WEINHEIM * NEW YORK * CHICHESTER * BRISBANE * SINGAPORE * TORONTO
CONTENTS 1 WHAT S QUANTUM OPTICS? 1 1.1 ON THE ROAD TO QUANTUM OPTICS 1
1.2 RESONANCE FLUORESCENCE 2 1.2.1 ELASTIC PEAK: LIGHT AS A WAVE 2 1.2.2
MOLLOW-THREE-PEAK SPECTRUM 3 1.2.3 ANTI-BUNCHING 5 1.3 SQUEEZING THE
FLUCTUATIONS 7 1.3.1 WHAT IS A SQUEEZED STATE? 7 1.3.2 SQUEEZED STATES
IN THE OPTICAL PARAMETRIC OSCILLATOR .... 9 1.3.3 OSCILLATORY PHOTON
STATISTICS 12 1.3.4 INTERFERENCE IN PHASE SPACE 13 1.4
JAYNES-CUMMINGS-PAUL MODEL 14 1.4.1 SINGLE TWO-LEVEL ATOM PLUS A SINGLE
MODE 15 1.4.2 TIME SCALES 15 1.5 CAVITY QED 16 1.5.1 AN AMAZING MASER 16
1.5.2 CAVITY QED IN THE OPTICAL DOMAIN 19 1.6 DE BROGLIE OPTICS 22 1.6.1
ELECTRON AND NEUTRON OPTICS 22 1.6.2 ATOM OPTICS 23 1.6.3 ATOM OPTICS IN
QUANTIZED LIGHT FIELDS 25 1.7 QUANTUM MOTION IN PAUL TRAPS 26 1.7.1
ANALOGY TO CAVITY QED 26 1.7.2 QUANTUM INFORMATION PROCESSING 26 1.8
TWO-PHOTON INTERFEROMETRY AND MORE 28 1.9 OUTLINE OF THE BOOK 29 2 ANTE
35 2.1 POSITION AND MOMENTUM EIGENSTATES 36 2.1.1 PROPERTIES OF
EIGENSTATES 36 2.1.2 DERIVATIVE OF WAVE FUNCTION 38 2.1.3 FOURIER
TRANSFORM CONNECTS X- AND P-SPACE 39 2.2 ENERGY EIGENSTATE 40 2.2.1
ARBITRARY REPRESENTATION 41 2.2.2 POSITION REPRESENTATION 42 2.3 DENSITY
OPERATOR: A BRIEF INTRODUCTION 44 XII CONTENTS 2.3.1 A STATE VECTOR IS
NOT ENOUGH! 44 2.3.2 DEFINITION AND PROPERTIES 48 2.3.3 TRACE OF
OPERATOR 49 2.3.4 EXAMPLES OF A DENSITY OPERATOR 51 2.4 TIME EVOLUTION
OF QUANTUM STATES 53 2.4.1 MOTION OF A WAVE PACKET 54 2.4.2 TIME
EVOLUTION DUE TO INTERACTION 55 2.4.3 TIME DEPENDENT HAMILTONIAN 57
2.4.4 TIME EVOLUTION OF DENSITY OPERATOR 61 3 WIGNER FUNCTION 67 3.1
JUMP START OF THE WIGNER FUNCTION 68 3.2 PROPERTIES OF THE WIGNER
FUNCTION 69 3.2.1 MARGINALS 69 3.2.2 OVERLAP OF QUANTUM STATES AS
OVERLAP IN PHASE SPACE ... 71 3.2.3 SHAPE OF WIGNER FUNCTION 72 3.3 TIME
EVOLUTION OF WIGNER FUNCTION 74 3.3.1 VON NEUMANN EQUATION IN PHASE
SPACE 74 3.3.2 QUANTUM LIOUVILLE EQUATION 75 3.4 WIGNER FUNCTION
DETERMINED BY PHASE SPACE 76 3.4.1 DEFINITION OF MOYAL FUNCTION 76 3.4.2
PHASE SPACE EQUATIONS FOR MOYAL FUNCTIONS 77 3.5 PHASE SPACE EQUATIONS
FOR ENERGY EIGENSTATES 78 3.5.1 POWER EXPANSION IN PLANCK S CONSTANT 79
3.5.2 MODEL DIFFERENTIAL EQUATION 81 3.6 HARMONIE OSCILLATOR 84 3.6.1
WIGNER FUNCTION AS WAVE FUNCTION 85 3.6.2 PHASE SPACE ENFORCES ENERGY
QUANTIZATION 86 3.7 EVALUATION OF QUANTUM MECHANICAL AVERAGES 87 3.7.1
OPERATOR ORDERING 88 3.7.2 EXAMPLES OF WEYL-WIGNER ORDERING 90 4 QUANTUM
STATES IN PHASE SPACE 99 4.1 ENERGY EIGENSTATE 100 4.1.1 SIMPLE PHASE
SPACE REPRESENTATION 100 4.1.2 LARGE-M LIMIT 101 4.1.3 WIGNER FUNCTION
105 4.2 COHERENT STATE 108 4.2.1 DEFINITION OF A COHERENT STATE 109
4.2.2 ENERGY DISTRIBUTION 110 4.2.3 TIME EVOLUTION 113 4.3 SQUEEZED
STATE 119 4.3.1 DEFINITION OF A SQUEEZED STATE 121 4.3.2 ENERGY
DISTRIBUTION: EXACT TREATMENT 125 4.3.3 ENERGY DISTRIBUTION: ASYMPTOTIC
TREATMENT 128 4.3.4 LIMIT TOWARDS SQUEEZED VACUUM 132 CONTENTS XIII
4.3.5 TIME EVOLUTION 135 4.4 ROTATED QUADRATURE STATES 136 4.4.1 WIGNER
FUNCTION OF POSITION AND MOMENTUM STATES 137 4.4.2 POSITION WAVE
FUNCTION OF ROTATED QUADRATURE STATES . . . 140 4.4.3 WIGNER FUNCTION OF
ROTATED QUADRATURE STATES 142 4.5 QUANTUM STATE RECONSTRUCTION 143 4.5.1
TOMOGRAPHIE CUTS THROUGH WIGNER FUNCTION 143 4.5.2 RADON TRANSFORMATION
144 5 WAVES AE LA WKB 153 5.1 PROBABILITY FOR CLASSICAL MOTION 153 5.2
PROBABILITY AMPLITUDES FOR QUANTUM MOTION 155 5.2.1 AN EDUCATED GUESS
156 5.2.2 RANGE OF VALIDITY OF WKB WAVE FUNCTION 158 5.3 ENERGY
QUANTIZATION 159 5.3.1 DETERMINING THE PHASE 159 5.3.2
BOHR-SOMMERFELD-KRAMERS QUANTIZATION 161 5.4 SUMMARY 163 5.4.1
CONSTRUCTION OF PRIMITIVE WKB WAVE FUNCTION 163 5.4.2 UNIFORM ASYMPTOTIC
EXPANSION 164 6 WKB AND BERRY PHASE 171 6.1 BERRY PHASE AND ADIABATIC
APPROXIMATION 172 6.1.1 ADIABATIC THEOREM 172 6.1.2 ANALYSIS OF
GEOMETRICAL PHASE 174 6.1.3 GEOMETRICAL PHASE AS A FLUX IN HUBERT SPACE
175 6.2 WKB WAVE FUNCTIONS FROM ADIABATICITY 176 6.2.1 ENERGY EIGENVALUE
PROBLEM AS PROPAGATION PROBLEM .... 177 6.2.2 DYNAMICAL AND GEOMETRICAL
PHASE 181 6.2.3 WKB WAVES REDERIVED 183 6.3 NON-ADIABATIC BERRY PHASE
185 6.3.1 DERIVATION OF THE AHARONOV-ANANDAN PHASE 186 6.3.2 TIME
EVOLUTION IN HARMONIE OSCILLATOR 187 7 INTERFERENCE IN PHASE SPACE 189
7.1 OUTLINE OF THE IDEA 189 7.2 DERIVATION OF AREA-OF-OVERLAP FORMALISM
192 7.2.1 JUMPS VIEWED FROM POSITION SPACE 192 7.2.2 JUMPS VIEWED FROM
PHASE SPACE 197 7.3 APPLICATION TO FRANCK-CONDON TRANSITIONS 200 7.4
GENERALIZATION 201 8 APPLICATIONS OF INTERFERENCE IN PHASE SPACE 205 8.1
CONNECTION TO INTERFERENCE IN PHASE SPACE 205 8.2 ENERGY EIGENSTATES 206
8.3 COHERENT STATE 208 8.3.1 ELEMENTARY APPROACH 209 XIV CONTENTS 8.3.2
INFLUENCE OF INTERNAL STRUCTURE 212 8.4 SQUEEZED STATE 213 8.4.1
OSCILLATIONS FROM INTERFERENCE IN PHASE SPACE 213 8.4.2 GIANT
OSCILLATIONS 216 8.4.3 SUMMARY 218 8.5 THE QUESTION OF PHASE STATES 221
8.5.1 AMPLITUDE AND PHASE IN A CLASSICAL OSCILLATOR 221 8.5.2 DEFINITION
OF A PHASE STATE 223 8.5.3 PHASE DISTRIBUTION OF A QUANTUM STATE 227 9
WAVE PACKET DYNAMICS 233 9.1 WHAT ARE WAVE PACKETS? 233 9.2 FRACTIONAL
AND FUELL REVIVALS 234 9.3 NATURAL TIME SCALES 237 9.3.1 HIERARCHY OF
TIME SCALES 237 9.3.2 GENERIC SIGNAL 239 9.4 NEW REPRESENTATIONS OF THE
SIGNAL 241 9.4.1 THE EARLY STAGE OF THE EVOLUTION 241 9.4.2 INTERMEDIATE
TIMES 244 9.5 FRACTIONAL REVIVALS MADE SIMPLE 246 9.5.1 GAUSS SUMS 246
9.5.2 SHAPE FUNCTION 246 10 FIELD QUANTIZATION 255 10.1 WAVE EQUATIONS
FOR THE POTENTIALS 256 10.1.1 DERIVATION OF THE WAVE EQUATIONS 256
10.1.2 GAUGE INVARIANCE OF ELECTRODYNAMICS 257 10.1.3 SOLUTION OF THE
WAVE EQUATION 260 10.2 MODE STRUCTURE IN A BOX 262 10.2.1 SOLUTIONS OF
HELMHOLTZ EQUATION 262 10.2.2 POLARIZATION VECTORS FROM GAUGE CONDITION
263 10.2.3 DISCRETENESS OF MODES FROM BOUNDARIES 264 10.2.4 BOUNDARY
CONDITIONS ON THE MAGNETIC FIELD 264 10.2.5 . ORTHONORMALITY OF MODE
FUNCTIONS 265 10.3 THE FIELD AS A SET OF HARMONIE OSCILLATORS 266 10.3.1
ENERGY IN THE RESONATOR 267 10.3.2 QUANTIZATION OF THE RADIATION FIELD
269 10.4 THE CASIMIR EFFECT 272 10.4.1 ZERO-POINT ENERGY OF A
RECTANGULAR RESONATOR 272 10.4.2 ZERO-POINT ENERGY OF FREE SPACE 274
10.4.3 DIFFERENCE OF TWO INFINITE ENERGIES 275 10.4.4 CASIMIR FORCE:
THEORY AND EXPERIMENT 276 10.5 OPERATORS OF THE VECTOR POTENTIAL AND
FIELDS 278 10.5.1 VECTOR POTENTIAL 278 10.5.2 ELECTRIC FIELD OPERATOR
280 10.5.3 MAGNETIC FIELD OPERATOR , 281 CONTENTS XV 10.6 NUMBER STATES
OF THE RADIATION FIELD 281 10.6.1 PHOTONS AND ANTI-PHOTONS 282 10.6.2
MULTI-MODE CASE 282 10.6.3 SUPERPOSITION AND ENTANGLED STATES 283 11
FIELD STATES 291 11.1 PROPERTIES OF THE QUANTIZED ELECTRIC FIELD 291
11.1.1 PHOTON NUMBER STATES 292 11.1.2 ELECTROMAGNETIC FIELD EIGENSTATES
293 11.2 COHERENT STATES REVISITED 295 11.2.1 EIGENVALUE EQUATION 295
11.2.2 COHERENT STATE AS A DISPLACED VACUUM 297 11.2.3 PHOTON STATISTICS
OF A COHERENT STATE 298 11.2.4 ELECTRIC FIELD DISTRIBUTION OF A COHERENT
STATE 299 11.2.5 OVER-COMPLETENESS OF COHERENT STATES 301 11.2.6
EXPANSION INTO COHERENT STATES 303 11.2.7 ELECTRIC FIELD EXPECTATION
VALUES 305 11.3 SCHROEDINGER CAT STATE 306 11.3.1 THE ORIGINAL CAT
PARADOX 306 11.3.2 DEFINITION OF THE FIELD CAT STATE 307 11.3.3 WIGNER
PHASE SPACE REPRESENTATION 307 11.3.4 PHOTON STATISTICS 310 12 PHASE
SPACE FUNCTIONS 321 12.1 THERE IS MORE THAN WIGNER PHASE SPACE 321
12.1.1 WHO NEEDS PHASE SPACE FUNCTIONS? 321 12.1.2 ANOTHER DESCRIPTION
OF PHASE SPACE 322 12.2 THE HUSIMI-KANO Q-FUNCTION 324 12.2.1 DEFINITION
OF Q-FUNCTION 324 12.2.2 Q-FUNCTIONS OF SPECIFIC QUANTUM STATES 324 12.3
AVERAGES USING PHASE SPACE FUNCTIONS 330 12.3.1 HEURISTIC ARGUMENT 330
12.3.2 RIGOROUS TREATMENT 333 12.4 THE GLAUBER-SUDARSHAN P-DISTRIBUTION
337 12.4.1 DEFINITION OF P-DISTRIBUTION 337 12.4.2 CONNECTION BETWEEN Q-
AND P-FUNCTION 338 12.4.3 P-FUNCTION FROM Q-FUNCTION 339 12.4.4 EXAMPLES
OF P-DISTRIBUTIONS 341 13 OPTICAL INTERFEROMETRY 349 13.1 BEAM SPLITTER
350 13.1.1 CLASSICAL TREATMENT 350 13.1.2 SYMMETRIE BEAM SPLITTER 352
13.1.3 TRANSITION TO QUANTUM MECHANICS 353 13.1.4 TRANSFORMATION OF
QUANTUM STATES 353 13.1.5 COUNT STATISTICS AT THE EXIT PORTS 356 13.2
HOMODYNE DETECTOR 357 XVI CONTENTS 13.2.1 CLASSICAL CONSIDERATIONS 357
13.2.2 QUANTUM TREATMENT 358 13.3 EIGHT-PORT INTERFEROMETER 361 13.3.1
QUANTUM STATE OF THE OUTPUT MODES . , 361 13.3.2 PHOTON COUNT STATISTICS
363 13.3.3 SIMULTANEOUS MEASUREMENT AND EPR 365 13.3.4 Q-FUNCTION
MEASUREMENT 367 13.4 MEASURED PHASE OPERATORS 370 13.4.1 MEASUREMENT OF
CLASSICAL TRIGONOMETRY 370 13.4.2 MEASUREMENT OF QUANTUM TRIGONOMETRY
372 13.4.3 TWO-MODE PHASE OPERATORS 374 14 ATOM-FIELD INTERACTION 381
14.1 HOW TO CONSTRUCT THE INTERACTION? 382 14.2 VECTOR
POTENTIAL-MOMENTUM COUPLING 382 14.2.1 GAUGE PRINCIPLE DETERMINES
MINIMAL COUPLING 383 14.2.2 INTERACTION OF AN ATOM WITH A FIELD 386 14.3
DIPOLE APPROXIMATION 389 14.3.1 EXPANSION OF VECTOR POTENTIAL 389 14.3.2
A-P-INTERACTION . 390 14.3.3 VARIOUS FORMS OF THE A * P INTERACTION 390
14.3.4 HIGHER ORDER CORRECTIONS 392 14.4 ELECTRIC FIELD-DIPOLE
INTERACTION 393 14.4.1 DIPOLE APPROXIMATION 393 14.4.2 ROENTGEN
HAMILTONIANS AND OTHERS 393 14.5 SUBSYSTEMS, INTERACTION AND
ENTANGLEMENT 395 14.6 EQUIVALENCE OF A * P AND R * E 396 14.6.1
CLASSICAL TRANSFORMATION OF LAGRANGIAN 397 14.6.2 QUANTUM MECHANICAL
TREATMENT 399 14.6.3 MATRIX ELEMENTS OF AE * P AND R * 1 399 14.7
EQUIVALENCE OF HAMILTONIANS H M AND H^ 400 14.8 SIMPLE MODEL FOR
ATOM-FIELD INTERACTION 402 14.8.1 DERIVATION OF THE HAMILTONIAN 402
14.8.2 ROTATING-WAVE APPROXIMATION 406 15 JAYNES-CUMMINGS-PAUL MODEL:
DYNAMICS 413 15.1 RESONANT JAYNES-CUMMINGS-PAUL MODEL 413 15.1.1 TIME
EVOLUTION OPERATOR USING OPERATOR ALGEBRA 414 15.1.2 INTERPRETATION OF
TIME EVOLUTION OPERATOR 416 15.1.3 STATE VECTOR OF COMBINED SYSTEM 418
15.1.4 DYNAMICS REPRESENTED IN STATE SPACE 418 15.2 ROLE OF DETUNING 420
15.2.1 ATOMIC AND FIELD STATES 420 15.2.2 RABI EQUATIONS 422 15.3
SOLUTION OF RABI EQUATIONS 423 15.3.1 LAPLACE TRANSFORMATION 424
CONTENTS XVII 15.3.2 INVERSE LAPLACE TRANSFORMATION 425 15.4 DISCUSSION
OF SOLUTION 426 15.4.1 GENERAL CONSIDERATIONS 427 15.4.2 RESONANT CASE
427 15.4.3 FAR OFF-RESONANT CASE 429 16 STATE PREPARATION AND
ENTANGLEMENT 435 16.1 MEASUREMENTS ON ENTANGLED SYSTEMS 435 16.1.1 HOW
TO GET PROBABILITIES 436 16.1.2 STATE OF THE SUBSYSTEM AFTER A
MEASUREMENT 439 16.1.3 EXPERIMENTAL SETUP 440 16.2 COLLAPSE, REVIVALS
AND FRACTIONAL REVIVALS 444 16.2.1 INVERSION AS TOOL FOR MEASURING
INTERNAL DYNAMICS 444 16.2.2 EXPERIMENTS ON COLLAPSE AND REVIVALS 447
16.3 QUANTUM STATE PREPARATION 451 16.3.1 STATE PREPARATION WITH A
DISPERSIVE INTERACTION 451 16.3.2 GENERATION OF SCHROEDINGER CATS 454
16.4 QUANTUM STATE ENGINEERING 454 16.4.1 OUTLINE OF THE METHOD 454
16.4.2 INVERSE PROBLEM 458 16.4.3 EXAMPLE: PREPARATION OF A PHASE STATE
461 17 PAUL TRAP 473 17.1 BASICS OF TRAPPING IONS 474 17.1.1 NO STATIC
TRAPPING IN THREE DIMENSIONS 474 17.1.2 DYNAMICAL TRAPPING 475 17.2
LASER COOLING 479 17.3 MOTION OF AN ION IN A PAUL TRAP 480 17.3.1
REDUCTION TO CLASSICAL PROBLEM 481 17.3.2 MOTION AS A SEQUENCE OF
SQUEEZING AND ROTATIONS 483 17.3.3 DYNAMICS IN WIGNER PHASE SPACE 486
17.3.4 FLOQUET SOLUTION 490 17.4 MODEL HAMILTONIAN 494 17.4.1
TRANSFORMATION TO INTERACTION PICTURE 495 17.4.2 LAMB-DICKE REGIME 496
17.4.3 MULTI-PHONON JAYNES-CUMMINGS-PAUL MODEL 498 17.5 EFFECTIVE
POTENTIAL APPROXIMATION 500 18 DAMPING AND AMPLIFICATION 507 18.1
DAMPING AND AMPLIFICATION OF A CAVITY FIELD 508 18.2 DENSITY OPERATOR OF
A SUBSYSTEM 509 18.2.1 COARSE-GRAINED EQUATION OF MOTION 509 18.2.2 TIME
INDEPENDENT HAMILTONIAN 511 18.3 RESERVOIR OF TWO-LEVEL ATOMS 511 18.3.1
APPROXIMATE TREATMENT 512 18.3.2 DENSITY OPERATOR IN NUMBER
REPRESENTATION 514 18.3.3 EXACT MASTER EQUATION 519 XVIII CONTENTS
18.3.4 SUMMARY 522 18.4 ONE-ATOM MASER 522 18.4.1 DENSITY OPERATOR
EQUATION 523 18.4.2 EQUATION OF MOTION FOR THE PHOTON STATISTICS 524
18.4.3 PHASE DIFFUSION 529 18.5 ATOM-RESERVOIR INTERACTION 532 18.5.1
MODEL AND EQUATION OF MOTION 532 18.5.2 FIRST ORDER CONTRIBUTION 533
18.5.3 BLOCH EQUATIONS 535 18.5.4 SECOND ORDER CONTRIBUTION 537 18.5.5
LAMB SHIFT 539 18.5.6 WEISSKOPF-WIGNER DECAY 540 19 ATOM OPTICS IN
QUANTIZED LIGHT FIELDS 549 19.1 FORMULATION OF PROBLEM 549 19.1.1
DYNAMICS 549 19.1.2 TIME EVOLUTION OF PROBABILITY AMPLITUDES 552 19.2
REDUCTION TO ONE-DIMENSIONAL SCATTERING 554 19.2.1 SLOWLY VARYING
APPROXIMATION 554 19.2.2 FROM TWO DIMENSIONS TO ONE 555 19.2.3 STATE
VECTOR 556 19.3 RAMAN-NATH APPROXIMATION 557 19.3.1 HEURISTIC ARGUMENTS
557 19.3.2 PROBABILITY AMPLITUDES 558 19.4 DEFLECTION OF ATOMS 559
19.4.1 MEASUREMENT SCHEMES AND SCATTERING CONDITIONS 559 19.4.2
KAPITZA-DIRAC REGIME 562 19.4.3 KAPITZA-DIRAC SCATTERING WITH A MASK 568
19.5 INTERFERENCE IN PHASE SPACE 571 19.5.1 HOW TO REPRESENT THE QUANTUM
STATE? 572 19.5.2 AREA OF OVERLAP 572 19.5.3 EXPRESSION FOR PROBABILITY
AMPLITUDE 573 20 WIGNER FUNCTIONS IN ATOM OPTICS 579 20.1 MODEL 579 20.2
EQUATION OF MOTION FOR WIGNER FUNCTIONS 581 20.3 MOTION IN PHASE SPACE
582 20.3.1 HARMONIE APPROXIMATION 583 20.3.2 MOTION OF THE ATOM IN THE
CAVITY 583 20.3.3 MOTION OF THE ATOM OUTSIDE THE CAVITY 585 20.3.4 SNAP
SHOTS OF THE WIGNER FUNCTION 586 20.4 QUANTUM LENS 587 20.4.1
DISTRIBUTIONS OF ATOMS IN SPACE 587 20.4.2 FOCAL LENGTH AND DEFLECTION
ANGLE 589 20.5 PHOTON AND MOMENTUM STATISTICS 590 20.6 HEURISTIC
APPROACH 592 CONTENTS XIX 20.6.1 FOCAL LENGTH 592 20.6.2 FOCAL SIZE 594
A ENERGY WAVE FUNCTIONS OF HARMONIE OSCILLATOR 597 A.L POLYNOMIAL ANSATZ
597 A.2 ASYMPTOTIC BEHAVIOR 599 A.2.1 ENERGY WAVE FUNCTION AS A CONTOUR
INTEGRAL 600 A.2.2 EVALUATION OF THE INTEGRAL I M 600 A.2.3 ASYMPTOTIC
LIMIT OF F M 603 A.2.4 BOHR S CORRESPONDENCE PRINCIPLE 603 B TIME
DEPENDENT OPERATORS 605 B.L CAUTION WHEN DIFFERENTIATING OPERATORS 605
B.2 TIME ORDERING 606 B.2.1 PRODUCT OF TWO TERMS . 607 B.2.2 PRODUCT OF
N TERMS 608 C SUESSMANN MEASURE 611 C.L WHY OTHER MEASURES FAIL 611 C.2
ONE WAY OUT OF THE PROBLEM 612 C.3 GENERALIZATION TO HIGHER DIMENSIONS
613 D PHASE SPACE EQUATIONS 615 D.L FORMULATION OF THE PROBLEM 615 D.2
FOURIER TRANSFORM OF MATRIX ELEMENTS 616 D.3 KINETIC ENERGY TERMS 617
D.4 POTENTIAL ENERGY TERMS 619 D.5 SUMMARY 620 E AIRY FUNCTION 621 E.L
DEFINITION AND DIFFERENTIAL EQUATION 621 E.2 ASYMPTOTIC EXPANSION 622
E.2.1 OSCILLATORY REGIME 623 E.2.2 DECAYING REGIME 624 E.2.3 STOKES
PHENOMENON 625 F RADIAL EQUATION 629 G ASYMPTOTICS OF A POISSONIAN 633 H
TOOLBOX FOR INTEGRALS 635 H.L METHOD OF STATIONARY PHASE 635 H.L.L
ONE-DIMENSIONAL INTEGRALS 635 H.1.2 MULTI-DIMENSIONAL INTEGRALS 637 H.2
CORNU SPIRAL 639 XX CONTENTS I AREA OF OVERLAP 643 LI DIAMOND
TRANSFORMED INTO A RECTANGLE 643 1.2 AREA OF DIAMOND 644 1.3 AREA OF
OVERLAP AS PROBABILITY 646 J P-DISTRIBUTIONS 649 J.L THERMAL STATE 649
J.2 PHOTON NUMBER STATE 650 J.3 SQUEEZED STATE . 651 K HOMODYNE KERNEL
655 K.L EXPLICIT EVALUATION OF KERNEL 655 K.2 STRONG LOCAL OSCILLATOR
LIMIT 656 L BEYOND THE DIPOLE APPROXIMATION 659 L.L FIRST ORDER TAYLOR
EXPANSION 659 L.L.L EXPANSION OF THE HAMILTONIAN 659 L.L.2 EXTENSION TO
OPERATORS 661 L.2 CLASSICAL GAUGE TRANSFORMATION 661 L.2.1 LAGRANGIAN
WITH CENTER-OF-MASS MOTION 662 L.2.2 COMPLETE TIME DERIVATIVE 663 L.2.3
HAMILTONIAN INCLUDING CENTER-OF-MASS MOTION 663 L.3 QUANTUM MECHANICAL
GAUGE TRANSFORMATION 664 L.3.1 GAUGE POTENTIAL 664 L.3.2 SCHROEDINGER
EQUATION FOR $ 667 M EFFECTIVE HAMILTONIAN 669 N OSCILLATOR RESERVOIR
671 N.L SECOND ORDER CONTRIBUTION 671 N.L.L EVALUATION OF DOUBLE
COMMUTATOR 671 N.L.2 TRACE OVER RESERVOIR 673 N.2 SYMMETRY RELATIONS IN
TRACE 673 N.2.1 COMPLEX CONJUGATES 674 N.2.2 COMMUTATOR BETWEEN FIELD
OPERATORS 674 N.3 MASTER EQUATION 675 N.4 EXPLICIT EXPRESSIONS FOR T, SS
AND G * * * * 676 N.5 INTEGRATION OVER TIME 677 O BESSEL FUNCTIONS 679
0.1 DEFINITION 679 0.2 ASYMPTOTIC EXPANSION 680 P SQUARE ROOT OF 6 683 Q
FURTHER READING 685 INDEX 688
|
| any_adam_object | 1 |
| author | Schleich, Wolfgang 1957- |
| author_GND | (DE-588)123022126 |
| author_facet | Schleich, Wolfgang 1957- |
| author_role | aut |
| author_sort | Schleich, Wolfgang 1957- |
| author_variant | w s ws |
| building | Verbundindex |
| bvnumber | BV011570477 |
| callnumber-first | Q - Science |
| callnumber-label | QC446 |
| callnumber-raw | QC446.2 |
| callnumber-search | QC446.2 |
| callnumber-sort | QC 3446.2 |
| callnumber-subject | QC - Physics |
| classification_rvk | UH 5600 |
| classification_tum | PHY 370f |
| ctrlnum | (OCoLC)41017894 (DE-599)BVBBV011570477 |
| dewey-full | 535 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 535 - Light and related radiation |
| dewey-raw | 535 |
| dewey-search | 535 |
| dewey-sort | 3535 |
| dewey-tens | 530 - Physics |
| discipline | Physik |
| edition | 1. ed. |
| format | Book |
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| genre | (DE-588)4123623-3 Lehrbuch gnd-content |
| genre_facet | Lehrbuch |
| id | DE-604.BV011570477 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T18:12:00Z |
| institution | BVB |
| isbn | 352729435X 9783527294350 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007790425 |
| oclc_num | 41017894 |
| open_access_boolean | |
| owner | DE-355 DE-BY-UBR DE-29T DE-20 DE-19 DE-BY-UBM DE-384 DE-91G DE-BY-TUM DE-703 DE-634 DE-83 DE-11 DE-188 |
| owner_facet | DE-355 DE-BY-UBR DE-29T DE-20 DE-19 DE-BY-UBM DE-384 DE-91G DE-BY-TUM DE-703 DE-634 DE-83 DE-11 DE-188 |
| physical | XX, 695 S. Ill., graph. Darst. |
| publishDate | 2001 |
| publishDateSearch | 2001 |
| publishDateSort | 2001 |
| publisher | Wiley-VCH |
| record_format | marc |
| spelling | Schleich, Wolfgang 1957- Verfasser (DE-588)123022126 aut Quantum optics in phase space Wolfgang P. Schleich 1. ed. Berlin [u.a.] Wiley-VCH 2001 XX, 695 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Espace des phases (Physique statistique) Optique quantique Phase space (Statistical physics) Quantum optics Phasenraum (DE-588)4139912-2 gnd rswk-swf Quasiklassische Näherung (DE-588)4296820-3 gnd rswk-swf Quantenoptik (DE-588)4047990-0 gnd rswk-swf (DE-588)4123623-3 Lehrbuch gnd-content Quantenoptik (DE-588)4047990-0 s Phasenraum (DE-588)4139912-2 s DE-604 Quasiklassische Näherung (DE-588)4296820-3 s GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007790425&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Schleich, Wolfgang 1957- Quantum optics in phase space Espace des phases (Physique statistique) Optique quantique Phase space (Statistical physics) Quantum optics Phasenraum (DE-588)4139912-2 gnd Quasiklassische Näherung (DE-588)4296820-3 gnd Quantenoptik (DE-588)4047990-0 gnd |
| subject_GND | (DE-588)4139912-2 (DE-588)4296820-3 (DE-588)4047990-0 (DE-588)4123623-3 |
| title | Quantum optics in phase space |
| title_auth | Quantum optics in phase space |
| title_exact_search | Quantum optics in phase space |
| title_full | Quantum optics in phase space Wolfgang P. Schleich |
| title_fullStr | Quantum optics in phase space Wolfgang P. Schleich |
| title_full_unstemmed | Quantum optics in phase space Wolfgang P. Schleich |
| title_short | Quantum optics in phase space |
| title_sort | quantum optics in phase space |
| topic | Espace des phases (Physique statistique) Optique quantique Phase space (Statistical physics) Quantum optics Phasenraum (DE-588)4139912-2 gnd Quasiklassische Näherung (DE-588)4296820-3 gnd Quantenoptik (DE-588)4047990-0 gnd |
| topic_facet | Espace des phases (Physique statistique) Optique quantique Phase space (Statistical physics) Quantum optics Phasenraum Quasiklassische Näherung Quantenoptik Lehrbuch |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007790425&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT schleichwolfgang quantumopticsinphasespace |