Preface ...................................................... xiii
About the Authors ............................................ xvii
Chapter 1 Quantum Field Theory ................................. 1
1.1 INTRODUCTION ............................................... 1
1.2 WHY QUANTUM FIELD THEORY? .................................. 2
1.3 WHAT IS A FIELD? ........................................... 3
1.4 CLASSICAL FIELD THEORY ..................................... 3
1.5 QUANTUM EQUATIONS FOR FIELDS ............................... 9
1.6 QUANTIZATION OF NONRELATIVISTIC WAVE EQUATION ............. 10
1.7 ELECTROMAGNETIC FIELD IN VACUUM ........................... 14
1.8 INTERACTION OF CHARGED PARTICLES WITH ELECTROMAGNETIC
FIELD ..................................................... 20
1.9 SPONTANEOUS EMISSION ...................................... 23
1.10 QUANTIZATION OF KLEIN-GORDON EQUATION ..................... 26
1.11 QUANTIZATION OF DIRAC FIELD ............................... 32
1.12 GAUGE FIELD THEORIES ...................................... 35
1.13 CONCLUDING REMARKS ........................................ 37
1.14 BIBLIOGRAPHY .............................................. 37
1.15 EXERCISES ................................................. 38
Chapter 2. Path Integral Formulation ........................... 41
2.1 INTRODUCTION .............................................. 41
2.2 TIME EVOLUTION OF WAVE FUNCTION AND PROPAGATOR ............ 42
2.3 PATH INTEGRAL REPRESENTATION OF PROPAGATOR ................ 43
2.4 CONNECTION BETWEEN THE PROPAGATOR AND THE CLASSICAL
ACTION .................................................... 45
2.5 SCHRЦDINGER EQUATION FROM PATH INTEGRAL FORMULATION ....... 48
2.6 TRANSITION AMPLITUDE OF A FREE PARTICLE ................... 50
2.7 SYSTEMS WITH QUADRATIC LAGRANGIAN ......................... 52
2.8 PATH INTEGRAL FOR HARMONIC OSCILLATOR ..................... 53
2.9 PATH INTEGRAL VERSION OF EHRENFEST'S THEOREM .............. 56
2.10 CONCLUDING REMARKS ........................................ 57
2.11 BIBLIOGRAPHY .............................................. 57
2.12 EXERCISES ................................................. 58
Chapter 3. Supersymmetric Quantum Mechanics .................... 59
3.1 INTRODUCTION .............................................. 59
3.2 SUPERSYMMETRIC POTENTIALS ................................. 60
3.3 RELATIONS BETWEEN THE EIGENSTATES OF TWO SUPERSYMMETRIC
HAMILTONIANS .............................................. 67
3.4 HIERARCHY OF SUPERSYMMETRIC HAMILTONIANS .................. 71
3.5 APPLICATIONS .............................................. 73
3.6 CONCLUDING REMARKS ........................................ 77
3.7 BIBLIOGRAPHY .............................................. 77
3.8 EXERCISES ................................................. 78
Chapter 4. Coherent and Squeezed States ........................ 81
4.1 INTRODUCTION .............................................. 81
4.2 THE UNCERTAINTY PRODUCT OF HARMONIC OSCILLATOR ............ 82
4.3 COHERENT STATES: DEFINITION AND UNCERTAINTY PRODUCT ....... 84
4.4 PHYSICAL MEANING OF COHERENT STATES ....................... 87
4.5 GENERATION OF COHERENT STATES ............................. 88
4.6 PROPERTIES OF COHERENT STATES ............................. 92
4.7 SQUEEZED STATES ........................................... 93
4.8 DEFORMED OSCILLATORS AND NONLINEAR COHERENT STATES ...... 98
4.9 CONCLUDING REMARKS ....................................... 103
4.10 BIBLIOGRAPHY ............................................. 103
4.11 EXERCISES ................................................ 107
Chapter 5. Berry's Phase, Aharonov-Bohm and Sagnac Effects .... 109
5.1 INTRODUCTION ............................................. 109
5.2 DERIVATION OF BERRY'S PHASE .............................. 110
5.3 ORIGIN AND PROPERTIES OF BERRY'S PHASE ................... 113
5.4 CLASSICAL ANALOGUE OF BERRY'S PHASE ...................... 115
5.5 EXAMPLES FOR BERRY'S PHASE ............................... 116
5.6 EFFECTS OF BERRY'S PHASE ................................. 117
5.7 APPLICATIONS OF BERRY'S PHASE ............................ 118
5.8 EXPERIMENTAL VERIFICATION OF BERRY'S PHASE ............... 120
5.9 PANCHARATNAM'S WORK ...................................... 122
5.10 THE AHARONOV-BOHM EFFECT ................................. 122
5.11 SAGNAC EFFECT ............................................ 128
5.12 CONCLUDING REMARKS ....................................... 131
5.13 BIBLIOGRAPHY ............................................. 132
5.14 EXERCISES ................................................ 134
Chapter 6. Phase Space Picture and Canonical Transformations .. 137
6.1 INTRODUCTION ............................................. 137
6.2 SQUEEZE AND ROTATION IN PHASE SPACE ...................... 138
6.3 LINEAR CANONICAL TRANSFORMATIONS ......................... 141
6.4 WIGNER FUNCTION .......................................... 142
6.5 TIME EVOLUTION OF THE WIGNER FUNCTION .................... 147
6.6 APPLICATIONS ............................................. 149
6.7 ADVANTAGES OF THE WIGNER FUNCTION ........................ 154
6.8 CONCLUDING REMARKS ....................................... 155
6.9 BIBLIOGRAPHY ............................................. 156
6.10 EXERCISES ................................................ 159
Chapter 7. Quantum Computers .................................. 161
7.1 INTRODUCTION ............................................. 161
7.2 WHAT IS A QUANTUM COMPUTER? .............................. 162
7.3 WHY IS A QUANTUM COMPUTER? ............................... 165
7.4 FUNDAMENTAL PROPERTIES ................................... 166
7.5 QUANTUM ALGORITHMS ....................................... 174
7.6 FEATURES OF QUANTUM COMPUTATION .......................... 182
7.7 QUANTUM COMPUTATION THROUGH NMR .......................... 183
7.8 WHY IS MAKING A QUANTUM COMPUTER EXTREMELY DIFFICULT? .... 184
7.9 CONCLUDING REMARKS ....................................... 184
7.10 BIBLIOGRAPHY ............................................. 185
7.11 EXERCISES ................................................ 187
Chapter 8. Quantum Cryptography ............................... 191
8.1 INTRODUCTION ............................................. 191
8.2 STANDARD CRYPTOSYSTEMS ................................... 192
8.3 QUANTUM CRYPTOGRAPHY-BASIC PRINCIPLE ..................... 193
8.4 TYPES OF QUANTUM CRYPTOGRAPHY ............................ 196
8.5 MULTIPARTY QUANTUM SECRET SHARING ........................ 202
8.6 APPLICATIONS OF QUANTUM CRYPTOGRAPHY ..................... 205
8.7 IMPLEMENTATION AND LIMITATIONS ........................... 206
8.8 FIBER-OPTICAL QUANTUM KEY DISTRIBUTION ................... 206
8.9 CONCLUDING REMARKS ....................................... 207
8.10 BIBLIOGRAPHY ............................................. 208
8.11 EXERCISES ................................................ 209
Chapter 9. Some Other Advanced Topics ......................... 211
9.1 INTRODUCTION ............................................. 211
9.2 QUANTUM THEORY OF GRAVITY ................................ 211
9.3 QUANTUM ZENO EFFECT ...................................... 217
9.4 QUANTUM TELEPORTATION .................................... 223
9.5 QUANTUM GAMES ............................................ 227
9.6 QUANTUM CLONING .......................................... 239
9.7 QUANTUM DIFFUSION ........................................ 243
9.8 QUANTUM CHAOS ............................................ 246
9.9 CONCLUDING REMARKS ....................................... 252
9.10 BIBLIOGRAPHY ............................................. 253
9.11 EXERCISES ................................................ 260
Chapter 10. Quantum Technologies .............................. 263
10.1 INTRODUCTION ............................................ 263
10.2 QUANTUM ENTANGLEMENT .................................... 264
10.3 QUANTUM ENTANGLED PHOTONS ............................... 266
10.4 GHOST IMAGING ........................................... 268
10.5 DETECTION OF WEAK AMPLITUDE OBJECT ...................... 270
10.6 ENTANGLED TWO-PHOTON MICROSCOPY ......................... 272
10.7 DETECTION OF SMALL DISPLACEMENTS ........................ 274
10.8 QUANTUM LITHOGRAPHY ..................................... 275
10.9 QUANTUM METROLOGY ....................................... 279
10.10 QUANTUM TELEPORTATION OF OPTICAL IMAGES ................. 282
10.11 CONCLUDING REMARKS ...................................... 283
10.12 BIBLIOGRAPHY ............................................ 283
10.13 EXERCISES ............................................... 286
Solutions to Selected Exercises ............................... 289
Index ......................................................... 293
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