1 Introduction ................................................. 1
2 Analogies Between Ballistic Electrons and Electromagnetic
Waves ........................................................ 9
2.1 Analog Parameters for Ballistic Electrons and
Classical Electromagnetic Waves ........................ 10
2.2 Geometrical Electron Optics ............................ 14
2.2.1 Electron Prism .................................. 15
2.2.2 Electron Lens ................................... 17
2.2.3 Magnetic Electron/Hole Focusing ................. 18
2.2.4 Electron Beam Splitter .......................... 21
2.3 Quantum/Electromagnetic Waveguides ..................... 22
2.3.1 Dispersion Equation ............................. 23
2.3.2 Coupled Electron Waveguides ..................... 25
2.4 Analogous Quantum/Electromagnetic Filters .............. 27
2.5 Analogous Quantum/Electromagnetic Tunneling
Structures ............................................. 29
2.5.1 Quantum/Electromagnetic Resonant Tunneling
Wells ........................................... 30
2.5.2 Quantum/Electromagnetic Resonant Tunneling
Wires ........................................... 32
2.5.3 Quantum/Electromagnetic Resonant Tunneling
Dots ............................................ 33
2.6 Photonic Band Crystals ................................. 36
2.7 Photonic Bloch Oscillations ............................ 40
2.8 Electron Diffraction ................................... 44
2.9 Electron Interference .................................. 47
2.10 Analog Quantum/Electromagnetic Devices with Non-
Uniform Cross-Section .................................. 50
2.10.1 Analog Quantum/Electromagnetic T-Shaped
Devices ......................................... 51
2.10.2 Analog Quantum/Electromagnetic Dots with Non-
Uniform Cross-Section ........................... 54
2.11 Quantum/Electromagnetic Cavities ....................... 56
2.12 Electromagnetic Analogs of Type II Semiconductor
Heterostructures ....................................... 58
3 Electron/Electromagnetic Multiple Scattering and
Localization ................................................ 63
3.1 Quantum/Electromagnetic Wave Propagation in
Disordered Media ....................................... 64
3.1.1 Microscopic Theory of Transport ................. 65
3.1.2 Single-Scattering Matrix ........................ 67
3.1.3 Velocities of Electromagnetic Waves in Random
Media ........................................... 68
3.1.4 Length Scales ................................... 72
3.2 Light Conductance ...................................... 73
3.3 Photonic Hall and Magnetoresistance Effects ............ 76
3.4 Interference Effects in Multiple Scattering ............ 79
3.4.1 Universal Conductance Fluctuations .............. 79
3.4.2 Light Intensity Correlations .................... 81
3.4.3 Weak Localization ............................... 88
3.5 Localization Criteria .................................. 93
3.5.1 Ioffe Regel Criterion for Localization .......... 94
3.5.2 Thouless Criterion for Localization ............. 95
3.5.3 Vanishing of Transport Mean Free Path as
Localization Criterion .......................... 98
3.6 Experimental Evidence of Light Localization ............ 98
4 Acoustic Analogies for Quantum Mechanics ................... 103
4.1 Acoustic Bloch Waves .................................. 103
4.2 Acoustic Analogs of Quasicrystals ..................... 105
4.3 Multiple Scattering and Localization of Acoustic
Waves ................................................. 106
4.4 Acoustic Wave Propagation in Nonlinear Disordered
Systems ............................................... 112
4.5 Acoustical Analog of Persistent Currents in
Mesoscopic Normal Metal Rings ......................... 115
4.6 Acoustic Casimir Effect ............................... 116
5 Optical Analogs for Multilevel Quantum Systems ............. 119
5.1 Optical Analog for a Two-Level Quantum System ......... 119
5.2 Dynamical Behavior of the Two-Level Optical Atom ...... 124
5.2.1 Adiabatic Regime ............................... 125
5.2.2 Rabi Oscillations .............................. 125
5.2.3 Multiphoton Transitions and Bloch-Siegert
Shifts ......................................... 127
5.2.4 Zener-Tunneling Regime ......................... 128
5.3 Macroscopic Optical Band Structure .................... 129
5.4 Comparison with Spin-Resonant Phenomena ............... 132
5.5 Limitations of the Optical Analog of a Quantum Two-
Level System .......................................... 135
5.6 Three- and Four-Level Optical Atoms ................... 136
5.7 Nonlinear Optical Atoms ............................... 137
5.8 Spectral Focusing in Two-Photon Processes ............. 138
5.9 Spectral Fresnel Lens ................................. 141
6 Particle Optics ............................................ 143
6.1 Particle Optics Versus Classical Optics ............... 145
6.2 Atom Interactions with Light .......................... 147
6.3 Geometrical Particle Optics ........................... 150
6.3.1 Collimation .................................... 153
6.3.2 Focusing ....................................... 154
6.3.3 Mirrors ........................................ 159
6.3.4 Atom Channeling ................................ 162
6.3.5 Beam Splitters ................................. 163
6.4 Particle Wave Optics .................................. 165
6.4.1 Diffraction .................................... 166
6.4.2 Interference ................................... 170
6.4.3 Holography ..................................... 175
6.5 Atom Waveguides ....................................... 177
6.5.1 Atom Coupler ................................... 180
6.5.2 Bloch Oscillations in Atom Optics .............. 181
6.5.3 Atomic Wavepackets ............................. 182
6.5.4 Atom Lenses and Mirrors in the Time Domain ..... 182
6.6 Quasiparticle Optics .................................. 184
7 Quantum/Classical Nonlinear Phenomena ...................... 187
7.1 Nonlinear Phenomena in Resonant Tunneling Diodes ...... 187
7.2 Nonlinear Barrier Traversal ........................... 191
7.3 Classical Nonlinear Analogs of Bose-Einstein
Condensates ........................................... 191
7.3.1 Four-Wave Mixing in the ВЕС .................... 194
7.3.2 ВЕС Solitons ................................... 195
7.3.3 ВЕС Holography ................................. 201
7.4 BECs and Gravitation .................................. 203
7.5 Nonlinear Atom Optics ................................. 206
7.6 Classical Analog of Andreev Reflection ................ 208
8 Quantum/Classical Phase Space Analogies .................... 211
8.1 Classical/Quantum Hamiltonian Formulation ............. 212
8.2 Quantum/Classical Systems with Identical Motion ....... 217
8.3 Operator Formalism in Classical Physics ............... 221
8.3.1 Differential Operators in Classical Optics ..... 221
8.3.2 Integral Operators in Classical Optics ......... 225
8.3.3 Operator Factorization ......................... 226
8.4 Quantum/Classical Chaos ............................... 227
8.5 Quantum/Classical Uncertainty Relations ............... 229
8.6 Quantum/Classical Phase Space Distribution
Functions ............................................. 232
8.7 Quantum/Classical Interference in Phase Space ......... 236
8.8 Quantum/Classical Transitions ......................... 240
8.9 Quantum/Classical Transformations ..................... 242
9 Analogies Between Quantum and Classical Computing .......... 247
9.1 Bits and Registers .................................... 249
9.2 Logical Operations .................................... 256
9.3 Computing Algorithms .................................. 261
9.4 Entangled States ...................................... 270
9.5 Teleportation ......................................... 276
10 Other Quantum/Classical Analogies .......................... 279
10.1 Transmission Line Analogy to Ballistic Electron
Motion ................................................ 279
10.2 Quantum Analog of the Electro-Optic Modulator ......... 280
10.3 Electronic Flute ...................................... 282
10.4 Quantum Anyon/Classical Vortex Analogy ................ 283
10.5 Mechanical Model of Rotational States in Even-Even
Nuclei ................................................ 285
10.6 Quantum/Classical Malus Law ........................... 287
10.7 Analogies Between the Wave Equation and the Time-
Independent Schrodinger Equation ...................... 288
10.7.1 Classical Analogs of Quantum Fock States ....... 288
10.7.2 Nonlinear Quantum/Classical Operators .......... 290
10.7.3 Optical Corrals ................................ 291
10.8 Analogies Between the Wave Equation and the Time-
Independent Dirac Equation ............................ 291
10.9 Analogies Between the Wave Equation and the Time-
Dependent Schrodinger Equation ........................ 293
10.9.1 Fractional Quantum Revivals and the
Fractional Optical Talbot Effect ............... 296
10.9.2 Non-Paraxial Case .............................. 298
10.10 Maxwell Equations in Spinor Form ..................... 299
10.11 Diffraction in Time .................................. 300
10.12 Quantum/Classical Tunneling .......................... 304
10.12.1 Setups for Direct Measurement of the
Quantum/Classical Tunneling Time .............. 308
10.12.2 Quantum/Classical Larmor Clocks ............... 311
10.13 Classical Analogs of the Aharonov-Bohm Effect ........ 314
References ................................................. 319
Index ......................................................... 341
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