347 Index a AC fields 81 119 electric 81, 109 116 laser 81, 136 magnetic 112 microwave 107 109 AC field traps see Traps AC Stark effect 82, 84, 90, 96, 97 101, 104 109 Adiabatic approximation 3, 10, 32 potential energy curves 6 8 Alternating gradient deceleration 155 trapping 160 161 Angle-resolved scattering 198 200, 271 272 Arthurs Dalgarno representation 211 213, 234 237 Atom molecule collisions 221 234 Avoided crossing 176, 178, 181, 269, 271 b Background scattering 246, 250 Barrierless reactions see Insertion chemical reactions Beamssee also Molecular beams focused 146 151 Gaussian laser 166 guided 149, 151 slow 151 155 Bessel functions 192, 193, 206, 208 Bethe threshold scattering 214 Blue shift 96 Body-fixed coordinate frame see Molecule-fixed coordinate frame Boltzmann averaging, 214, 284 Born Oppenheimer approximation 1, 32 Bose Einstein Condensation 262, 293 Bosons 115, 200, 201, 284 Bound state calculations 253 255 Bound states laser-field aligned 134 quantum pendulum 127, 129 131 resonant 241, 246, 252 Breit-Wigner equation 252, 253 Buffer gas cooling 164 COPYRIGHTED MATERIAL c Canonically conjugate variables 113 114 Center-of-mass separation 12, 32, 75, 79, 189, 200, 260 Molecules in Electromagnetic Fields: From Ultracold Physics to Controlled Chemistry, First Edition. Roman V. Krems. 2019 John Wiley & Sons, Inc. Published 2019 by John Wiley & Sons, Inc.
348 Index Centrifugal barrier 192, 206, 241, 266, 268 269, 275 force 14 Channel closed 240 241, 243 246, 248 coupled 198, 201, 203, 249 incoming 193 195, 266 269, 279, 289 open 240 241, 243, 249 outgoing 193 195, 266 269, 279 scattering 190, 193 195, 198, 201, 203, 279 threshold 253, 256, 279, 285 Chemical reactions 140 142, 152, 191, 215, 239, 258, 260, 266, 274, 283 296 Classical field Hamiltonian 115 116 particle Hamiltonian in fields, 59 particle Lagrangian in fields 36, 59 Clebsch Gordan coefficients 18, 20, 25, 34, 68, 212, 226, 228, 235, 301 305, 311, 318 319 series 18, 235, 302 Coherent control of scattering 189, 259 superposition 99, 118, 124, 194, 233 234 Collision cross section differential 196 199, 203, 204, 271 272 integral 199 200, 204, 277 Collision-induced absorption of photons 109 Collision thresholds 253, 256, 279, 285 Confined geometry, 280 282 Cooling buffer-gas 164 evaporative 171, 258, 294 laser 162 163 sympathetic 171 Coriolis couplings 22 Coupled channel calculations 204 208, 211 212, 217, 224, 234 237 resonances 249 252, 256, 279 Crossing avoided 176, 178, 181, 269, 271 real 176, 269 Cross section see Collision cross section d DC fields electric 35 magnetic 59 DC Stark effect 35, 37, 38 linear 40, 42, 45, 56 quadratic 40 41, 45, 56 DC Zeeman effect 59 De Broglie wavelength 196, 199, 287 Debye unit of electric dipole moment 38 39, 49, 56, 168 Deceleration optical 155 Rydberg 154 Stark 150, 152 154, 161, 289 Zeeman 154, 165 Detuning 94 96, 166 168 Differential scattering cross sections 196 199, 203, 204, 271 272 Dipolar interactions 183, 186 electric 288 magnetic 28 30, 33 Dipole approximation 116 Dipole polarizability 99 101 Dirac electron 61 equation 2, 60 64, 78 sea 61
Index 349 e Earnshaw s theorem 155 158 Elastic scattering 207, 214, 217, 239, 249, 255 in two dimensions 278 280 Electric dipole moment 36 40, 43, 82, 99 Electric field 36 dynamic 81, 109 116 operators 115 quantization 112 116 static 35 Electric traps see Traps Entangled state 202 Evaporative cooling see Cooling f Fermions 61, 200, 201, 275, 284 285 Feshbach projection operators 243 246 resonances, 239 242 Fine structure 5, 14 17, 20, 48, 51, 72, 141 Floquet matrix 84, 88 89, 90, 93, 95, 97, 108, 117, 186 theorem 84 86, 128 two-mode theory 92 93, 138 g Gauss law 156 unit of magnetic field 78, 164, 268 Gaussian laser beam 166 Gauss-Legendre polynomials 223 Green s operator 242, 244, 245, 247 h High-field seekers electric 134, 146, 150, 153 155, 157 161, 166, 167, 171, 176, 292 magnetic 71, 73, 146, 164, 171, 176, 264, 267, 270 Hund s cases 21 24, 27, 51, 53, 68, 74, 101 102, 230 Hyperfine interactions 5, 28, 76 77 electric quadrupole 31 fermi contact 29 magnetic dipole 30 Hyperfine relaxation 265 i Incoherent sum 272 Inelastic collisions 141, 199, 211, 214 215, 217, 239, 257, 263 275 in two dimensions 277 280 Insertion chemical reactions 191 Integral scattering cross section see Collision cross section Intensity electromagnetic wave 81, 105, 118, 134, 137, 150, 166, 167, 181, 186, 273 Inversion of coordinate system see Parity Ion trap 158 159 j Jacobi-Anger expansion 277 3j-symbols 303 k K-matrix, 207, 208, 252 l Laboratory-fixed coordinate frame see Space-fixed coordinate frame Ladder operators, 48, 304 see also Raising/lowering operators Lambda-doubling 51 56 Laser cooling see Cooling Laser field deceleration, 155 Laserfielddeflection 150
350 Index Laser fields 81, 104 105, 131 134, 136, 137 140, 165 167, 175, 181, 288 Laserfieldtrapsee Traps Log-derivative method 205 207, 209, 218, 254, 256 Long wavelength approximation 116 Low-energy scattering threshold laws 214, 275 Low-field seekers electric 146, 148, 150, 153 155, 157 161, 166, 171, 176, 292 magnetic 71, 73, 146, 162, 164, 165, 171, 176, 264, 267, 270 m Magnetic dipole moment 28, 63 64 Magnetic field 36 dynamic 112 operators 115 quantization 112 116 static 59 Magnetic trap see Traps Mathieu differential equation 84, 128 functions 128 Maxwell Boltzmann distribution 214, 259, 284 Maxwell s equations 109, 156, 157 Microwave trap see Traps Molecular beams 146 155, 203, 257, 289 Molecular synchrotron 150, 161, 289 Molecule-fixed coordinate frame 17, 19, 24, 25, 66, 102, 104, 307 308 Multi-channel resonances 249 252, 256, 279 scattering 204 208, 211 212, 217, 224, 234 237 n Non-adiabatic couplings Coriolis 22 derivative 16 o Open scattering channel see Channel Optical deceleration, 155 see also Deceleration Optical dipole trap, 165 167 see also Traps Optical lattice 168 171, 272 273 Orbital angular momentum 2, 9, 12, 15, 18, 19, 32, 63, 64, 194, 210, 275, 279, 299 Oscillating dipole 99 p Parity 17, 20, 23 27, 37, 40 41, 44, 53, 54, 55, 65, 68, 123, 124, 126, 132, 134, 141, 175, 176, 179, 181, 232, 269 Partial wave expansion 171, 191, 201, 266 states 230, 234, 272, 275, 277, 285 Paul trap 158 159 Periodic Hamiltonians 82 84, 128 Permanent dipole moment 38, 142, 181, 183, 233 Photon fields 88, 115, 116 Polarizability dipole 99 101 dynamic 96, 98 electronic 101 103 rotational 103 tensor 97, 98 vibrational 103 Potential energy curves 3, 7, 8, 11, 72 Projection operators 47, 243 246 P-wave scattering 275, 284, 285 q Quadrupole field potential 148 150, 157, 169 guide 161 moment 28, 31, 37, 76 trap 163, 164, 169 Quantum scattering 188
Index 351 Quasi-bound states 239, 241, 252 Quasi-low-dimensional geometry 186, 273, 280, 288 Quasi-two-dimensional scattering 280 282 r Rabi frequency 166, 167, 264 Raising/lowering operators, 22, 33, 66, 22, 304 see also Ladder operators Rate constants 214, 284, 285, 286, 288 Reactive scattering 140 142, 152, 191, 215, 239, 258, 260, 266, 274, 281, 284 286, 295 Red shift 96 Relaxation collision-induced 264 270, 272, 286 photon-induced in collisions 109 Resonances 266 Breit-Wigner formula 252, 253 Feshbach 239 242 multiple-channel 249 252 positions 249, 252 256 shape 239 242, 272 273 single-channel 249 widths 241, 249 252 Riccati Bessel functions 206, 208 Rigid rotor approximation 4, 14 in combined fields 181, 183 186 in a DC electric field 125, 127, 129 131, 219 in a laser field 107, 132, 134 135, 138 in a magnetic field 221 223 in a microwave field 108, 119, 232 233 Rotating wave approximation (RWA) 94 97 Rydberg constant 6 decelerator, 154 (see also Deceleration) s Scattering amplitude 193, 194 196, 197 198, 202, 246, 280 crosssection (see Collision cross section) rate 214, 284, 285, 286, 288 resonances (see Resonances) Shape resonances see Resonances Slow molecular beams 149, 151 155, 271 Space-fixed coordinate frame 17, 19, 25, 75, 98, 100, 123, 136, 140, 145, 183, 186, 188 189, 210, 235, 284, 290, 293, 299, 307 308 Spinor 60 Spin orbit interaction 54 Spin relaxation 270 273, 290 Spin rotation interaction 46, 48, 74, 78, 175 176, 221, 224 225 Spin spin interaction 49 51, 74, 78, 225, 226 229 Stark deceleration see Deceleration Stark shifts AC (see AC Stark effect) DC (see DC Stark effect) Stern Gerlach experiment 146, 147, 151 S-wave scattering 275, 284, 285 Sympathetic cooling see Cooling Synchronous rotation 121, 137 Synchrotron see Molecular Synchrotron t Thermalization 164 Threshold collisions 214, 275 Total angular momentum representation (see Arthurs Dalgarno representation)
352 Index Traps AC field traps 160 161 DC electric field traps 158, 159 ions traps, 158 159 (see also Paul trap) laser field traps 165 167 magnetic field traps 162 165 microwave trap 167 Tunneling chemistry 295 doublets 134, 175, 182 resonant scattering 241 Two-dimensional scattering 276 280 Two-frequency laser field Floquet theory 92 93, 138 molecular centrifuge 136 140 optical lattices 168 171 u Ultracold chemistry 283 296 collisions 171, 261, 266, 268, 273, 275 molecules 173, 182, 258 reactions 284 temperature 171, 187 v Vibrational energy 3 5, 10 14 Hamiltonian 12, 221 levels 13 14 polarizability (see Polarizability) state parity 24 wave functions 13 14, 151, 223 w Wave de Broglie 196, 199, 287 electromagnetic 81, 109 116 equation, 110 Wave number 111 Wave vector 111 Wigner D-functions 18, 53, 230, 231, 309 313 Wigner Eckart theorem 44, 47, 74, 100, 124, 139, 210, 218 220, 223, 226, 227, 228 Wigner 3j symbols 303 304 Wigner threshold laws 214, 275, 277 279 Wigner Witmer rules 33 z Zeeman decelerator see Deceleration Zeeman effect 59 Zeeman relaxation 270 273, 290 Zero-temperature reaction rate 214, 215, 268, 284 286