Contents 9 Radiation and matter 205 9 1 Transition rates 9.2 921 Master equations 9.2.2 Equilibrium and black-body radiation 0301124 9.3 Interaction of matter and radiation 9.4 Spontaneous emission by atoms 9.4.1 Dipole approxim tion 9.42 Transition rates 93 Selection rules 9.5 Blue glow:Cherenkov radiation 9.5.1 Emission rate and spectrum of Cherenkov radiation 9.6 Bremsstrahlung 97 Processes in lasers 9.7.1 Master equation for lasers 9.7.2 Photon number distribution Exercises Solutions 10 Coherentstates 10.1 Superpositions 10.2 Excitation of an oscillator 44404 10.3 Properties of the coherent state 10.4 Back to the laser 10.4.1 Optical coherence time 10.4.2 Maxwell-Bloch equations 10.5 Coherent states of matter 10.5.1 Cooper pair box 49555 Exercises Solutions 265 PART IV DISSIPATIVE QUANTUM MECHANICS 267 11 Dissipative quantum mechanics 11.1 Clas ical damped oscillato 11.1.Dynam cal susceptibility 11.1.2 Damped electric oscillator 11.2 Quantum description 11.2.1 Difficulties with the quantum description 11.2.2 Solution:Many degrees of freedom 112.3 Boson bath 11.2.4 Quantum equations of motion 11.2.5 Diagonalizationviii Contents 9 Radiation and matter 205 9.1 Transition rates 206 9.2 Emission and absorption: General considerations 207 9.2.1 Master equations 210 9.2.2 Equilibrium and black-body radiation 211 9.3 Interaction of matter and radiation 214 9.4 Spontaneous emission by atoms 218 9.4.1 Dipole approximation 218 9.4.2 Transition rates 219 9.4.3 Selection rules 222 9.5 Blue glow: Cherenkov radiation 223 9.5.1 Emission rate and spectrum of Cherenkov radiation 225 9.6 Bremsstrahlung 227 9.7 Processes in lasers 229 9.7.1 Master equation for lasers 231 9.7.2 Photon number distribution 232 Exercises 235 Solutions 238 10 Coherent states 240 10.1 Superpositions 240 10.2 Excitation of an oscillator 241 10.3 Properties of the coherent state 244 10.4 Back to the laser 249 10.4.1 Optical coherence time 250 10.4.2 Maxwell–Bloch equations 252 10.5 Coherent states of matter 256 10.5.1 Cooper pair box 257 Exercises 262 Solutions 265 PART IV DISSIPATIVE QUANTUM MECHANICS 267 11 Dissipative quantum mechanics 269 11.1 Classical damped oscillator 269 11.1.1 Dynamical susceptibility 270 11.1.2 Damped electric oscillator 272 11.2 Quantum description 273 11.2.1 Difficulties with the quantum description 273 11.2.2 Solution: Many degrees of freedom 274 11.2.3 Boson bath 274 11.2.4 Quantum equations of motion 275 11.2.5 Diagonalization 277