Introduction to Modern Quantum Optics
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1 Introduction to Modern Quantum Optics Jin-Sheng Peng Gao-Xiang Li Huazhong Normal University, China Vfe World Scientific» Singapore* * NewJerseyL Jersey* London* Hong Kong
2 IX CONTENTS Preface PART I. Theory of the interaction between atom and radiation field Chapter 1. Three pictures in quantum mechanics 1.1. The Schrödinger picture The Heisenberg picture The interaction picture Equation of motion in the interaction picture A formal solution of the state vector \P J (t)) by the perturbation theory The density operator Density operator and its general properties Solution of the equation of motion for the density operator 20 Chapter 2. Two-level atom and the optical Bloch equation 2.1. Two-level atom Hamiltonian of a two-level atom interacting with an electromagnetic field The optical Bloch equation Description of the dynamical behavior of a two-level atom interacting with the radiation field by the density matrix Density matrix equation describing a two-level atom without decay 32
3 X о Contents Density matrix equation of a two-level atom with decay 34 Chapter 3. Quantized description of radiation field 3.1. Classical description of the electromagnetic field in vacuum Quantization of the radiation field Quantization of the electromagnetic field Momentum and spin of the photon State functions describing the light field Photon-number states The coherent states of light The phase operators and the phase states Chaotic states of light 72 Chapter 4. Dicke Hamiltonian and Jaynes-Cummings Model 4.1. Dicke Hamiltonian of an atom interacting with the radiation field Spontaneous emission of an excited atom The Jaynes-Cummings model 87 Chapter 5. Quantum theory of a small system coupled to a reservoir 5.1. Classical Langevin equation and Fokker-Planck equation Langevin equation Fokker-Planck equation Master equation for a quantum harmonic oscillator and a two-level atom Master equation for a quantum harmonic oscillator Master equation for a two-level atom coupled to a bath field Characteristic function and the quasi-probability distribution for the quantum harmonic oscillator Normal ordering representation Anti-normal ordering representation Symmetric ordering representation 125
4 о Contents XI PART II. The quantum properties of light Chapter 6. Coherence of light 6.1. Classical coherence of light Temporal coherence of light Spatial coherence of light The first-order correlation function The higher-order correlation function Quantum theory of the coherence of light Quantum correlation functions Bunching and antibunching effects of light Intermode correlation property for the two-mode field 155 Chapter 7. Squeezed states of light 7.1. Squeezed states of a single-mode field Squeezed coherent states Squeezed vacuum field Squeezed states of a two-mode radiation field Higher-order squeezing of a radiation field and the amplitude square squeezing Higher-order squeezing of a radiation field Amplitude square squeezing Independence of the different definitions of the squeezing for the radiation field Squeezing of light in the Jaynes-Cummings model 190 Chapter 8. Resonance fluorescence 8.1. Resonance fluorescence distribution of a two-level atom Dressed canonical transformation Spectral distribution of the resonance fluorescence of a two-level atom Linewidth of the fluorescence spectrum Intensity distribution of the resonance fluorescence spectrum 214
5 xii о Contents 8.2. Resonance fluorescence spectra of a three-level atom Hamiltonian of a three-level atom under the interaction of a bimodal field Resonance fluorescence spectrum of a three-level atom interacting with a strong and a weak monochromatic laser field Resonance fluorescence spectral distribution of a three-level atom driven by two strong laser fields Single-atom resonance fluorescence described by the density matrix theory 236 Chapter 9. Superfluorescence 9.1. Elementary features of superfluorescence Quasi-classical description of superfluorescence Quantum theoretical description of superfluorescence Heisenberg equation of the system Dicke model for superfluorescence Quantum statistical properties of superfluorescence Superfluorescent beats Basic characteristics of the superfluorescent beats Superfluorescent beats in the Dicke model 278 Chapter 10. Optical Bistability Basic characteristics and the production mechanism of optical bistability Quantum description of the dispersive optical bistability Hamiltonian describing the optical bistability system Optical bistability properties of the system 297 Chapter 11. Effects of virtual photon processes Relation between the Lamb shift of a Hydrogen atom and the virtual photon field 305
6 о Contents xiii Influence of the virtual photon field on the phase fluctuations of the radiation field Time evolution of the phase operator in the atom-field coupling system with the rotating-wave approximation Time evolution of the phase operator without the rotating-wave approximation Influences of the virtual photon processes on the squeezing of light Squeezing of the field in the two-photon Jaynes-Cummings model with the rotating-wave approximation Influences of the virtual photon processes on the squeezing of light 323 PART III. Quantum properties of atomic behavior under the interaction of a radiation field Chapter 12. Collapses and revivals of atomic populations Time evolution of the atomic operator of a two-level atom under the interaction of a classical electromagnetic field Periodic collapses and revivals of an atom interacting with a quantized field Time development of atomic operators under the interaction of the field in a number state \m) Periodic collapses and revivals of the atom under the interaction of a coherent field Periodic collapses and revivals of the atom in the two-photon Jaynes-Cummings model Time evolution of the atomic operators for a three-level atom interacting with a single-mode field Time evolution of the state vector of the system Periodic collapses and revivals of the atomic populations 354 Chapter 13. Squeezing effects of the atomic operators Definition of the atomic operator squeezing 361
7 XIV Contents Squeezing of atomic operators in the two-photon Jaynes-Cummings model Squeezing of atomic operators in the vacuum field Squeezing of atomic operators in the superposition state field Squeezing of atomic operators in the coherent state field Squeezing of atomic operators in the resonance fluorescence system 377 Chapter 14. Coherent trapping of the atomic population Atomic population coherent trapping and phase properties in the system of a V-configuration three-level atom interacting with a bimodal field Time evolution of the state vector of the system Time evolution of the phase operator in the atom-field coupling system Coherent trapping of the atomic population Coherent trapping of the atomic population for a V-configuration three-level atom driven by a classical field in a heat bath Time evolution of the reduced density matrix p of the atom Steady-state behavior and the coherent trapping of the atomic populations 396 Chapter 15. Quantum characteristics of a two-atom system under the interaction of the radiation field Hamiltonian of a two-atom system with the dipole-dipole interaction Hamiltonian of the electric dipole-dipole interaction between two atoms Hamiltonian of a two-atom system with the dipole-dipole interaction induced by the fluctuations of the vacuum field Quantum characteristics of the two-atom coupling system under the interaction of a weak field Time evolution of the atomic population inversion of a two-atom system Influence of the dipole-dipole interaction on the squeezing of atomic operators 416
8 о Contents xv Periodic collapses and revivals and the coherent population trapping in the two-atom system under the interaction of a coherent field Periodic collapses and revivals of atomic populations in the two-atom system Atomic population coherent trapping in the two-atom coupling system 431 Chapter 16. Autoionization of the atom in a laser field Autoionization of the atom in a weak laser field Autoionization of the atom under the interaction of a strong laser field Above threshold ionization of the atom in a strong laser field Influences of the second-order ionization processes on the low-energy photoelectron spectrum Higher-energy photoelectron spectrum and the peak switching effect 466 Chapter 17. Motion of the atom in a laser field Atomic diffraction and deflection in a standing-wave field State function of the system of an atom interacting with a standing-wave field Diffraction of the atom under the interaction of a laser field Deflection of the atom in a standing wave field Force on an atom exerted by the radiation field Quasi-classical description of the radiation force Description of the radiative dipole force by means of the dressed state method 501 Chapter 18. Laser cooling Decelerating the motion of atoms by use of a laser field Quantum theoretical description of the laser cooling Hamiltonian describing the system of a polarization laser field interacting with a quasi-two-level atom 524
9 XVI о Contents Time evolution of the density matrix elements of the atomic internal states Radiation force acting on the atom by the laser field Physical mechanism of the laser cooling Limited temperature of the laser cooling Atomic momentum diffusion in a laser field Equilibrium temperature of the laser cooling Laser cooling below the one-photon recoil energy by the velocity-selective coherent population trapping 554 Index 559
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