Atoms and Molecules Interacting with Light Atomic Physics for the Laser Era

Transcription

1 Atoms and Molecules Interacting with Light Atomic Physics for the Laser Era Peter van der Straten Universiteit Utrecht, The Netherlands and Harold Metcalf State University of New York, Stony Brook This in-depth textbook with a focus on atom-light interactions prepares students for research in a fast-growing and dynamic field. Intended to accompany the laser-induced revolution in atomic physics, it is a comprehensive text for the emerging era in atomic, molecular and optical science. Utilising an intuitive and physical approach, the text describes two-level atom transitions, including appendices on Ramsey spectroscopy, adiabatic rapid passage and entanglement. With a unique focus on optical interactions, the authors present multi-level atomic transitions with dipole selection rules, and M1/E2 and multiphoton transitions. Conventional structure topics are discussed in some detail, beginning with the hydrogen atom and these are interspersed with material rarely found in textbooks such as intuitive descriptions of quantum defects. The final chapters examine modern applications and include many references to current research literature. The numerous exercises and multiple appendices throughout enable advanced undergraduate and graduate students to balance theory with experiment. Part I. Atom-Light Interaction: 1. The classical physics pathway; Appendix 1.A. Damping force on an accelerating charge; Appendix 1.B. Hanle effect; Appendix 1.C. Optical tweezers; 2. Interaction of two-level atoms and light; Appendix 2.A. Pauli matrices for motion of the bloch vector; Appendix 2.B. The Ramsey method; Appendix 2.C. Echoes and interferometry; Appendix 2.D. Adiabatic rapid passage; Appendix 2.E Superposition and entanglement; 3. The atom-light interaction; Appendix 3.A. Proof of the oscillator strength theorem; Appendix 3.B. Electromagnetic fields; Appendix 3.C. The dipole approximation; Appendix 3.D. Time resolved fluorescence from multi-level atoms; 4. Forbidden' transitions; Appendix 4.A. Higher order approximations; 5. Spontaneous emission; Appendix 5.A. The quantum mechanical harmonic oscillator; Appendix 5.B. Field quantization; Appendix 5.C. Alternative theories to QED; 6. The density matrix; Appendix 6.A. The Liouville von Neumann equation; Part II. Internal Structure: 7. The hydrogen atom; Appendix 7.A. Center- For more information, and to order, visit: February x 174 mm 527pp 160 b/w illus. 31 tables Hardback Original price $69.99

2 Contents PART ONE ATOM-LIGHT INTERACTION page 5 1 The Classical Physics Pathway Introduction Damped Harmonic Oscillator Introduction Spectrum of Emitted Radiation The Damped Driven Oscillator Radiated Power Scattering of Radiation The Bohr Model Introduction Energy Levels debroglie Waves 13 1.A Damping Force on an Accelerating Charge 14 1.B Hanle effect 16 1.C Optical Tweezers 17 2 Interaction of Two-Level Atoms and Light Introduction Quantum Mechanical View of Driven Optical Transitions Rabi Oscillations Introduction The Rotating Wave Approximation and Rotating Frame Transformation Dynamical Solutions Eigenvalues and Eigenfunctions 25

3 iv Contents 2.4 The Dressed Atom Picture The Bloch Vector and Bloch Sphere 29 2.A Pauli Matrices for Motion of the Bloch Vector 31 2.B The Ramsey Method 31 2.C Echoes and Interferometry 37 2.D Adiabatic Rapid Passage 40 2.E Superposition and Entanglement 41 3 The Atom-Light Interaction Introduction The Three Primary Approximations Electric Dipole Approximation Perturbation Approximation The Rotating Wave Approximation Revisited Light Fields of Finite Spectral Width Averaging over the Spectral Width Scattering Cross-section Calculation Again Oscillator Strength Selection Rules What are Selection Rules? Selection Rules for Electric Dipole Transitions Experimental Application of Dipole Selection Rules 54 3.A Proof of the Oscillator Strength Theorem 55 3.B Electromagnetic Fields 56 3.B.1 Laser Light 56 3.B.2 Light from Classical Sources 59 3.C The Dipole Approximation 60 3.D Time Resolved Fluorescence From Multi-Level Atoms 61 3.D.1 Introduction 61 3.D.2 Time Resolved Excited State Spectroscopy 62 3.D.3 The Continuous Light Case 66 4 Forbidden Transitions Introduction Extending the Electric Dipole Approximation Magnetic Dipole Transitions Electric Quadrupole Transitions Extending the Perturbation Approximation The Next Higher Order Process Non-Linear Optics Two Different Electromagnetic Fields 79

4 Contents v Misconceptions About Intermediate States, Resonances, and A Still Higher Order Processes 82 4.A Higher Order Approximations 82 5 Spontaneous Emission Introduction Einstein A and B Coefficients Einstein s Calculation Importance of This Result Discussion of this Semi-Classical Description The Wigner-Weisskopf Model 90 5.A The Quantum Mechanical Harmonic Oscillator 92 5.B Field Quantization 93 5.C Alternative Theories to QED 96 6 The Density Matrix Introduction Basic Concepts Pure States Mixed States The Optical Bloch Equations Power Broadening and Saturation A The Liouville-von Neumann Equation 107 PART TWO INTERNAL STRUCTURE The Hydrogen Atom Introduction The Hamiltonian of Hydrogen Solving the Angular Part Solving the Radial Part Asymptotic Properties The Radial Solutions The Scale of Atoms Optical Transitions in Hydrogen Introduction Radial Part of the Dipole Matrix Element Angular Part of the Dipole Matrix Element Lifetime of the States A Center-of-Mass Motion 128

5 vi Contents 7.B Coordinate Systems B.1 Spherical Coordinates B.2 Parabolic Coordinates C Commuting Operators D Matrix Elements of the Radial Wavefunctions Fine Structure Introduction The Relativistic Mass Term The Fine Structure Spin-Orbit Term The Effect of the Magnetic Moment The Interaction Energy The Thomas Correction to the Fine Structure (Spin- Orbit) Term Evaluation of Spin-Orbit Terms Spin-orbit Interaction for Other Atoms The Darwin Term Summary of Fine Structure The Dirac Equation The Lamb Shift A The Sommerfeld Fine-Structure Constant B Measurements of the Fine Structure Effects of the Nucleus Introduction Motion, Size, and Shape of the Nucleus Nuclear Motion Nuclear Size Nuclear Shape Nuclear Magnetism - Hyperfine Structure Atomic Orbital Angular Momentum l Atomic Orbital Angular Momentum l = Hyperfine Energies for Hydrogen Hyperfine Energies for Other Atoms A Interacting Magnetic Dipoles B Hyperfine Structure for Two Spin 1 / 2 Particles C The Hydrogen Maser The Alkali-Metal Atoms Introduction Quantum Defect Theory Non-Penetrating Orbits 173

6 Contents vii 10.4 Model Potentials Optical Transitions in Alkali-Metal Atoms Radial Part Angular Part A Quantum Defects for the Alkalis B Numerov method Atoms in Magnetic Fields Introduction The Hamiltonian for the Zeeman Effect Zeeman Shifts in the Presence of the Spin-Orbit Interaction Strong Fields Weak fields Intermediate Fields A The Ground State of Atomic Hydrogen B Positronium C The Non-crossing Theorem D Passage Through an Anticrossing: Landau-Zener Transitions Atoms in Electric Fields Introduction Electric Field Shifts in Spherical Coordinates Stark Effect in Hydrogen, n= The Non-Linear Stark Effect Electric Field Shifts in Parabolic Coordinates Hydrogen in Parabolic Coordinates Linear Stark Effect in Parabolic Coordinates Quadratic Stark Effect in Parabolic Coordinates Atoms Other Than Hydrogen Summary Rydberg Atoms Introduction The Bohr model and Quantum Defects Again Rydberg Atoms in External Fields Rydberg Atoms in Magnetic Fields Rydberg Atoms in Electric Fields Energy Estimates and Quantum Defects Numerical Calculations Field Ionization Experimental Description Some Results of Rydberg Spectroscopy 224

7 viii Contents Stark spectroscopy Precision Measurements on High l States Electric Field Calibration Circular Rydberg States Coulomb Blockade The Helium Atom Introduction Symmetry The Exchange Operator The Addition of Two Spins The Eigenfunctions The Hamiltonian for Helium The Independent Particle Model The Symmetrized Wavefunctions Variational Methods Variational Method for the Ground State Variational Model for the Singly Excited States Doubly Excited States A Variational Calculations B Detail on the Variational Calculations of the Ground State The Periodic System of the Elements The Independent Particle Model The Pauli Symmetrization Principle The Aufbau Principle Coupling of Many-Electron Atoms Russel-Saunders Coupling j- j Coupling Possible Combinations for Two Electrons Hund s Rules Hartree-Fock Model The Periodic Table A Paramagnetism B The Color of Gold Molecules Introduction A Heuristic Description Quantum Description of Nuclear Motion Born-Oppenheimer Approximation Nuclear eigenfunctions 285

8 Contents ix Rovibrational Energies Bonding in Molecules The van der Waals Interaction Covalent Bonding Ionic Bonding Electronic States of Molecules Optical Transitions in Molecules Introduction Transition Strength Vibrational Effects in Molecular Spectra Rotational Effects in Molecular Spectra A Morse Potential Binding in the Hydrogen Molecule The Hydrogen Molecular Ion The Molecular Orbital Approach to H The Valence Bond Approach to H Improving the Methods Nature of the H 2 Bond A Confocal Elliptical Coordinates B One-electron Two-center Integrals C Electron-Electron Interaction in Molecular Hydrogen Ultra-Cold Chemistry Introduction Long-Range Molecular Potentials LeRoy-Bernstein Method Scattering Theory The Scattering Length Feshbach Molecules 344 PART THREE APPLICATIONS Optical Forces and Laser Cooling Two Kinds of Optical Forces Low Intensity Laser Light Pressure A Two-Level Atom at Rest Atomic Beam Slowing and Collimation Optical Molasses Two-Level Atoms Moving in a Standing Wave Intuitive Discussion of Optical Molasses 360

9 x Contents 19.5 Temperature Limits Experiments in Three-Dimensional Optical Molasses Cooling Below the Doppler Temperature Polarization and Interference Lin-Perp-Lin Polarization Gradient Cooling The Damping Force and the Temperature Limit Confinement of Neutral Atoms Dipole Force Optical Traps Single-Beam Optical Traps for Two-Level Atoms Blue Detuned Optical Traps Magnetic Traps Introduction Magnetic Confinement Motion of Atoms in a Quadrupole Trap Magneto-Optical Traps Introduction Cooling and Compressing Atoms in a MOT Capturing Atoms in a MOT Optical Lattices Quantum States of Motion Properties of 3D Lattices Spectroscopy in 3D Lattices Quantum Transport in Optical Lattices Bose-Einstein Condensation Introduction The Road to BEC Quantum Statistics Mean-Field Description of the Condensate Interference of Two Condensates Quantum Hydrodynamics The Superfluid-Mott Insulator Transition A Distribution Functions B Density of States Cold Molecules Slowing, Cooling and Trapping Molecules Stark Slowing of Molecules Buffer Gas Cooling Binding Cold Atoms into Molecules Photo-association 429

10 Contents xi Magneto-association Vibrational state transfer by STIRAP A Case Study: Photo-association Spectroscopy Three Level Systems Introduction The Spontaneous and Stimulated Raman Effects Coherent Population Trapping Autler Townes and EIT Stimulated Rapid Adiabatic Passage Slow Light Observations and Measurements A General Case for δ 1 δ Fundamental Physics Precision Measurements and QED The Lamb Shift Anomalous Electron Magnetic Moment Atomic Clocks Variation of the Constants Exotic Atoms and Antimatter Positronium Muonium Muonic Hydrogen Pionic Hydrogen Anti-hydrogen Bell Inequalities Parity Violation and the Anapole Moment Measuring Zero 471 PART FOUR APPENDIX 473 Appendix A Notation and Definitions 475 Appendix B Units and Notation 480 Appendix C Angular Momentum in Quantum Mechanics 483 Appendix D Transition Strengths 490 Notes 501 Bibliography 502 Index 521