Quantum and Atom Optics


Posted here are my notes for a course in quantum and atom optics at the graduate level. Caveat emptor: I believe these notes to be of high quality, but there will be many typrographical and other errors. Further, these notes are still under construction and will be modified frequently, and during construction there may be sections that are incomplete, sloppy, or just plain wrong.. I will put corrections in as I find them, and you can always contact me if you have corrections or comments.



You can download the notes here as one big file: (pdf, many MB). Instructors may contact me for a version with solutions to problems included.



If you use these notes for your class, please let me know!



Topics Covered:

  1. Classical Light-Atom Interactions: Polarizability, Lorentz Model, Oscillator Strength, Atom Optics, Dipole Force, Radiation Pressure, Laser Cooling, Atom-Mirror Interaction, Atom-Atom Interaction (superradience)
  2. Coherence: Wiener-Khinchin Theorem, Optical Wiener-Khinchin Theorem, Visibility, Coherence Time, Second-Order Coherence, Hanbury-Brown–Twiss Experiment
  3. Rate Equations: Quantization, Relations between Einstein Coefficients, Absorption Coefficient, Saturation
  4. Quantum State: Density Operator, Purity, Unitary Time-Evolution Operator, Heisenberg and Interaction Pictures, Wigner Distribution, Weyl Correspondence, Moyal Bracket, Husimi Function, Entanglement, Cloning, Peres-Horodecki Criterion (and Suffiency for Gaussian States), Indistinguishability, Exchange Interaction, Church of the Larger Hilbert Space
  5. Two-Level Atom: Parity, Rotating-Wave Approximation, Rabi Flopping, Dressed States, Adiabatic Passage and Landau-Zener Crossings, Bloch Sphere, Ramsey Fringes, Spin and Photon Echoes, Optical Bloch Equations, Resolvent, Torrey's Solutions, Classical Limit, Rate-Equation Limit, Saturation Intensity, Cross Section, Power Broadening, Coherent and Incoherent Scattering, Quantum Regression Theorem, Mollow Triplet, Mollow Probe Absorption Spectrum, Antibunching, Lamb-Dip Spectroscopy, Radiation Pressure, Dipole Force, Adiabatic Approximation, Bragg Scattering, Fokker-Planck Equation, Optical Force Fluctuations, Doppler Limit, Bloch-Siegert Shift
  6. Three-Level Atom: Stimulated Raman Effect, Raman Cooling, Atom Interferometry, Population Trapping, VSCPT, Electromagnetically Induced Transparency, Stimulated Raman Adiabatic Passage (STIRAP), Quantum Beats, Steady-State Quantum Beats
  7. Field Quantization: Hamiltonian Structure, Single-Mode Quantization, Many-Mode Quantization, Helmholtz Theorem, Transverse Delta Function, Field Commutators
  8. Atom-Field Interaction: Lorentz Force, Minimal Coupling, Power-Zienau Transformation, Aharonov-Bohm Effect
  9. Jaynes-Cummings Model and Cavity QED: Atom Coupled to a Single Field Mode, Dynamics, Collapses and Revivals, Dressed States, Vacuum Rabi Doublet, Photon Blockade, Atom-Photon Molecule, Cavity Damping and Pumping
  10. Spontaneous Emission: Weisskopf-Wigner Model, Fine-Structure Degeneracy, Master Equation, Nonexponential Decay
  11. Casimir-Polder Potential: Renormalization, Thomas-Reiche-Kuhn Sum Rule, Asymptotic Behavior, Excited-Level Shifts and Classical Antenna Behavior, Power-Zienau Transformation in Half Space, Coulomb-Gauge Calculation, Lamb Shift