Quantum and Atom Optics

Posted here are my notes for a course in quantum and atom optics at the graduate level. I will update these notes regularly and 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).

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