PHYS 685: Quantum Optics (Winter 2007)

Instructor: Daniel A. Steck
Office: 277 Willamette      Phone: 346-5313      email: dsteck@uoregon.edu
Office hours: TTh 10-11, and by appointment (best to email first)
Course home page: http://atomoptics.uoregon.edu/~dsteck/teaching/07winter/phys685

Schedule: TTh 8:30-9:50 (am), 318 Willamette
Course reference number: 26006
Credits: 4
Prerequisites: PHYS 684

Links: news, course notes, homework sets and keys.

Course overview

This is a continuation of quantum optics from last term. This course will provide a broad overview of quantum-mechanical interactions between light and matter. We will focus mainly on light-atom interactions and thus we will also do some atomic structure.

Recommended Texts:


Note that the above books are not required, and we will not follow any particular text. The above texts are useful references, however. There are many other excellent standard texts that you may find useful for this course, some of the classics and good modern works are listed here. Titles with call numbers are on reserve in the science library. You should consider obtaining the Dover titles, since they are cheap.

General Quantum Optics Atom Optics Atomic Physics and Atomic Structure Quantum Electrodynamics Laser Physics

Grades

Grades for the course will be based on homework and a take-home final exam. The relative weights will be as follows:

Homework: about 4-6 problem sets will be assigned during the term.

Final exam: the final exam is a take-home exam, and is due by noon on Tuesday, 20 March. It will be assigned one week in advance.

Pass/fail grading option: a passing grade requires the equivalent of a C- grade on all the course work (homework and final).

Syllabus

This is a tentative outline of topics we will cover in this (and the following) course in the sequence. Note that this is way ambitious for the probable duration of this course.

  1. Classical Atom–Field Interactions
    1. Lorentz Model of the Atom
    2. Polarizability, Cross Section
    3. Oscillator Strength
    4. Classical Radiation Damping
    5. Refractive Index
    6. Mechanical Effects of Light

  2. Semiclassical Atom–Field Interactions: Rate Equations
    1. Einstein Rate Equations
    2. Density of States
    3. Relation Between A and B Coefficients
    4. Cross Section and Saturation Intensity
    5. Resonant Gain and Absorption

  3. Two-Level Quantum-Mechanical Atom Interacting with a Classical Field
    1. Electric Dipole Interaction: Schrödinger Equation Treatment
    2. Density Operator; Schrödinger, Heisenberg, and Interaction Pictures
    3. Spontaneous Emission: Optical Bloch Equations
    4. Resonance Fluorescence
      1. Quantum Regression Theorem
      2. Elastic and Inelastic Scattering
      3. Mollow Triplet and Probe Absorption Spectra
      4. Lamb Dip Spectroscopy
    5. Dressed States, Bloch–Siegert Shift
    6. Adiabatic Passage: Landau–Zener Tunneling
    7. Mechanical Effects
      1. Radiation Pressure
      2. Laser Cooling and the Doppler Limit
      3. Dipole Force and the Adiabatic Approximation; Dipole Traps
      4. Stochastic Dipole Force
    8. Connection with the Classical Atom
    9. Atom in a Thermal Field
    10. Connection with Rate Equations
    11. Minimal-Coupling Hamiltonian and Gauge Invariance

  4. Quantum Theory of Open Systems
    1. Stochastic Calculus
      1. Wiener Process
      2. Itô Calculus
      3. Stratonovich Calculus
      4. Cauchy Process
    2. Lindblad Form of the Master Equation
    3. System–Reservoir Derivation of the Master Equation
    4. Heisenberg-Langevin Formalism (and the Ornstein-Uhlenbeck process)
    5. Master Equation for Spontaneous Emission
    6. Quantum Measurement
      1. Stochastic Master Equation: Quantum Jumps
      2. Stochastic Master Equation: Homodyne Detection
      3. Stochastic Schrödinger Equation
      4. Detector Inefficiency and Multiple Observers
      5. Positive Operator-Valued Measures

  5. More Complicated Quantum-Mechanical Atoms Interacting with a Classical Field
    1. Stimulated and Spontaneous Raman Transitions
    2. Coherent Population Trapping and VSCPT Cooling
    3. Lamb Dip Spectroscopy Revisited: Crossover Resonances
    4. Lasing Without Inversion
    5. Autler–Townes Effect
    6. Hanle Effect
    7. Quantum Jumps and the Quantum Zeno Effect

  6. Structure of Simple Atoms
    1. Angular Momentum, Tensor Operators, and the Spherical Basis
    2. Fine Structure
    3. Zeeman and Stark Effects (Breit–Rabi Formula)
    4. Hyperfine Structure
    5. Anomalous Zeeman and Stark Effects
    6. Algebra of Dipole Matrix Elements, Wigner–Eckhart Theorem, and Selection Rules
    7. Optical Pumping of Hyperfine Levels
    8. Sub-Doppler Laser Cooling Mechanisms
    9. Magic Wavelengths

  7. Quantum-Mechanical Atom–Field Interactions
    1. Quantization of the Electromagnetic Field
    2. Jaynes-Cummings Model, Dressed States Revisited
    3. Quantum Vacuum Effects
      1. Spontaneous Emission: Weisskopf–Wigner Theory
      2. Lamb Shift
      3. Casimir–Polder Forces
      4. Enhancement and Suppression of Spontaneous Emission
      5. Vacuum Drag Forces
      6. Unruh Effect
    4. Dissipation and Measurement in Cavity QED
    5. Cavity QED: Input-Output Formalism
    6. Quantization of a Traveling Wave
    7. Resolvent Formalism
    8. Connection to the Classical Field

  8. Coherence of the Quantum Electromagnetic Field
    1. Coherence Heirarchy and the Wiener–Khinchin Theorem
    2. Experiment of Hanbury-Brown and Twiss
    3. Squeezed Light
    4. Bunching and Antibunching of Photons
    5. Parametric Downconversion
    6. Hong–Ou–Mandel Interference
    7. Interference of Independent Photons

  9. Quantum Theory of the Laser
    1. Master Equation and Fokker–Planck Equation
    2. Threshold Behavior
    3. Laser Oscillation and Gain Saturation
    4. Transient Behavior: Vacuum Seeding and Relaxation Oscillations
    5. Frequency Pulling
    6. Schawlow–Townes Limit
    7. Injection Locking
    8. Photon Statistics

  10. Bose-Einstein Condensation in Dilute Gases
    1. Gross–Pitaevskii Equation
    2. Bogoliubov Linearization
    3. Hartree–Fock–Bogoliubov Approximation
    4. Production of BECs
    5. Coherence Properties
    6. Dispersion and Superfluid Behavior