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1. Introduction
2. Classical Molasses and Beam Slowing
2.1. The Spontaneous Light Force
2.2. 1D Optical Molasses
2.3. The Doppler Cooling Limit
2.4. Beam Slowing |
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2.5. Energy vs. Momentum Picture
2.6. 3D Molasses and Higher Intensity
2.7. Momentum and Spatial Diffusion |
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3. The QED Hamiltonian |
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4. Properties of Light
4.1. The Quantized Radiation Field
4.1.1. Thermal States (Chaotic Light)
4.1.2. Coherent States; Q(Alpha) Representation
4.1.3. Fluctuations, Noise, and Second Order Coherence
4.1.4. Single Photon States and the Hanbury-Brown Twiss Experiment |
Assignment 1 due |
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4.2. Squeezed States of Light
4.2.1. The Displacement and Squeeze Operators
4.2.2. Generation of Squeezed States, Classical Squeezing
4.2.3. Homodyne Detection
4.2.4. Teleportation |
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4.2.5. Beam Splitter and Homodyne Detection
4.2.6. Experiments with Squeezed Light |
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4.3. Interferometry and Entanglement
4.3.1. Gravitational Wave Detection
4.3.2. Heisenberg Limited Interferometry |
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4.3.3. Entanglement |
Assignment 2 due |
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5. Basic Aspects of the Interaction between Light and Atoms |
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5.1. Transition Amplitudes and Diagrams
5.2. Some Interaction Processes between Photons and Atoms
5.2.1. Emission
5.2.2. Absorption
5.2.3. Scattering
5.3. Resonant Scattering and Radiative Corrections |
Assignment 3 due |
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5.4. Interaction by Photon Exchange and Collisions
5.4.1. Van der Waals Interaction |
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5.4.2. Casimir Interactions
5.4.3. Langevin Model for Inelastic Collisions |
Assignment 4 due |
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5.4.4. Elastic Collisions between Cold Atoms
5.4.5. s-wave Scattering
6. Master Equation |
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7. Optical Bloch Equations
7.1. Derivation
7.2. Rotating-wave Approximation |
Assignment 5 due |
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7.3. Adiabatic Elimination of Coherences
7.4. Steady-state Solution
7.5. Spectrum of Emitted Light |
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7.6. Mean Radiation Forces
7.6.1. Radiation Pressure Force
7.6.2. Reactive Force
7.7. Moving Atoms, Friction Force |
Assignment 6 due |
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7.8. Diffusion in a Standing Wave
7.9. Experiments on the Stimulated Light Force
8. The Dressed Atom Approach
8.1. Derivation of the Energy Levels of the Dressed Atom |
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8.2. Resonance Fluorescence in the Dressed Atom Picture
8.3. Dipole Forces within the Dressed Atom Picture
8.3.1. Mean Dipole Force for an Atom at Rest
8.3.2. Mean Dipole Force for a Slowly Moving Atom
8.3.3. Energy Balance in a Small Displacement |
Assignment 7 due |
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8.3.4. Momentum Diffusion due to Dipole Force Fluctuations
8.3.5. Atoms Moving in a Standing Wave
8.3.6. Cooling in a Standing Wave
9. Spontaneous Light Force Traps |
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10. Quantum Monte Carlo Wavefunction Method
10.1. Basic Concepts
10.2. MCWF Procedure |
Assignment 8 due |
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10.3. Proof of Equivalence to the Optical Bloch Equations
11. Models of Decoherence
11.1. Decoherence - Definition and Perspective
11.2. Three Models of Phase Damping
11.2.1. Random Phase Noise
11.2.2. Elastic Collisions
11.2.3. Random Phase Flips
11.3. Jaynes-Cummings Collapses and Revivals |
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12. Ion Traps
12.1. Hamiltonians and Cooling
12.1.1. The Ion Trap Physical System
12.1.2. The Hamiltonian
12.1.3. Sideband Cooling - Process and Limits
12.1.4. Experimental Observations of Sideband Cooling |
Assignment 9 due |
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12.2. Quantum Control of Single Ions
12.2.1. The Challenge of Quantum State Preparation
12.2.2. Review of Unusual States
12.2.3. Motional State Control in Ion Traps
12.2.4. Motional Fock, Coherent, and Schroedinger Cat States
12.2.5. Recipe for Arbitrary Motional States |
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12.3. Quantum Computation with Trapped Ions
12.3.1. Quantum Gates and Circuits
12.3.2. The Cirac-Zoller CNOT
12.3.3. Geometric Phase Gate |
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13. Magnetic Traps and Evaporative Cooling
13.1. Stability, Majorana Flops, Magnetic Levitation
13.2. Wing's Theorem
13.3. Magnetic Trap Configurations |
Assignment 10 due |
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13.4. Evaporative Cooling
14. Bose-Einstein Condensation
14.1. Homogeneous Interacting Bose Gas, Bogoliubov Solution
14.2. Elementary Excitations |
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14.3. Inhomogeneous Bose Gas, Nonlinear Schrödinger Equation
14.4. The Thomas-Fermi Approximation
14.5. Hydrodynamic Flow of a Superfluid |
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