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Calendar

Lec # Topics KEY DATES
1 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
2 2.5. Energy vs. Momentum Picture
2.6. 3D Molasses and Higher Intensity
2.7. Momentum and Spatial Diffusion
3 3. The QED Hamiltonian
4 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
5 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
6 4.2.5. Beam Splitter and Homodyne Detection
4.2.6. Experiments with Squeezed Light
7 4.3. Interferometry and Entanglement
4.3.1. Gravitational Wave Detection
4.3.2. Heisenberg Limited Interferometry
8 4.3.3. Entanglement Assignment 2 due
9 5. Basic Aspects of the Interaction between Light and Atoms
10 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
11 5.4. Interaction by Photon Exchange and Collisions
5.4.1. Van der Waals Interaction
12 5.4.2. Casimir Interactions
5.4.3. Langevin Model for Inelastic Collisions
Assignment 4 due
13 5.4.4. Elastic Collisions between Cold Atoms
5.4.5. s-wave Scattering

6. Master Equation
14 7. Optical Bloch Equations
7.1. Derivation
7.2. Rotating-wave Approximation
Assignment 5 due
15 7.3. Adiabatic Elimination of Coherences
7.4. Steady-state Solution
7.5. Spectrum of Emitted Light
16 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
17 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
18 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
19 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
20 10. Quantum Monte Carlo Wavefunction Method
10.1. Basic Concepts
10.2. MCWF Procedure
Assignment 8 due
21 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
22 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
23 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
24 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
25 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
26 13.4. Evaporative Cooling

14. Bose-Einstein Condensation
14.1. Homogeneous Interacting Bose Gas, Bogoliubov Solution
14.2. Elementary Excitations
27 14.3. Inhomogeneous Bose Gas, Nonlinear Schrödinger Equation
14.4. The Thomas-Fermi Approximation
14.5. Hydrodynamic Flow of a Superfluid