Contents
Introduction
Quantisation of electromagnetism
Revision: Lagrangian for electromagnetism
Eliminating redundant variables
Canonical quantisation; photon modes
Approximations of light-matter coupling
Further reading
Quantum electrodynamics in other gauges
Freedom of choice of gauge and classical equations
Transformation to the electric dipole gauge
Electric dipole gauge for semiclassical problems
Pitfalls of perturbation
Further reading
Jaynes Cummings model
Semiclassical limit
Single mode quantum model
Many mode quantum model --- irreversible decay
Further properties of collapse and revival
Density matrices for 2 level systems
Density matrix equation for relaxation of two-level system
Dephasing in addition to relaxation
Power broadening of absorption
Further reading
Resonance Fluorescence
Spectrum of emission into a reservoir
Quantum regression ``theorem''
Resonance fluorescence spectrum
Further reading
Quantum stochastic methods
Quantum jump formalism
Heisenberg-Langevin equations
Fluctuation dissipation theorem
Further reading
Cavity Quantum Electrodynamics
The Purcell effect in a 1D model cavity
Weak to strong coupling via density matrices
Examples of Cavity QED systems
Further reading
Superradiance
Simple density matrix equation for collective emission
Beyond the simple model
Further reading
The Dicke model
Phase transitions, spontaneous superradiance
No-go theorem: no vacuum instability
Radiation in a box; restoring the phase transition
Dynamic superradiance
Further Reading
Lasers and micromasers
Density matrix equations for a micromaser and a laser
Laser rate equations
Laser Linewidth
Further reading
More on lasers
Density matrix equation
Spontaneous emission, noise, and parameter
Single atom lasers
Further reading
Three levels, and coherent control
Semiclassical introduction
Coherent evolution alone; why does EIT occur
Dark state polaritons
Further reading
Bibliography