Quantum Optics 2024
Lectures:
From classical Maxwell equations to representing the electromagnetic field Hamiltonian as a set of (quantum) harmonic oscillators.
Linear optics and single photons.
Mach-Zender interferometer. Some basic metrology. Hong-Ou-Mandel effect.
Quantum vs. semiclassical photodetection.
Photon count distribution and a classical bound. Homodyne detection. Introducing the Wigner function.
Quantum state tomography. Other phase space distributions - Q and P functions.
Homodyne detection and correlation functions using the P function language. Introducing light-matter coupling.
Perturbative approach to atomic transitions. Jaynes-Cumming Hamiltonian as the minimal model.
Losses in quantum mechanics. Master equation formalism. Example: damped harmonic oscillator.
Spontaneous emission via the master equation. Phase space picture leads to the Fokker-Planck equation.
More on the master equation. Atomic decay to a squeezed bath. Towards the quantum theory of lasers.
Master equation for a laser. Scully-Lamb model.
Quantum trajectories.
Collective effects. Tavis-Cummings and Dicke models. Superradiance.
Dark state polaritons and single photon nonlinearities.
Useful sources:
D. Walls, G. Millburn, Quantum Optics
Wolfgang Schleich, Quantum Optics in Phase Space
C. C. Gerry and Peter Knight, Introductory Quantum Optics
H. Carmichael, Statistical methods in quantum optics
S. Haroche, J. Raimond, Exploring the quantum
Oral exam
Choose one topic from section A and prepare a short (7mins) description. Question from section B will be randomly selected at the exam
A0. Properties of quantum states of light. (coherence, photon number statistics, ...)
A1. Photodetection theory and correlation functions.
A2. Phase estimation using the Mach-Zender interferometer.
A3. Squeezed states of light and their basic properties.
A4. Phase space description of single mode light in different representations.
A5. Quantum state tomography.
A6. Light-matter interactions. Perturbation theory and selection rules.
A7. Open quantum systems. Ideas behind the master equation approach and a simple example.
A8. How do lasers work?
A9. Collective effects in matter-light coupling and the superradiance phenomenon.
A10. Dark state polaritons.
B1. Electromagnetic field modes and their quantization.
B2. Hong-Ou-Mandel effect.
B3. Homodyne detection of field quadratures.
B4. Quantum description of interference.
B5. Photon bunching and antibunching. Hanbury, Brown and Twiss effect.
B6. Phase space description of coherent and squeezed states.
B7. Production of photon pairs using parametric amplification.
B8. Janes-Cummings model and its basic properties.
B9. Spontaneous emission via the master equation.
B10. Schroedinger cat state, its nonclassical properties and decoherence.
B11. Description of open system dynamics via quantum trajectories.
B12. The Dicke model and its phase transition.