Quantum Optics

Lecturer: Tom Stace

Course Outline

1. Quantization of the Free EM Field & Hamiltonians for Quantum Optics (2 hours): Starting from the classical Maxwell's equations for the EM field, we'll quantise the field operators to present the quantum description of the field in the form of the EM Hamiltonian and related commutation relations. We'll revisit creation and annihilation operators for a harmonic oscillator, and relate them to the EM field operators to derive the 'second quantised' version of the EM Hamiltonian. We might also discuss the role of gauges in the quantisation procedure. Look at the physical interpretation of the creation and annihilation operators in the momentum and position bases. Quantum description of an optical cavity, the action of beam splitters and phase shifters. Conclude with Hong-Ou-Mandel experiment to illustrate
2. States of light and their detection (single mode Fock states, coherent states, squeezed states squeezed states). (1 hour): Discuss the vacuum, number (Fock) states, coherent states and squeezed states of a single mode. Discuss the classical analogues of these states and outline the Wigner functions on phase space. Photon counting versus homodyne detection (measuring conjugate properties: photon number vs phase)
3. The Jaynes-Cummings model of atom-optical interaction: Collapses and Revivals.(1 hour): Derive the coupling between an atom and the EM field in a cavity, and present the two-level approximation. Analyse the system treating the field as classical, then as quantum mechanical and show similarities and differences. Solid state analogues.
4. Open quantum systems (including master equations, trajectories and measurement) (2 hours): Discrete system interacting with a continuum. Density matrix. Born-Markov approximation. Decoherence and dephasing. Conditional dynamics and interpretation of trajectories. Interpretation of decoherence as a 'measurement by the environment'. Vacuum noise in beam splitters.

Prerequisite

The prerequisite for the course will be electromagnetism and third year quantum mechanics (at least having seen the quantisation of a harmonic oscillator).