Lecturers: J. Donegan, P. Eastham

Rationale: This module provides material supporting research students, both experimental and theoretical, embarking on projects in nanoscale materials in 2,1 and 0 dimensional systems and nanoscale coupled light-matter systems. It demonstrates the application of concepts from undergraduate quantum mechanics and electromagnetism in a modern research field, and outlines extensions necessitated by research work such as quantum electrodynamics.

Module Aims: To overview the fundamental concepts of optical effects in nanoscale systems and coupled light-matter systems, particularly as they apply to semiconductor nanostructures and microcavities.

Module Learning Outcomes: On successful completion of this module, students will be able to:
1) Understand the nature of lower dimensional nanoscale systems, particularly the variation of the density of states.
2) Develop a detailed understanding of the optical properties of quantum wells.
3) Solve simple problems related to lower dimensional systems.
4) Write model Hamiltonians for electromagnetism with nanoscale semiconductor structures; explain how such models originate from Maxwell’s equations, the Schrodinger equation, and the bandstructure of semiconductors.
5) Solve these models for simple cases, such as perfect planar microcavities.
6) Appreciate key effects of quantum confinement in a hybrid matter-light system, including the formation of cavity resonances, polaritons, and changes in radiative decay rates.

Teaching and Learning Methods, including contact hours:  
Frontal Teaching: 18 hrs
Individual Reading: 64 hrs
Assignments: 32 hrs (8 assignments, 24 hrs individual work, 8 hrs classes)

Quantum confinement in finite and infinite potentials.
Density of states in 3, 2, 1 and 0 dimensional systems.
Semiconductor bandstructures, transitions and selection rules.
Optical effects in quantum wells, coupled quantum wells, and superlattices.
Optical effects in wires and dots.
Growth and fabrication of nanostructures.
Reflection and refraction at interfaces, transfer matrix methods, distributed Bragg reflectors, microcavities.
Solutions of the wave equation in resonant structures.
Exciton-polariton spectra, homogeneous and inhomogeneous linewidths, effects of disorder.
Second quantized formalism.
Quantization of the electromagnetic field.
Theory of two-level atom in an optical cavity: Rabi oscillations, Jaynes-Cummings ladder.
Radiative lifetimes and the Purcell effect.
Quantum theory of polaritons.
Collective effects: lasing, parametric oscillation, superradiance, polariton condensation.

Evaluation of the module: Student performance on assessments compared with learning outcomes. Student feedback collected twice during the module. We will also seek feedback from supervisors and other relevant staff members.

Indicative Reading and Resources:
Quantum Semiconductor Structures, C. Weisbuch and B. Vinter

Microcavities, A. Kavokin, J. Baumberg, G. Malpuech, F. Laussy (Oxford University Press, 2007, ISBN 0199228949)

Introduction to Nanophotonics, S. Gaponenko (to be published, may be appropriate)
Quantum Optics, M. Scully and M. Suhail Zubairy (Cambridge University Press, 1997, ISBN 0521435951).
Quantum Optics: An Introduction, M. Fox (Oxford University Press 2006, ISBN 0198566735)
Confined Photon Systems, eds. Benisty, Gerard, Houdre, Rarity (Springer Lecture Notes in Physics, 1999, ISBN 3540664351)

Notes provided in lectures.