Novel Quantum Condensates in Excitonic Matter

These lectures interleave discussion of a novel physical problem of a new kind of condensate with teaching of the fundamental theoretical tools of quantum condensed matter field theory. Polaritons and excitons are light mass composite bosons that can be made inside solids in a number of different ways. As bosonic particles, they are liable to make a phase coherent ground state - generically called a Bose-Einstein condensate (BEC) - and these lectures present some models to describe that problem, as well as general approaches to the theory. The focus is very much to explain how mean-field-like approximations that are often presented heuristically can be derived in a systematic fashion by path integral methods. Going beyond the mean field theory then produces a systematic approach to calculation of the excitation energies, and the derivation of effective low energy theories that can be generalised to more complex dynamical and spatial situations than is practicable for the full theory, as well as to study statistical properties beyond the semi-classical regime. in particular, for the polariton problem, it allows one to connect the regimes of equilibrium BEC and non-equilibrium laser. The lectures are self-sufficient, but not highly detailed. The methodological aspects are covered in standard quantum field theory texts and the presentation here is deliberately cursory: the approach will be closest to the book of Altland and Simons. Since these lectures concern a particular type of condensate, reference should also be made to texts on BEC, for example by Pitaevskii and Stringari. A recent theoretically focussed review of polariton systems covers many of the technical issues associated with the polariton problem in greater depth and provides many further references.