Novel Quantum Condensates in Excitonic Matter
Abstract
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 BoseEinstein 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 meanfieldlike 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 semiclassical regime. in particular, for the polariton problem, it allows one to connect the regimes of equilibrium BEC and nonequilibrium laser. The lectures are selfsufficient, 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 [1]. Since these lectures concern a particular type of condensate, reference should also be made to texts on BEC, for example by Pitaevskii and Stringari [2]. A recent theoretically focussed review of polariton systems is [3] covers many of the technical issues associated with the polariton problem in greater depth and provides many further references.
 Publication:

Lectures on the Physics of Strongly Correlated Systems XIII: Thirteenth Training Course in the Physics of Strongly Correlated Systems
 Pub Date:
 August 2009
 DOI:
 10.1063/1.3225478
 Bibcode:
 2009AIPC.1162...15L
 Keywords:

 71.35.y;
 03.75.Kk;
 03.50.Kk;
 71.20.Nr;
 73.23.Hk;
 Excitons and related phenomena;
 Dynamic properties of condensates;
 collective and hydrodynamic excitations superfluid flow;
 Other special classical field theories;
 Semiconductor compounds;
 Coulomb blockade;
 singleelectron tunneling