Closure relations for composite bosons: difference between polaritons and Wannier or Frenkel excitons

Details Closure relations for composite bosons: difference between polaritons and Wannier or Frenkel excitons Closure relations for composite bosons: difference between polaritons and Wannier or Frenkel excitons

2008-06-27

arxiv.org/abs/0806.4521v2

Physics

Condensed Matter

Mesoscale and Nanoscale Physics

Scientific paper

10.1103/PhysRevB.78.235303

We derive the closure relation for $N$ polaritons made of three different types of excitons: bosonized excitons, Frenkel or Wannier excitons. In the case of polaritons made of Wannier excitons, we show how this closure relation, which appears as non-diagonal, may reduce to the one of $N$ elementary bosons, the photons, with its $1/N!$ prefactor, or to the one of $N$ Wannier excitons, with its $(1/N!)^2$ prefactor. Widely different forms of closure relations are thus found depending on the composite bosons at hand. Comparison with closure relations of excitons, either bosonized or kept composite as Frenkel or Wannier excitons, allows us to discuss the influence of a reduction of the number of internal degrees of freedom, as well as the importance of the composite nature of the particles and the existence of fermionic components.

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