Quantized Fields in a Nonlinear Dielectric Medium: A Microscopic Approach

Details Quantized Fields in a Nonlinear Dielectric Medium: A Microscopic Approach Quantized Fields in a Nonlinear Dielectric Medium: A Microscopic Approach

1996-08-26

arxiv.org/abs/atom-ph/9608002v1

Physics

Atomic Physics

44 pages LaTex, no figures, submitted for publication

Scientific paper

10.1103/PhysRevA.55.678

Theories which have been used to describe the quantized electromagnetic field interacting with a nonlinear dielectric medium are either phenomenological or derived by quantizing the macroscopic Maxwell equations. Here we take a different approach and derive a Hamiltonian describing interacting fields from one which contains both field and matter degrees of freedom. The medium is modelled as a collection of two-level atoms, and these interact with the electromagnetic field. The atoms are grouped into effective spins and the Holstein- Primakoff representation of the spin operators is used to expand them in one over the total spin. When the lowest-order term is combined with the free atomic and field Hamiltonians, a theory of noninteracting polaritons results. When higher-order terms are expressed in terms of polariton operators, standard nonlinear optical interactions emerge.

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