Multipole interaction between atoms and their photonic environment

Details Multipole interaction between atoms and their photonic environment Multipole interaction between atoms and their photonic environment

2003-07-04

arxiv.org/abs/quant-ph/0307031v1

Phys. Rev. A 68, 013822 (2003)

Physics

Quantum Physics

17 pages, to be published in Physical Review A

Scientific paper

10.1103/PhysRevA.68.013822

Macroscopic field quantization is presented for a nondispersive photonic dielectric environment, both in the absence and presence of guest atoms. Starting with a minimal-coupling Lagrangian, a careful look at functional derivatives shows how to obtain Maxwell's equations before and after choosing a suitable gauge. A Hamiltonian is derived with a multipolar interaction between the guest atoms and the electromagnetic field. Canonical variables and fields are determined and in particular the field canonically conjugate to the vector potential is identified by functional differentiation as minus the full displacement field. An important result is that inside the dielectric a dipole couples to a field that is neither the (transverse) electric nor the macroscopic displacement field. The dielectric function is different from the bulk dielectric function at the position of the dipole, so that local-field effects must be taken into account.

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