Multipole interaction between atoms and their photonic environment

Abstract

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.

17 pages, to be published in Physical Review A

References in corpus (5)

• Three-dimensional quantization of the electromagnetic field in dispersive and absorbing inhomogeneous dielectrics
• QED commutation relations for inhomogeneous Kramers-Kronig dielectrics
• Intermolecular energy transfer in the presence of dispersing and absorbing media
• Spontaneous emission rate of an excited atom placed near a nanofiber
• Transient QED effects in absorbing dielectrics

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• Enhanced spontaneous emission from nanodiamond colour centres on opal photonic crystal
• Field quantization in inhomogeneous anisotropic dielectrics with spatio-temporal dispersion
• Few-mode Field Quantization for Multiple Emitters
• Quantizing polaritons in inhomogeneous dissipative systems
• Gauge-invariant theory of truncated quantum light-matter interactions in arbitrary media
• A dual-Lagrangian description adapted to quantum optics in dispersive and dissipative dielectric media
• Space-time propagation of photon pulses in dielectric media,illustrations with beam splitters
• Description of spontaneous photon emission and local density of states in presence of a lossy polaritonic inhomogenous medium
• Mode expansions in the quantum electrodynamics of photonic media with disorder
• Quantifying the breakdown of the rotating-wave approximation in single-photon superradiance