Mode-selective quantization and multimodal effective models for spherically layered systems

Abstract

We propose a geometry-specific, mode-selective quantization scheme in coupled field-emitter systems which makes it easy to include material and geometrical properties, intrinsic losses as well as the positions of an arbitrary number of quantum emitters. The method is presented through the example of a spherically symmetric, non-magnetic, arbitrarily layered system. We follow it up by a framework to project the system on simpler, effective cavity QED models. Maintaining a well-defined connection to the original quantization, we derive the emerging effective quantities from the full, mode-selective model in a mathematically consistent way. We discuss the uses and limitations of these effective models.

Non-hermitian Hamiltonian description for quantum plasmonics: from dissipative dressed atom picture to Fano states

“…so thatÊ ω,n is the electric field operator associated to the LSP n mode. This leads us to define the bosonic creation operator for a given position of the emitter, satisfying the commutation relation [â ω ′ ,n ′ (r d ),â † ω,n (r d )] = δ(ω − ω ′ )δ n,n ′ [22,30] a ω,n (r d ) = 1 i κ ω,n (r d )…”

“…Finally, we define the effective Hamiltonian H ef f so that i ∂ t |Ψ ef f (t) =Ĥ ef f |Ψ ef f (t) . Identifying the dynamics of the wavefunctions in the discrete and continuum descriptions, we obtain the matrix representation of the effective Hamiltonian in the basis {|e, ∅ , |g, 1 1 , · · · , |g, 1 N } [30,39]…”

Quantum description and emergence of nonlinearities in strongly coupled single-emitter nanoantenna systems

“…To understand the different coupling regimes, we use a quantum description and derive an effective Hamiltonian [57][58][59] whose structure is completely analogous to cavity QED Hamiltonians. The derivation is based on a first-principles method corresponding to the coupling of a single two-level system with a reservoir of harmonic oscillators: the Fano diagonalization [63,64].…”

“…II, we derive a quantization procedure based on Refs. [57][58][59] and extend it to an arbitrary shaped nanoantenna by linking the Jaynes-Cummings coupling g with numerical solutions of the local density of states. The effective non-Hermitian Hamiltonian is then shown to be equivalent to a quantum master equation description of the QE-plasmon system where the plasmonic mode is described as a mixture of bright and dark modes.…”

Quantization of Quasinormal Modes for Open Cavities and Plasmonic Cavity Quantum Electrodynamics

“…and can be expanded in basis functions of the Green's function as in Refs. [49][50][51][52]. Inspired by this elegant approach [49], we use instead an expansion using few dominating (regularized) QNMs as in G QNM (r, r , ω), so that the source field expression of the electric field operator can be rewritten,…”