Abstract
Based on a formalism that describes atom-light interactions in terms of the classical electromagnetic Green's function, we study the optical response of atoms and other quantum emitters coupled to one-dimensional photonic structures, such as cavities, waveguides, and photonic crystals. We demonstrate a clear mapping between the transmission spectra and the local Green's function that allows to identify signatures of dispersive and dissipative interactions between atoms. We also demonstrate the applicability of our analysis to problems involving three-level atoms, such as electromagnetically induced transparency. Finally we examine recent experiments, and anticipate future observations of atom-atom interactions in photonic bandgaps.
Highlights
As already noticed by Purcell in the first half of the past century, the decay rate of an atom can be either diminished or enhanced by tailoring its dielectric environment [1,2,3]
Based on a formalism that describes atom-light interactions in terms of the classical electromagnetic Green’s function, we study the optical response of atoms and other quantum emitters coupled to one-dimensional photonic structures, such as cavities, waveguides, and photonic crystals
In a recent experiment [38], the authors have observed signatures of collective atom-light interactions in the transmission spectra of atoms coupled to an alligator photonic crystal waveguide
Summary
As already noticed by Purcell in the first half of the past century, the decay rate of an atom can be either diminished or enhanced by tailoring its dielectric environment [1,2,3]. Very recently, the first experiments of atoms [38] and superconducting qubits [39] interacting with evanescent modes in the band gap of photonic crystal waveguides have been reported Within this context, it has become a necessity to understand the rich spectral signatures of atom-like emitters interacting through the guided modes of quasi-one-dimensional nanophotonic structures within a unified framework that extends beyond those of cavity [40] or waveguide QED [41]. In the first part of the article, we summarize the procedure to obtain an effective atom-atom Hamiltonian, in which the guided-mode fields are effectively eliminated and the atom interactions are written in terms of Green’s functions [42,43,44] We apply this formalism to a collection of atoms in different quasi-one-dimensional dielectric environments, and analyze the atomic transmission and reflection spectra in terms of the eigenvalues of the matrix consisting of the Green’s functions between every pair of atoms. In analogy to its classical counterpart, the electric field operator at frequency ω can be written in terms of bosonic annihilation (creation) operators f (f†) as [42]
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