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Interaction of atomic systems with quantum vacuum beyond electric dipole approximation

Miriam Kosik, O. Burlayenko, Carsten Rockstuhl, Ivan Fernandez‐Corbaton, Karolina Słowik

Published Jan 1, 2020• 6 citations
Publisher

Abstract

The photonic environment can significantly influence emission properties and interactions among atomic systems. In such scenarios, frequently the electric dipole approximation is assumed that is justified as long as the spatial extent of the atomic system is negligible compared to the spatial variations of the field. While this holds true for many canonical systems, it ceases to be applicable for more contemporary nanophotonic structures. To go beyond the electric dipole approximation, we propose and develop in this article an analytical framework to describe the impact of the photonic environment on emission and interaction properties of atomic systems beyond the electric dipole approximation. Particularly, we retain explicitly magnetic dipolar and electric quadrupolar contributions to the light-matter interactions. We exploit a field quantization scheme based on electromagnetic Green’s tensors, suited for dispersive materials. We obtain expressions for spontaneous emission rate, Lamb shift, multipole-multipole shift and superradiance rate, all being modified with dispersive environment. The considered influence could be substantial for suitably tailored nanostructured photonic environments, as demonstrated exemplarily.

DOI
10.5445/ir/1000118967

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The photonic environment can significantly influence emission properties and interactions among atomic systems. In such scenarios, frequently the electric dipole approximation is assumed that is justified as long as the spatial extent of the atomic system is negligible compared to the spatial variations of the field. While this holds true for many canonical systems, it ceases to be applicable for more contemporary nanophotonic structures. To go beyond the electric dipole approximation, we propose and develop in this article an analytical framework to describe the impact of the photonic environment on emission and interaction properties of atomic systems beyond the electric dipole approximation. Particularly, we retain explicitly magnetic dipolar and electric quadrupolar contributions to the light-matter interactions. We exploit a field quantization scheme based on electromagnetic Green’s tensors, suited for dispersive materials. We obtain expressions for spontaneous emission rate, Lamb shift, multipole-multipole shift and superradiance rate, all being modified with dispersive environment. The considered influence could be substantial for suitably tailored nanostructured photonic environments, as demonstrated exemplarily.
The photonic environment can significantly influence emission properties and interactions among atomic systems. In such scenarios, frequently the electric dipole approximation is assumed that is justified as long as the spatial extent of the atomic system is negligible compared to the spatial variations of the field. While this holds true for many canonical systems, it ceases to be applicable for more contemporary nanophotonic structures. To go beyond the electric dipole approximation, we propose and develop in this article an analytical framework to describe the impact of the photonic environment on emission and interaction properties of atomic systems beyond the electric dipole approximation. Particularly, we retain explicitly magnetic dipolar and electric quadrupolar contributions to the light-matter interactions. We exploit a field quantization scheme based on electromagnetic Green's tensors, suited for dispersive materials. We obtain expressions for spontaneous emission rate, Lamb shift, multipole-multipole shift and superradiance rate, all being modified with dispersive environment. The considered influence could be substantial for suitably tailored nanostructured photonic environments, as demonstrated exemplarily.
Abstract We derive a light–matter interaction Hamiltonian to describe a quantum system embedded in a dispersive environment and coupled with the electromagnetic field. We include in this theory the spatial extension of the system, taken into account through its wavefunction. This enables us to overcome the divergence problem of the Green tensor propagator that arises from a point-like approximation of the quantum system. Thus the formalism can be applied to generalize the expressions for the spontaneous emission rate and the Lamb shift for a quantum system defined by a spatially extended dipole. In particular, these quantities can be modified by the asymmetry of the spatial structure of the atomic system as demonstrated in two test-bed examples.
Summary form only given. In the pioneering work of Purcell, the possibility to control spontaneous emission lifetimes of quantum emitters by tailoring their electromagnetic surroundings was widely investigated and verified in various types of cavities or band-gap environments. This includes semiconductor microstructures, photonic crystals, and plasmonic nanoparticles. Due to the extraordinary ability of plasmonic nanostructures to confine light into subwavelength spatial domains, steps beyond the paradigmatic electric dipole approximation in the theoretical description of this process may be necessary. In this contribution, we focus on the case of multiple in general nonidentical two-level emitters, sharing the same electromagnetic surroundings, whose local density of states could be tailored by a neighbouring nanostructure. In this case, the surroundings may serve as a long-distance emitter-emitter interaction carrier, or it may trigger collective emission processes, in analogy to Dicke superradiance. We describe these phenomena taking into account the electric dipole, magnetic dipole and electric quadrupole components of light-matter interaction Hamiltonian.
In this paper, we study the collective effects which appear as a pair of quantum emitters is positioned in close vicinity to a plasmonic nanoparticle. These effects include multipole-multipole interaction and collective decay, the strengths and rates of which are modified by the presence of the nanoparticle. As a result, entanglement is generated between the quantum emitters, which survives in the stationary state. To evaluate these effects, we exploit the Green's tensor-based quantization scheme in the Markovian limit, taking into account the corrections from light-matter coupling channels higher than the electric dipole. We find these higher-order channels to significantly influence the collective rates and degree of entanglement, and in particular, to qualitatively influence their spatial profiles. Our findings indicate that, apart from quantitatively modifying the results, the higher-order interaction channels may introduce asymmetry into the spatial distribution of the collective response.
We present a general theoretical framework to capture light-matter interactions beyond the electric-dipole approximation (EDA), applicable to extended nano- and microscale materials interacting with spatially structured electric fields without truncation at finite multipolar order. The approach is based on the Power-Zienau-Woolley (PZW) Hamiltonian for light-matter interactions and a representation of the material's Hamiltonian in a basis of maximally localized Wannier functions (MLWFs), obtainable from first-principles calculations. We utilize this approach to clarify the limitations of the ubiquitous dipole approximation. We consider electric fields with both uniform and non-uniform intensities and a range of ratios of system size to the wavelength of light. Through this analysis, we identify the conditions under which the EDA breaks down, leading to significant errors in the light-induced dynamics. Contrary to conventional belief, we find that the EDA is remarkably robust for uniformly illuminated 1-D or 2-D materials when light propagates perpendicular to the material. For 3-D materials or non-perpendicular illumination of lower-dimensional materials, conventional wisdom holds and the EDA begins to break down when the wavelength becomes comparable to the system size. Furthermore, the EDA fails when the material is illuminated partially or non-uniformly. For slowly varying field intensities this failure can be corrected by finite-order multipolar corrections. However, for fields that vary substantially, correcting via multipolar terms becomes computationally impractical. In contrast, our approach captures beyond-dipole light-matter interactions at the computational cost of a standard dipole calculation. This efficiency enables accurate first-principles simulations of spatially structured light-matter dynamics in nanoscale devices, quantum materials, and interfaces.
We derive a rigorous theory of the interaction between photons and spatially extended excitons confined in quantum dots in inhomogeneous photonic materials. We show that beyond the dipole approximation, the radiative decay rate is proportional to a nonlocal interaction function, which describes the interaction between light and spatially extended excitons. In this regime, light and matter degrees of freedom cannot be separated and a complex interplay between the nanostructured optical environment and the exciton envelope function emerges. We illustrate this by specific examples and derive a series of important analytical relations, which are useful for applying the formalism to practical problems. In the dipole limit, the decay rate is proportional to the projected local density of optical states, and we obtain the strong and weak confinement regimes as special cases.