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arXiv:2007.06320 · New Journal of Physics

Light interaction with extended quantum systems in dispersive media

Giovanni Scala, Francesco Vincenzo Pepe, Paolo Facchi A, Saverio Pascazio, Karolina Słowik

Published Dec 1, 2020• 7 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1088/1367-2630/abd204

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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.
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.
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.
Solving the challenging problem of the amplification and generation of an electromagnetic field in nanostructures enables us to implement many properties of the electromagnetic field at the nanoscale in practical applications. A first-principles quantum-mechanical consideration of such a problem is sufficiently restricted by the exponentially large number of degrees of freedom and does not allow the electromagnetic-field dynamics to be described if it involves a high number of interacting atoms and modes of the electromagnetic field. Conversely, the classical description of electromagnetic fields is incorrect at the nanoscale due to the high level of quantum fluctuations connected to high dissipation and noise levels. In this paper, we develop a framework with a significantly reduced number of degrees of freedom, which describes the quantum spatial dynamics of electromagnetic fields interacting with atoms. As an example, we consider the interaction between atoms placed in a metallic subwavelength groove and demonstrate that a spontaneously excited electromagnetic pulse propagates with the group velocity. The developed approach may be exploited to describe nonuniform amplification and propagation of electromagnetic fields in arbitrary dispersive dissipative systems.
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Abstract We investigate (non‐relativistic) atomic systems interacting with quantum electromagnetic field (QEF). The resulting model describes spontaneous emission of light from a two‐level atom surrounded by various initial states of the QEF. We assume that the quantum field interacts with the atom via the standard, minimal‐coupling Hamiltonian, with the A2 term neglected. We also assume that there will appear at most single excitations (photons). By conducting the analysis on a general level we allow for an arbitrary initial state of the QEF (which can be for instance: the vacuum, the ground state in a cavity, or the squeezed state). We derive a Volterra‐type equation which governs the time evolution of the amplitude of the excited state. The two‐point function of the initial state of the QEF, integrated with a combination of atomic wavefunctions, forms the kernel of this equation.