Tricarico, Roberto (2020) Light-matter interaction in open systems: from nanoparticles to atoms. [Tesi di dottorato]

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In this doctoral thesis, we are going to present three selected topics on light-matter interaction in open systems. The three chapters can be read independently and their content is organized as follows. In chapter 1 we discuss the full-retarded light-scattering by homogeneous and isotropic nanoparticles, both in the plasmonic and in the dielectric case. We do it by introducing a modal expansion for the scattered field, whose basis elements do not depend on the material constituting the scattering object. As a matter of fact, by solving a permittivity independent auxiliary eigenvalue problem, it is possible to generate a set of material independent modes (MIMs) that are able to efficiently reconstruct the scattered field. The eigenvalues of the aforementioned problem are the eigen-permittivities of the nanoparticle and we say that a given MIM resonates when the corresponding eigenpermittivity approaches the permittivity of the scatterer. This material picture allows a clear separation of the roles played by shape and material in the scattering problem: the shape determines the basis elements of the expansion and the material weighs their contribution to the scattered pattern. In chapter 2 we provide a full-retarded quantum theory of the plasmon excitations in arbitrarily shaped metal nanoparticles and dimers. The continuous energy oscillation between the kinetic energy of the free electrons in the metal and the Coulomb energy associated to the charge accumulation on the surface of the nanoparticle, is the physical origin of the electrostatic plasmon resonances. In the long-wavelength limit, the electron fluid motion oscillates without decaying and, providing a modal expansion for the electron displacement field, a canonical quantization procedure can be applied to define the plasmons: quasiparticles describing the collective motion of the electrons. When we exit the quasistatic regime and enter the full-retarded one, the nanoparticles start to radiate power to infinity and, as a consequence, these oscillations shift in energy and decay in time. At the quantum level, this process is described by the plasmon-photon interaction Hamiltonian that we rigorously derive and discuss in its various approximations. Eventually, we provide non-perturbative formulas to compute the radiative decay rate and the frequency shift of the plasmon excitations, valid for arbitrarily shaped metal nanoparticles and dimers in the full-retarded regime. These formulas do not use full-wave modal expansions but only electrostatic ones, and it makes them efficient tools to compute these quantities. In chapter 3 we discuss Rydberg ensembles of atoms, in the electromagnetic induced transparency setup, as a possible route to realize photon-photon nonlinear interaction. Thanks to the blockade mechanism provided by Rydberg atoms, a single photon is indeed able to saturate the atomic response of a considerably large portion of the ensemble, that appears opaque to a second incoming one. While the continuous wave response of such a medium was largely studied in the past, the pulse dynamics has been explored only recently. Interestingly, it has been observed that the transient light can be more antibunched than the CW one. Our goal is to understand what the physical origin of this behaviour is, and whether this effect actually reflects a stronger nonlinearity.

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