PhD Defence by Mads Anders Jørgensen

Single-photon superradiance in nanophotonics: a multiple-scattering perspective

by Mads Anders Jørgensen

Supervisors
Principal supervisor: Associate Professor Martijn Wubs, DTU Electro Denmark
Co-supervisor: Associate Professor Nicolas Stenger, DTU Electro Denmark
Co-supervisor: Associate Professor Sanshui Xiao, DTU Electro Denmark

Evaluation Board
Professor Niels Gregersen, DTU Electro, Denmark
Professor Carsten Henkel, Univeristy of Potsdam, Germany 
Professor Klaus Mølmer, University of Copenhagen, Denmark

Master of the Ceremony
Senior Researcher Philip Trøst Kristensen, DTU Electro, Denmark

Abstract:
Collective emission in solids is the foundation of many promising technologies, and the environment plays a key role in determining both the interaction between emitters and the resulting collective emission characteristics. In this thesis, we study collective single-photon emission from two or more quantum emitters with a focus on three cases: (i) The impact of the Rotating-Wave Approximation on collective emission rates, (ii) how collective emission from emitters in a thin dielectric layer is affected by the environment in an experimentally relevant three-layer structure, and (iii) how the addition of a dielectric nanopillar, used in experiments to localize emitters, affects the single-emitter and collective emission from emitters in a thin-layer dielectric situated on top of the nanopillar. In all three cases, multiple-scattering plays an important conceptual role.

In the first case, we examine how single-photon superradiant emission rates are affected by applying the Rotating-Wave Approximation (RWA) in the dipole-interaction Hamiltonian, valid for arbitrary lossless and non-dispersive media. We do this through a multiple-scattering formalism from which the medium-specific electromagnetic propagator is seen to mediate the interaction between emitters. If the RWA is not used, this propagator is the classical Green’s function of the medium, but with the RWA the propagator is shown to be the classical Green’s function plus an additional real, position-dependent error. In the vector theory of electromagnetism of free space, the inter-emitter interaction strength is wrong by a factor of two in the near-field. For the scalar theory, we instead find that the relative error diverges in the near-field.

While it is often claimed that the RWA only affects the collective Lamb shifts, we find that also collective decay rates are affected in general. We quantify the RWA-induced error in the predicted collective decay rates from two detuned emitters as well as for three identical emitters in various configurations in free space. The maximal error in the collective decay rates is found in the intermediate field, and not in the near-field where the error of the interaction is largest. We find a qualitatively different impact of the RWA on the collective emission from two identical emitters compared to the collective emission from three or more identical emitters. This is because two identical emitters are an example of a class of ring systems with discrete rotational symmetry, which we identify as exhibiting collective emission with no error from making the RWA. 

In the second case we study collective emission in layered media. Inspired by ongoing experiments in our research group on quantum emitters in thin-layer materials, we examine the case of collective emission from quantum (defect) emitters inside a thin layer of hexagonal boron nitride (hBN). We calculate the full retarded Green’s function of the layered medium where guided modes appear as poles of a multiplescattering parameter. We focus especially on the role of guided modes in mediating the interaction between emitters for both dielectric and noble metal substrates. 

In order to realize strong collective emission, it is necessary that the photonmediated interaction between the emitters is also strong. Surface plasmons are often used to enhance the interaction between light and matter. While we find that guided modes, both waveguide modes and surface plasmon polaritons, help the long-range interaction between emitters, it is not so straightforward for emitter separations on the order of the optical wavelength or smaller. In the near- and intermediate fields, the guided mode and radiative contributions to the interaction can cancel, thereby reducing the total inter-emitter interaction and the superradiant decay rate. So while the far-field enhancement of the interaction due to guided modes is to be expected, the Green’s function of the medium is essential in determining whether guided modes enhance collective emission for emitters in the near- and intermediate fields, where the interaction is also much stronger than in the far-field. 

A final point of study in the second case is a highly efficient, and predominantly one-way, energy transfer between donor and acceptor emitters in the three-layer medium. Here we utilize the strong dependence of the single-emitter decay rates on the distance to the metal interface to demonstrate a situation where the cross density of optical states between the donor and acceptor emitters is larger than the local density of optical states at the position of the donor. In this way, energy transfer to the acceptor becomes the preferred channel through which energy can leave the donor, beating the spontaneous single-emitter decay.

The third case is an extension of the second, and it was initiated as part of the external stay at Aalborg University. Recent developments have shown that defect emitters in hBN can be localized with the help of dielectric nanopillars. With the use of the Green’s Function Volume Integral Equation Method, we investigate how such a nanopillar affects both single- and collective emission properties in two situations: one where the thin layer of hBN lies rigidly on top of the pillar, and one where the hBN is curved around the pillar, using realistic experimental geometries. We find that the pillar induces a change in the emission properties of single emitters, with Fabry-Pérot-like oscillations as the pillar dimensions are varied. For a specific pillar used in experiments, the pillar tends to reduce the interaction strength and the superradiant decay rate for emitters on top. We attribute this to the fact that the pillar can act as a waveguide, leading away light that would otherwise have contributed to the total photon-mediated inter-emitter interaction. Interestingly, we find that emitters on opposite edges of a pillar with dimensions used in experiments in our group coincide with a local maximum (minimum) of the two-emitter superradiant (subradiant) decay rate. We believe that our results can help guide experimental studies seeking to realize collective emission in thin-layer media.