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Abstract

In condensed matter physics, material science and quantum chemistry, recent experimental progress has laid the foundation to control and alter the properties of matter at will by coupling strongly to individual photons or even just the vacuum fluctuations of the electromagnetic field. This is usually realized by changing the photonic environment and with this the photon field, e.g., by using high-Q optical cavities or plasmonic nanostructures to which the matter system is then strongly coupled to. The ensuing strong coupling brings about novel states of matter with hybrid light-matter character known as polaritons. These hybridized systems allow to control material properties and chemistry in an unprecedented way such as altering chemical reactions, room-temperature polariton lasing, enhance charge and energy transfer, to name but a few. To better understand these intriguing effects, numerous theoretical studies have been performed, most of which are based on simple approximate models. These simplified models capture correctly the main features of the emerging novel physics but overlook important details pertaining to the coupled system. To overcome these restrictions, ab-initio methods such as quantum electrodynamical density-functional theory ( QEDFT ) that treat matter and photons on the same quantized footing have recently been developed. This method allow an in-depth modeling of the light-matter system from first principles. However, the application of these theoretical methods is so far still limited. This is, on the one hand, due to missing efficient numerical schemes to solve the resulting equations. On the other hand, it remains unclear in which cases a full ab-initio simulation would provide novel insights and uncovers new effects.

This work presents a first-principles linear-response formulation of QEDFT that captures the hallmark of strong light-matter coupling (Rabi splitting between polaritons) usually identified in linear spectroscopy. Crucial in the linear-response formulation is the stability of matter. While in the usual models this issue is irrelevant, we show how answering this question can shed light on the long-lasting debate about the existence of a Dicke superradiant phase. We extend three linear-response methods for matter-only systems to the linear-response framework of QEDFT that makes the problem computationally feasible. These methods are shown to be numerically equivalent and capture excited-states properties of strongly coupled light-matter systems which is identified by the emergence of polaritonic peaks not only in the matter spectrum but also the photonic spectrum. These strong coupling features are not captured by standard many-body methods that discard the photon degrees of freedom. This opens new possibilities to investigate different situations with complex systems coupled to many photon modes such as non-perturbative first-principles calculation of lifetimes of excited-states, beyond the single molecule limit and dissipation, and Lorentz to Fano transition of lineshapes in strong coupling. Making QEDFT practical now provides a route to analyze and propose experiments at the interface between quantum chemistry, nanoplasmonics and quantum optics and present novel observables that describes the strong coupling between light and matter. Beyond the linear response, this work also highlights new avenues of the down-conversion process that become available in ab-initio simulations of coupled light-matter systems. By changing the photonic environment in an experimentally feasible way, we can engineer hybrid light-matter states that enhance at the same time the efficiency of the down-conversion process and the non-classicality of the generated photons. In addition, we show that this also causes the down-conversion to occur at earlier times with potential to overcome detrimental decoherence effects. By coupling the signal modes to virtual and polaritonic states we propose an inverse (high-) harmonic generation that acts as an N-photon gun (source). Such a cavity-controlled down-conversion process will not be captured using standard non-linear optics approach since the field is treated classically and only as an external perturbation and with a quantum optics approach, it becomes less accurate due to the simplification of the matter subsystem to a few "relevant" energy levels.