The observation of electromagnetic counterparts to both high energy neutrinos and gravitational waves marked the beginning of a new era in astrophysics. The multi-messenger approach allows us to gain new insights into the most energetic events in the Universe such as gamma-ray bursts, supernovas, and black hole mergers. Real-time multi-messenger alerts are the key component of the observational strategies to unravel the transient signals expected from astrophysical sources. Focusing on the high-energy regime, we present a historical perspective of multi-messenger observations, the detectors and observational techniques used to study them, the status of the multi-messenger alerts and the most significant results, together with an overview of the future prospects in the field.

The extragalactic gamma-ray sky is dominated by blazars, active galactic nuclei (AGN) with a relativistic jet that is closely aligned with the line of sight. Galaxies develop an active nucleus if the central supermassive black hole (BH) accretes large amounts of ambient matter and magnetic flux. The inflowing mass accumulates around the plane perpendicular to the accretion flow's angular momentum. The flow is heated through viscous friction and part of the released energy is radiated as blackbody or non-thermal radiation, with luminosities that can dominate the accumulated stellar luminosity of the host galaxy. A fraction of the accretion flow luminosity is reprocessed in a surrounding field of ionised gas clouds. These clouds, revolving around the central BH, emit Doppler-broadened atomic emission lines. The region where these broad-line-emitting clouds are located is called broad-line region (BLR). About one in ten AGN forms an outflow of radiation and relativistic particles, called a relativistic jet. According to the Blandford-Znajek mechanism, this is facilitated through electromagnetic processes in the magnetosphere of a spinning BH. The latter induces a magnetospheric poloidal current circuit, generating a decelerating torque on the BH and inducing a toroidal magnetic field. Consequently, rotational energy of the BH is converted to Poynting flux streaming away mainly along the rotational axis and starting the jet. One possibility for particle acceleration near the jet base is realised by magnetospheric vacuum gaps, regions temporarily devoid of plasma, such that an intermittent electric field arises parallel to the magnetic field lines, enabling particle acceleration and contributing to the mass loading of the jets. Magnetised structures, containing bunches of relativistic electrons, propagate away from the galactic nucleus along the jets. Assuming that these electrons emit synchrotron radiation and that they inverse-Compton (IC) up-scatter abundant target photons, which can either be the synchrotron photons themselves or photons from external emitters, the emitted spectrum can be theoretically determined. Additionally taking into account that these emission regions move relativistically themselves and that the emission is Doppler-boosted and beamed in forward direction, the typical two-hump spectral energy distribution (SED) of blazars is recovered. There are however findings that challenge this well-established model. Short-time variability, reaching down to minute scales at very high energy gamma rays, is today known to be a widespread phenomenon of blazars, calling for very compact emission regions. In most models of such optically thick emission regions, the gamma-ray flux is usually pair-absorbed exponentially, without considering the cascade evolving from the pair-produced electrons. From the observed flux, it is often concluded that emission emanates from larger distances where the region is optically thin, especially from outside of the BLR. Only in few blazars gamma-ray attenuation associated with pair absorption in the BLR was clearly reported. With the advent of sophisticated high-energy or very high energy gamma-ray detectors, like the Fermi Large Area Telescope or the Major Atmospheric Gamma-ray Imaging Cherenkov telescopes, besides the extraordinarily fast variability spectral features have been found that cannot be explained by conventional models reproducing the two-hump SED. Two such narrow spectral features are discussed in this work. For the nearby blazar Markarian 501, hints to a sharp peak around 3 TeV have been reported from a multi-wavelength campaign carried out in July 2014, while for 3C 279 a spectral dip was found in 2018 data, that can hardly be described with conventional fitting functions. In this work it is examined whether these spectral peculiarities of blazar jet emission can be explained, if the full radiation reprocessing through an IC pair cascade is accounted for. Such a cascade is the multiple concatenation of IC scattering events and pair production events. In the cascades generally considered in this work, relativistic electrons and high-energy photons are injected into a fixed soft target photon field. A mathematical description for linear IC pair cascades with escape terms is delivered on the basis of preliminary works. The steady-state kinetic equations for the electrons and for the photons are determined, whereby it is paid attention to an explicit formulation and to motivating the correct integration borders of all integrals from kinematic constraints. In determining the potentially observable gamma-ray flux, both the attenuated injected flux and the flux evolving as an effect of IC up-scattering, pair absorption and escape are incorporated, giving the emerging spectra very distinct imprints. Much effort is dedicated to the numerical solution of the electrons' kinetic equation via iterative schemes. It is explained why pointwise iteration from higher to lower Lorentz factors is more efficient than iterating the whole set of sampling points. The algorithm is parallelised at two positions. First, several workers can perform pointwise iterations simultaneously. Second, the most demanding integral is cut into a number of part integrals which can be determined by multiple workers. Through these measures, the Python code can be readily applied to simulate steady-state IC pair cascades with escape. In the case of Markarian 501 the developed framework is as follows. The AGN hosts an advection-dominated accretion flow with a normalised accretion rate of several \(10^{-4}\) and an electron temperature near \(10^{10}\) K. On the one hand, the accretion flow illuminates the few ambient gas clouds with approximate radius \(10^{11}\) m, which reprocess a fraction 0.01 of the luminosity into hydrogen and helium emission lines. On the other hand, the gamma rays from the accretion flow create electrons and positrons in a sporadically active vacuum gap in the BH magnetosphere. In the active gap, a power of roughly 0.001 of the Blandford-Znajek power is extracted from the rotating BH through a gap potential drop of several \(10^{18}\) V, generating ultra-relativistic electrons, which subsequently are multiplied by a factor of about \(10^6\) through interaction with the accretion flow photons. This electron beam propagates away from the central engine and encounters the photon field of one passing ionised cloud. The resulting IC pair cascade is simulated and the evolving gamma-ray spectrum is determined. Just above the absorption troughs due to the hydrogen lines, the spectrum exhibits a narrow bump around 3 TeV. When the cascaded emission is added to the emission generated at larger distances, the observed multi-wavelength SED including the sharp peak at 3 TeV is reproduced, underlining that radiation processes beyond conventional models are motivated by distinct spectral features. The dip in the spectrum of 3C 279 is addressed by a similar cascade model. Three types of injection are considered, varying in the ratio of the photon density to the electron density and varying in the spectral shape. The IC pair cascade is assumed to happen either in the dense BLR photon field with a luminosity of several \(10^{37}\) W and a radial size of few \(10^{14}\) m or in the diluted photon field outside of the BLR. The latter scenario is however rejected as the spectral slope around several 100 MeV and the dip at few 10 GeV cannot be reconciled within this model. The radiation cascaded in the BLR can explain the observational data, irrespective of the assumed injected rate. It is therefore concluded that for this period of gamma-ray emission, the radiation production happens at the edge of the BLR of 3C 279. Both investigations show that IC pair cascades can account for fine structure seen in blazar SEDs. It is insufficient to restrict the radiation transport to pure exponential absorption of an injection term. Pair production and IC up-scattering by all generations of photons and electrons in the optically thick regime critically shape the emerging spectra. As the advent of future improved detectors will provide more high-precision spectra, further observations of narrow spectral features can be expected. It seems therefore recommendable to incorporate cascading into conventional radiation production models or to extend the model developed in this work by synchrotron radiation.

We investigated emission properties of photonic structures with InAs/InGaAlAs/InP quantum dashes grown by molecular beam epitaxy on a distributed Bragg reflector. In high-spatial-resolution photoluminescence experiment, well-resolved sharp spectral lines are observed and single-photon emission is detected in the third telecommunication window characterized by very low multiphoton events probabilities. The photoluminescence spectra measured on simple photonic structures in the form of cylindrical mesas reveal significant intensity enhancement by a factor of 4 when compared to a planar sample. These results are supported by simulations of the electromagnetic field distribution, which show emission extraction efficiencies even above 18% for optimized designs. When combined with relatively simple and undemanding fabrication approach, it makes this kind of structures competitive with the existing solutions in that spectral range and prospective in the context of efficient and practical single-photon sources for fiber-based quantum networks applications.

This thesis studies connections between quantum information measures and geometric features of spacetimes within the AdS/CFT correspondence. These studies are motivated by the idea that spacetime can be thought of as an effect emerging from an underlying entanglement structure in the AdS/CFT correspondence. In particular, I study generalized entanglement measures in two-dimensional conformal field theories and their holographic duals. Unlike the ordinary entanglement entropy of a spatial subregion typically used in the AdS/CFT context, the generalization considered here measures correlations between different fields as well as between spatial degrees of freedom. I present a new gauge invariant definition of the generalized entanglement entropy applicable to both mixed and pure states as well as explicit results for thermal states of the S_N-orbifold theory of the D1/D5 system. Along the way, I develop computation techniques for conformal blocks on the torus and apply them to the calculation of the ordinary entanglement entropy for large central charge CFTs at finite size and finite temperature. The generalized Ryu-Takayanagi formula arising from these studies provides further support for the idea that entanglement and geometry are intrinsically linked in AdS/CFT. The results show that the holographic dual to the generalized entanglement entropy given by the length of a geodesic winding around black hole horizons or naked singularities probes subregions of spacetime that are inaccessible to Ryu-Takayanagi surfaces, thereby solving the puzzle of how these features of the spacetime are encoded in the boundary theory. Furthermore, I investigate quantum circuits embedded in two-dimensional conformal field theories as well as computational complexity measures therein. These investigations are motivated by conjectures relating computational complexity in conformal field theories to geometric features of black hole geometries. In this thesis, I study quantum circuits built up from conformal transformations. I investigate examples of computational complexity measures in these circuits related to geometric actions on coadjoint orbits of the Virasoro group and to the Fubini-Study metric. I then work out relations between these computational complexity measures and the dual gravitational theory. Moreover, I construct a bulk dual to the circuits in consideration and use this construction to study geometric realizations of computational complexity measures from first principles. The results of this part on the one hand rule out some possibilities for dual realizations of computational complexity in two-dimensional CFTs put forward in previous work while on the other hand providing a new robust dual realization of a computational complexity measure based on the Fubini-Study distance.

Emergent phenomena in condensed matter physics like, e.g., magnetism, superconductivity, or non-trivial topology often come along with a surprise and exert great fascination to researchers up to this day. Within this thesis, we are concerned with the analysis of associated types of order that arise due to strong electronic interactions and focus on the high-\(T_c\) cuprates and Kondo systems as two prime candidates. The underlying many-body problem cannot be solved analytically and has given rise to the development of various approximation techniques to tackle the problem. In concrete terms, we apply the auxiliary particle approach to investigate tight-binding Hamiltonians subject to a Hubbard interaction term to account for the screened Coulomb repulsion. Thereby, we adopt the so-called Kotliar-Ruckenstein slave-boson representation that reduces the problem to non-interacting quasiparticles within a mean-field approximation. Part I provides a pedagogical review of the theory and generalizes the established formalism to encompass Gaussian fluctuations around magnetic ground states as a crucial step to obtaining novel results. Part II addresses the two-dimensional one-band Hubbard model, which is known to approximately describe the physics of the high-\(T_c\) cuprates that feature high-temperature superconductivity and various other exotic quantum phases that are not yet fully understood. First, we provide a comprehensive slave-boson analysis of the model, including the discussion of incommensurate magnetic phases, collective modes, and a comparison to other theoretical methods that shows that our results can be massively improved through the newly implemented fluctuation corrections. Afterward, we focus on the underdoped regime and find an intertwining of spin and charge order signaled by divergences of the static charge susceptibility within the antiferromagnetic domain. There is experimental evidence for such inhomogeneous phases in various cuprate materials, which has recently aroused interest because such correlations are believed to impact the formation of Cooper pairs. Our analysis identifies two distinct charge-ordering vectors, one of which can be attributed to a Fermi-surface nesting effect and quantitatively fits experimental data in \(\mathrm{Nd}_{2-\mathrm{x}}\mathrm{Ce}_\mathrm{x}\mathrm{CuO}_4\) (NCCO), an electron-doped cuprate compound. The other resembles the so-called Yamada relation implying the formation of periodic, double-occupied domain walls with a crossover to phase separation for small dopings. Part III investigates Kondo systems by analyzing the periodic Anderson model and its generalizations. First, we consider Kondo metals and detect weakly magnetized ferromagnetic order in qualitative agreement with experimental observations, which hinders the formation of heavy fermions. Nevertheless, we suggest two different parameter regimes that could host a possible Kondo regime in the context of one or two conduction bands. The part is concluded with the study of topological order in Kondo insulators based on a three-dimensional model with centrosymmetric spin-orbit coupling. Thereby, we classify topologically distinct phases through appropriate \(\mathbb{Z}_2\) invariants and consider paramagnetic and antiferromagnetic mean-field ground states. Our model parameters are chosen to specifically describe samarium hexaboride (\(\mbox{SmB}_6\)), which is widely believed to be a topological Kondo insulator, and we identify topologically protected surface states in agreement with experimental evidence in that material. Moreover, our theory predicts the emergence of an antiferromagnetic topological insulator featuring one-dimensional hinge-states as the signature of higher-order topology in the strong coupling regime. While the nature of the true ground state is still under debate, corresponding long-range magnetic order has been observed in pressurized or alloyed \(\mbox{SmB}_6\), and recent experimental findings point towards non-trivial topology under these circumstances. The ability to understand and control topological systems brings forth promising applications in the context of spintronics and quantum computing.