Proefschrift Universiteit van Amsterdam. / Met lit. opg. - Met samenvatting in het Nederlands.

Proefschrift Universiteit van Amsterdam. / Met lit. opg. - Met samenvatting in het Nederlands.

Proefschrift Universiteit van Amsterdam. / Met lit. opg. - Met samenvatting in het Nederlands.

Thesis--Leyden. / In Periodical Room.

Proefschrift Universiteit van Amsterdam. / Met lit. opg. - Met samenvatting in het Nederlands.

Proefschrift Universiteit van Amsterdam. / Auteursnaam op omslag: Vinod Baldew. Met lit. opg. - Met samenvatting in het Nederlands.

Proefschrift Universiteit van Amsterdam. / Met lit. op. - Samenvatting in het Nederlands.

Motivated by the sustained interest in Bose Einstein condensates and the recent progress in the understanding of topological phases in condensed matter systems, we study quantum condensates and possible topological phases of bosons in coupled light-matter excitations, so-called polaritons. These bosonic quasi-particles emerge if electronic excitations (excitons) couple strongly to photons. In the first part of this thesis a polariton Bose Einstein condensate in the presence of disorder is investigated. In contrast to the constituents of a conventional condensate, such as cold atoms, polaritons have a finite life time. Then, the losses have to be compensated by continued pumping, and a non-thermal steady state can build up. We discuss how static disorder affects this non-equilibrium condensate, and analyze the stability of the superfluid state against disorder. We find that disorder destroys the quasi-long range order of the condensate wave function, and that the polariton condensate is not a superfluid in the thermodynamic limit, even for weak disorder, although superfluid behavior would persist in small systems. Furthermore, we analyze the far field emission pattern of a polariton condensate in a disorder environment in order to compare directly with experiments. In the second part of this thesis features of polaritons in a two-dimensional quantum spin Hall cavity with time reversal symmetry are discussed. We propose a topological invariant which has a nontrivial value if the quantum spin Hall insulator is topologically nontrivial. Furthermore, we analyze emerging polaritonic edge states, discuss their relation to the underlying electronic structure, and develop an effective edge state model for polaritons.

Strongly correlated systems on geometrically frustrated lattices can stabilize a large number of interesting phases that includes a wide array of novel Mott insulators in both bosonic and electronic systems. Charge fluctuations in a Mott insulator are suppressed due to strong mutual interaction among the particles. The presence of frustration is of particular importance as the physics it offers is often rich, unexpectedly complicated, and continues to raise many open questions. The thesis elucidates some of these issues on a kagome lattice where strong interactions among the particles in the Mott phase impose non-trivial local constraints depending on the filling fraction on the lattice. These Mott insulators, in addition to featuring unusual magnetic and/or charge ordering, can also harbor topologically ordered states of quantum matter, e.g., resonating valence bond liquids realized in certain quantum dimer models on non-bipartite lattices. The dimer models can be regarded as low-energy effective theories for different types of bosonic models in the strong-coupling limit. Exploring this connection is a central theme of this thesis with the aim of realizing novel strongly correlated ground states. Past studies of these models have revealed the existence of various ordered and disordered phases with distinct signatures. Among these low-energy phases, the presence of a stable topological liquid at a particular point, known as Rokhsar-Kivelson point, in the phase diagram is notable. The classical versions of the dimer model are also known to have garnered a vast interest in various fields ranging from problems of pure mathematical origin to ones in physical chemistry as well as statistical physics. Pioneered by Kasteleyn, several analytical works came forward to exactly calculate the partition function of the problem from which other physical observables can be derived. Classical numerical methods are extensively applied to these models to verify the analytical predictions. We introduce a new classical algorithm here to compute the correlation functions of a classical dimer model on a square (bipartite) and a triangular (non-bipartite) lattice based on a tensor network construction. The method, called tensor network renormalization group, turns out to be a powerful tool for simulating short-ranged gapped systems as inferred from our results benchmarked against the classical Monte-Carlo technique and compared with past analytical studies. One should note that the quantum dimer model at the Rokhsar-Kivelson point can also be described as an infinite temperature canonical ensemble of classical dimers because of the particular structure of the ground state which is an equal weight superposition in the configuration manifold. The geometry of the lattice plays a pivotal role in deciding the nature of the phases that arise in the dimer models. Many physical properties of the dimer liquid phase can be extracted in the simple classical setting which certainly allows for a deep understanding of the classical models to be developed. The liquid phase is gapped on non-bipartite lattices and gapless on bipartite lattices, which is reflected in the decay of correlation functions with spatial distances. In general on non-bipartite lattices, the topological nature of the dimer liquid is characterized by a Z2 topological order which survives even when the model is perturbed away from the Rokhsar-Kivelson point. Stability of this liquid phase not only depends on the lattice geometries but notably on dimer concentrations also. In this context, we focus on a particular variant of the dimer model on a triangular lattice which is known as the quantum fully packed loop model. The model is composed of nonintersecting closed loops made of dimers and governed by the same Hamiltonian as the quantum dimer model. The loop model provides an effective low-energy description of a strongly correlated bosonic system at 1/3 filling on the kagome lattice. The corresponding Bose-Hubbard Hamiltonian consists of nearest-neighbor hopping and all possible repulsive interactions within a hexagonal plaquette. Conspicuous features of the zero-temperature phase diagram for this model include (i) presence of a stable Z2 liquid even without any Rokhsar-Kivelson potential term (in distinction to the standard quantum dimer model), and (ii) an unconventional phase transition from the liquid phase to a novel crystalline phase that has nematic order (dubbed lattice nematic). For a deeper understanding of the physics, a mapping to an Ising gauge theory is presented. The gauge theoretic description provides a useful way to predict the nature of the quantum phase transition to lie in the O(3) universality class. Finally a fermionic model at the same 1/3 filling is considered in which the ground state exhibits a number of exotic local orderings resulting from the spin-charge interplay of electrons. The Hamiltonian comprises nearest-neighbor hopping, strong on-site Coulomb interaction, and repulsive interaction terms only between nearest-neighbors. In the strong correlation limit, this fermionic problem maps to a two-color fully packed loop model – a model in which the loop segments carry an additional quantum number as color on a honeycomb lattice. The effective theory is governed by coherent three-particle ring exchanges and nearest-neighbor antiferromagnetic spin exchanges. The competition between these two leads to a phase diagram composed of a novel plaquette ordered state (known as the plaquette phase) that undergoes phase transition to a new kind of charge ordered state which we call a short loop phase. From our numerical analysis, we conclude that the plaquette phase features an unusual antiferromagnetic order with gapless spin excitations while the charge-ordered state is subjugated by spin fluctuations of localized electrons arranged in small hexagonal loops on the kagome lattice.

In dieser Arbeit wird die Suche nach geladenen Higgs Bosonen (H±) vorgestellt. Dafür wurden Proton–Proton Kollisionen, die bei einer Schwerpunktsenergie von 13 TeV in den Jahren 2015 und 2016 mit einer integrierten Luminosität von 36.1 fb−1 mit dem ATLAS-Experiment produziert wurden, untersucht. Die Existenz solcher geladener Higgs Bosonen wird in verschiedenen Modellen jenseits des Standardmodells vorhergesagt und ist auch dadurch motiviert, das dass Standardmodell nicht immer eine Erklärung für verschiedenste beobachtete Phänomene liefern kann. Diese Arbeit konzentriert sich auf geladene Higgs Bosonen, die eine höhere Masse als das top Quark besitzen und über H± → tb zerfallen. Die H± Produktion, in Verbindung mit einem top und einem bottom Quark pp → tbH±, wird im Massenbereich von 200 bis 2000 GeV untersucht. Die Suche nach H± in dieser Arbeit beschränkt sich auf Endzustände mit einem geladenen Lepton und mehreren Jets. Mit Hilfe eines boosted decision trees werden verschiedenste kinematische Variablen miteinander kombiniert, um dadurch das H± Signal besser von dem Standardmodell Untergrund unterscheiden zu können. Es wurde kein signifikanter Unterschied zum vorhergesagten Standardmodell-Untergrund gemessen und deshalb Ausschlussgrenzen für den Produktionswirkungsquerschnitt mal Verzweigungsverhältnis dieses H± Zerfalls berechnet. Weitere Ausschlussgrenzen wurden für den tanβ Parameter des MSSM Modells für die mhmod− und hMSSM Benchmark-Szenarien bestimmt. Die Ergebnisse dieser Arbeit übertreffen alle bisherigen Ausschlussgrenzen - insbesondere werden zum ersten Mal Erkenntnisse über den Massenbereich bis zu 2000 GeV gewonnen. / This thesis presents a search for charged Higgs bosons produced in proton–proton collisions at a centre-of-mass energy of 13 TeV, using 36.1 fb−1 of data collected by the ATLAS detector at the LHC in 2015 and 2016. The existence of charged Higgs bosons is predicted by various theories Beyond the Standard Model and it is motivated by the inadequacy of the Standard Model to explain some observed experimental phenomena. The work focuses on charged Higgs bosons heavier than the top quark and decaying via H± → tb. The production in association with a top and a bottom quark (pp → tbH±) is investigated in the mass range between 200 and 2000 GeV. A final state containing one charged lepton and jets is considered. Multiple kinematic variables are combined using a boosted decision tree (BDT) in order to separate signal and background. The output of the BDT is used to perform a profile likelihood fit of the Monte Carlo predictions to the observed data. No significant excess of events above the expected Standard Model background is observed, therefore upper limits are set for the cross-section of the charged Higgs boson production times the branching fraction of its decay. Limits are also provided for the tanβ parameter of the MSSM, in the mhmod− and hMSSM benchmark scenarios. The work improves the reach of all previous searches, including for the first time masses ranging up to 2000 GeV.