We propose a new setup for creating Majorana bound states in a two-dimensional electron gas Josephson junction. Our proposal relies exclusively on a supercurrent parallel to the junction as a mechanism of breaking time-reversal symmetry. We show that combined with spin-orbit coupling, supercurrents induce a Zeeman-like spin splitting. Further, we identify a new conserved quantity---charge-momentum parity---that prevents the opening of the topological gap by the supercurrent in a straight Josephson junction. We propose breaking this conservation law by adding a third superconductor, introducing a periodic potential, or making the junction zigzag-shaped. By comparing the topological phase diagrams and practical limitations of these systems we identify the zigzag-shaped junction as the most promising option.@en

Majorana bound states (MBS) have non-Abelian exchange statistics, which means exchanging the position of two MBS changes the state of the system. This attracted attention for multiple reasons: It is a quantum effect without a classical analogue, it introduces topology to condensed matter physics and the non-Abelian exchange processes allow quantum computing with intrinsic error protection. For a long time research on MBS was purely theoretical, because there was no experimentally accessible idea how to create them. This changed with the appearance of a recipe combining conventional superconductivity, semiconductors and a magnetic field. Now such setups exist and their conductance indicates the successful creation of MBS, but challenges regarding their quality, conclusive detection and control remain. In this thesis I propose different strategies for avoiding open experimental problems when creating MBS, and identify new pathways for detecting them. Most proposals for creating MBS are similar in two regards: They confine electrons to lower dimensional systems, for example a 1-dimensional wire, and they use magnetic field to couple to the electron spin. I start this thesis by developing a system where the magnetic field forces electrons onto cyclotron orbits, thereby spatially confining them without relying on the system’s geometry. This leads to an increased resilience against imperfections. Imperfections in real systems are not the only technical problem. One example is the combination of superconductivity and a magnetic field. Superconductors expel weak magnetic fields, while strong magnetic fields induce vortices in the superconductor which have a nonsuperconducting region in their core. In order to avoid these problems I turn to a completely different regime and develop a system that does not require a magnetic field to create MBS. Instead the role of the magnetic field is taken by a combination of supercurrents and spin-orbit coupling in the semiconductor. Then I turn to the detection of MBS, which is always a competition between two goals: finding a unique signature only caused by MBS and relying on a simple setup. One well-established signature of MBS is single electron transport through a superconductor, because without MBS a superconductor only transports electrons in pairs. Of course single electron transport is not a unique signature at all: it happens in most conductors. That makes it hard to distinguish MBS from undesired side effects. I develop a setup that adds falsifiability to this signature. In addition to detecting single electron transport, my scheme allows to block it if it is due to MBS, therefore making MBS and a normal conduction channel distinguishable. In the last part of my thesis I do not propose a system, but instead I analyze and simulate an unexpected outcome of an experiment. My colleagues were studying a driven superconducting resonator coupled to a Josephson junction (two superconductors separated by a short barrier) with the goal of using it to detect MBS. Completely unexpectedly it turned out to be a high quality microwave laser. In a collaborative effort we explain this previously overlooked phenomenon. @en

Superconducting electronic devices have reemerged as contenders for both classical and quantum computing due to their fast operation speeds, low dissipation, and long coherence times. An ultimate demonstration of coherence is lasing. We use one of the fundamental aspects of superconductivity, the ac Josephson effect, to demonstrate a laser made from a Josephson junction strongly coupled to a multimode superconducting cavity. A dc voltage bias applied across the junction provides a source of microwave photons, and the circuit's nonlinearity allows for efficient down-conversion of higher-order Josephson frequencies to the cavity's fundamental mode. The simple fabrication and operation allows for easy integration with a range of quantum devices, allowing for efficient on-chip generation of coherent microwave photons at low temperatures.

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Majorana bound states (MBS) differ from the regular zero energy Andreev bound states in their nonlocal properties, since two MBS form a single fermion. We design strategies for detection of this nonlocality by using the phenomenon of Coulomb-mediated Majorana coupling in a setting which still retains falsifiability and does not require locally separated MBS. Focusing on the implementation of MBS based on the quantum spin Hall effect, we also design a way to probe Majoranas without the need to open a magnetic gap in the helical edge states. In the setup that we analyze, long range MBS coupling manifests in the h/e magnetic flux periodicity of tunneling conductance and supercurrent. While h/e is also the periodicity of Aharonov-Bohm effect and persistent current, we show how to ensure its Majorana origin by verifying that switching off the charging energy restores h/2e periodicity conventional for superconducting systems.

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