Spins in Josephson Junctions

Quantum technology is an exciting research area that has gained a lot of interest in the past few decades with the advances made in quantum computing. The quantum computer promises speedups that are impossible to achieve with classical computers. It does so by exploiting quantum mechanical properties such as entanglement and superposition with the quantum bit, or qubit, as its main building block.

Today, quantum computers are in their infancy and realizing a computer powerful enough to perform useful calculations poses major challenges. The fragility of qubits being the main difficulty. Approaches to mitigate this include implementing error correction schemes or alternative qubit designs. Topological qubits are part of the latter category and exploit the robustness of topologically invariant states to small perturbations to create more stable qubits.

In this thesis we explore semiconductor-superconductor hybrid nanowire structures and in particular the interaction of electron spins in quantum dots with superconductivity. When connected to superconductors, arrays of superconductor quantum dot hybrids can host Majorana states, a promising approach to realizing topological qubits. Creating Majoranas in quantum dots, as opposed to traditional methods, offers greater control over their properties. Additionally, understanding the interaction between spins in these quantum dots superconductor hybrids could enable new readout methods or coupling mechanisms between superconducting and spin qubits.

We start by investigating a nanowire SNS Josephson junction with signatures of Majorana states. A nanowire junction is capacitively coupled to an on-chip microwave detector made from a Josephson tunnel junction. We monitor the Josephson radiation frequency as a function of magnetic field and find a transition from a $2\pi$ to a $4\pi$-periodic Josephson current-phase relation, consistent with a topological transition.

In a different device, we investigate a multi-orbital double quantum dot Josephson junction. We measure the excitations between doublet and singlet states that arise in a quantum dot weakly coupled to a superconducting lead, also known as Yu-Shiba-Rusinov (YSR) states. With increased dot-lead coupling we observe a supercurrent and reveal its current-phase relation, both in the single and multi-orbit regime. We show that in the single-orbital regime the supercurrent sign follows an even-odd charge occupation effects. In the even charge parity sector, we observe a supercurrent blockade when the spin ground state transitions to a triplet -- demonstrating a direct spin to supercurrent conversion. For yet stronger dot-lead coupling we find a rectified current-phase relation at the transition between even and odd charge states. We investigate this apparent non-equilibrium effect and think about possible explanations.

To conclude, we discuss possible applications in spin qubit state readout and extensions of the device geometry towards realizing a Kiteav chain able to host Majorana states.