STSM of Patrik Recher at Universidad Autónoma de Madrid (Spain)

Transport properties of topological superconductors hosting Majorana bound states

The aim of the stay was the theoretical investigation of hybrid superconductor semiconductor systems that have excitations that could be used for quantum computation purposes in the future.

We investigated the Andreev bound states (ABSs) of a Josephson junction containing a nanowire with spin-orbit coupling that splits the spin levels at non-time reversal symmetric points. Such split spin-pairs could be used as an Andreev spin qubit (ASQ).

The main idea of our project is to investigate in detail the level structure of the ABSs in a multichannel quantum wire with Rashba spin-orbit coupling and to calculate their dipole moment. To manipulate the ASQ we envision to use an extended manifold of ABSs and utilize a master equation approach to find the dynamics of the reduced density matrix of the system. We consider an ac gate voltage that couples capacitively to the ABSs and also modifies the spin-orbit coupling constant. By this we are investigating possible transitions between the ABSs induced by the ac-electric field. To this end, the Josephson junction is coupled to a cavity mode that allows for dispersive read-out of the ASQ.

The stay at UAM was very fruitful for me for acquiring an enhanced understanding of a smart coupling of ABSs to ac-electric fields. We hope to obtain profound insights into the dynamics of the ASQ with the help of our theoretical model soon. In the future, we would like to consider also hybrid superconductor semiconductor systems possessing Majorana bound states which can serve as building blocks for another type of qubit.