Probing Majorana States in S-TI-S Josephson Junctions by Resonator and Transmon Measurements*

The observation of Majorana zero modes and their non-abelian statistics is critical to the development of topologically-protected quantum computers. Lateral S-TI-S Josephson junctions made from depositing s-wave superconductors on a topological insulator substrate are predicted to host localized Majorana zero modes in a weak vertical magnetic field. The critical current and hence inductive energy of such a junction is thought to be partially dependent on the parity of Majorana pairs in the junction, with experimental evidence suggestive but thus far inconclusive. To make a more definitive test, we are creating quantum circuits incorporating S-TI-S junctions to probe for parity sensitivity in the inductive energy via microwave resonator and transmon experiments.