Towards Qubit Spectroscopy of the Fraunhofer Pattern in S-Sm Josephson Junctions

Hybrid superconductor-semiconductor Josephson junctions(S-Sm JJs) are the fundamental building block for voltage-tunable superconducting qubits and some of the topological qubits. In an S-Sm JJ, conduction channels in the weak link give rise to superconducting phase-dependent bound states known as the Andreev bound states (ABSs). Here, we present a series of experiments that build towards the qubit spectroscopy of the planar epi-Al/InAs JJs tuned by an external magnetic field. Within a perpendicular magnetic field, the phase across a planar JJ has a gradient along the width of the JJ and the JJ's critical current follows a Fraunhofer pattern. We incorporate the magnetic-field-tuned JJ in a Transmon circuit to form the "Fraunhofer qubit" and we perform two-tone spectroscopy to resolve the Fraunhofer pattern at the nodes. Moreover, the ABSs of a wide JJ are suspected to be spatially localized and thus observe different phases, resulting in different ABSs splitting due to differences in transparency and phase. We discuss our results of current-biased JJ Fraunhofer pattern measurements and the progress towards resolving spatially-separated ABSs near their low-frequency "sweet spots" via qubit spectroscopy.