Evolution of microwave spectroscopy in topological planar Josephson junctions

The implementation of Josephson junctions (JJs) in superconducting devices represents a promising approach toward the realization of quantum computing. From a theoretical perspective, planar JJs have been proposed as a platform for exploring topological phases [1-2] and Majorana bound states (MBS) [3]. Experimentally, π-phase jumps in the ground state accompanied by minima in the critical current have been observed, indicating the closing and reopening of the superconducting gap [4]. To probe the properties of JJs, microwave spectroscopy has been widely employed [5-7]. For long junctions, as the number of Andreev levels increases, the measurements become more challenging though. In this work, we consider a planar JJ coupled to a superconducting resonator, which is capacitively coupled to a coplanar waveguide. We perform measurement simulations for disordered junctions with varying numbers of Andreev levels and study their implications for the transmission coefficient of the probe signal. Furthermore, we analyze the effect of quasiparticle (QP) poisoning on the resonator frequency shift in the non-driven regime, the shift differences arising from occupancy variations in the driven regime for various QP configurations, and possible strategies to improve the readout resolution. Overall, our results provide an improved framework for studying topological JJs and the selection rules emerging from the topological phase.

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