Flux-tunable transmon incorporating a van der Waals superconductor via an Al/AlO$_x$/4Hb-TaS$_2$ Josephson junction

Abstract: Incorporating van der Waals (vdW) superconductors into Josephson elements extends circuit-QED beyond conventional Al/AlO$_x$/Al tunnel junctions and enables microwave probes of unconventional condensates and subgap excitations. In this work, we realize a flux-tunable transmon whose nonlinear inductive element is an Al/AlO$_x$/4Hb-TaS$_2$ Josephson junction. The tunnel barrier is formed by sequential deposition and full in-situ oxidation of ultrathin Al layers on an exfoliated 4Hb-TaS$_2$ flake, followed by deposition of a top Al electrode, yielding a robust, repeatable hybrid junction process compatible with standard transmon fabrication. Embedding the device in a three-dimensional copper cavity, we observe a SQUID-like flux-dependent spectrum that is quantitatively reproduced by a standard dressed transmon--cavity Hamiltonian, from which we extract parameters in the transmon regime. Across measured devices we obtain sub-microsecond energy relaxation ($T_1$ from $0.08$ to $0.69~μ$s), while Ramsey measurements indicate dephasing faster than our $16$ ns time resolution. We also find a pronounced discrepancy between the Josephson energy inferred from spectroscopy and that expected from the Ambegaokar--Baratoff relation using room-temperature junction resistances, pointing to nontrivial junction physics in the hybrid Al/AlO$_x$/4Hb-TaS$_2$ system. Although we do not resolve material-specific subgap modes in the present geometry, this work establishes a practical route to integrating 4Hb-TaS$_2$ into coherent quantum circuits and provides a baseline for future edge-sensitive designs aimed at enhancing coupling to boundary and subgap degrees of freedom in vdW superconductors.