Approaching the ultrastrong coupling regime between an Andreev level and a microwave resonator
Josephson junctions formed in semiconductor nanowires host Andreev bound states and serve as a physical platform to realize Andreev qubits tuned by electrostatic gating. With the Andreev bound state being confined to the nanoscale weak link, it couples to a circuit-QED architecture via the state-dependent supercurrent flowing through the weak link. Thus, increasing this coupling strength is a crucial challenge for this architecture. Here, we demonstrate the fabrication and microwave characterization of a weak link which is defined in an InAs-Al (core-half shell) nanowire and embedded in a superconducting loop with a lumped-element resonator patterned from a thin NbTiN film with high kinetic inductance. We investigated several devices with various weak link lengths and performed spectroscopy that revealed pair transitions and single-quasiparticle transitions arising from spin-orbit split Andreev bound states. Our approach offers a compact geometry and a large resonator impedance above 12 k$Ω$ at a resonator frequency of 8 GHz, which facilitates large coupling in the system. For the pair transitions, the experimentally observed energy level splitting demonstrates the coupling to an Andreev level of 490 MHz. We apply a perturbative model that shows good agreement with the experimental data and extract the maximum coupling of 968~MHz. Moreover, we show that the coupling is even stronger to an Andreev level with a higher transmission. In addition, spectroscopy of single-quasiparticle transitions reveals spin-orbit split Andreev bound states with the extracted spin-photon coupling of 77 MHz.