Approaching the ultrastrong coupling regime between an Andreev level and a microwave resonator

Abstract: 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 an InAs nanowire weak link 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 of spin-degenerate and spin-orbit split Andreev bound states for the shorter and longer weak links, respectively. Our approach offers a compact geometry and a large resonator impedance above 12 k$\Omega$ at a resonator frequency of 8 GHz, which results in a measured coupling strength reaching 1.95 GHz to the Andreev level and 77 MHz to the Andreev spin. Our spectroscopic data are in good agreement with existing theoretical models and demonstrate ultrastrong coupling to the Andreev pair qubit with the coupling strength approaching the bare resonator and qubit frequencies.