Efficient flip-chip and on-chip-based modulation of flux-tunable superconducting resonators
We demonstrate the efficient modulation of flux-tunable superconducting resonators (FTRs) using flip-chip or on-chip-based input coils. The FTRs we use are aluminum-based quarter-wave coplanar waveguide resonators terminated with 100um or 200um-wide square loop dc superconducting quantum interference devices (SQUIDs) employing 1um-sized Josephson junctions. We employ SQUIDs with a geometric loop inductance of up to 0.7nH to increase the flux transfer efficiency. The geometric inductance of the SQUID results in a non-zero screening parameter $\beta_L$, whose branch switching effect is mitigated by using asymmetric junctions. We achieve flux modulation of the FTRs by more than one GHz and flux responsivities of up to tens of GHz/$\Phi_0$ with uA-scale on-chip currents. We compare flip-chip with on-chip input-coil-based flux modulation, where the former is realized through galvanically connected and closely spaced chips, while the latter is achieved through superconducting air-bridge connections. We achieve a flux-transfer efficiency from the input coil to the SQUID loop of up to 20%. Our work paves the way for efficient low current flux modulation of FTRs and sensitive measurement of flux signals.