Superconducting Non-reciprocal Bandpass Filter Based on Spatio-Temporal Inductance Modulation*

Passives such as ferrite circulators, isolators, and bandpass filters are used in superconducting quantum computers. However, ferrites are bulky and cannot be integrated into superconducting qubit chips. Recognition of the need for compact, non-magnetic non-reciprocal(NR) components has inspired research of NR devices based on parametric modulation using JJs and SQUIDs. To this end, we propose the concept of a NR-Band Pass Filter, (NR-BPF) that combines the functionality of a conventional BPF with an isolator based on the concept of Spatio-Temporal Inductance Modulation (STIM). The BPF follows a capacitively-coupled shunt resonator architecture which is implemented as parallel combination of finger capacitor and a 7-stacked SQUIDs that behave as flux-controlled nonlinear inductors. We analyzed the NR-BPF using Floquet scattering matrices to create frequency translational admittance matrices for time-modulated SQUIDs. Under the right modulation criteria of modulation frequency, phase, and depth, the signals entering the BPF in the forward direction experience little-to-no insertion loss while the signals in the backward direction are converted to intermodulation frequencies, thus realizing RF isolation. Post layout simulations of  NR-BPF tuned to 4.8 GHz and modulated at 700 MHz achieves <1 dB insertion loss from 4.4 GHz to 5.2 GHz and isolation greater than 20 dB from 4.7 GHz to 4.9 GHz. The DC flux bias of the SQUIDs can be leveraged to tune the center frequency from 3.5 GHz to 6 GHz.