Coherent-Feedback Notch Filtering for Purcell Suppression

Abstract

We study Purcell filtering in dispersive qubit readout from the viewpoint of environmental spectrum shaping. In dispersive readout, stronger coupling between the readout cavity and the external field improves measurement speed, but also enhances Purcell relaxation of the qubit. To address this trade-off, we introduce coherent feedback (CF) into the design of a notch-type Purcell filter. Using Fermi’s golden rule, the Purcell rate is related to the environmental spectrum seen from the qubit, enabling a transfer-function-based analysis of the proposed filter. Under idealized assumptions including lossless components, perfect phase matching, and ideal circulators, the proposed CF filter completely suppresses the Purcell rate at the qubit frequency while preserving the effective coupling near the readout frequency. These results suggest coherent feedback as an alternative design option for Purcell filtering.