Digital Homodyne and Heterodyne Detection for Stationary Bosonic Modes

Homo- and heterodyne detection are fundamental techniques for measuring propagating electromagnetic fields. However, applying these techniques to stationary fields confined in cavities poses a challenge. As a way to overcome this challenge, we propose to use repeated indirect measurements of a two-level system interacting with the cavity. We demonstrate numerically that the proposed measurement scheme faithfully reproduces measurement statistics of homo- or heterodyne detection. The scheme can be implemented in various physical architectures, including circuit quantum electrodynamics. Our results pave the way for implementation of quantum algorithms requiring linear detection of stationary modes, including quantum verification protocols.