Microwave quantum optics as a direct probe of the Overhauser field in a quantum dot circuit quantum electrodynamics device

We show theoretically that a quantum dot circuit quantum electrodynamics device can be used as a probe of the Overhauser field in quantum dots. By coupling a transmission line to the interdot tunneling gate, an electromagnetically induced transparency scheme can be established, whose Fano-type interference leads to a sharp curvature in the reflection spectrum around resonance. This sharp feature persists even in the presence of the fluctuating spin bath, rendering a high-resolution method to extract the bath's statistical information. For strong nuclear spin fields, the reflection spectrum exhibits an Autler-Townes splitting, where the peak locations indicate the strengths of the Overhauser field gradient.