  We show theoretically that a quantum-dot circuit quantum electrodynamics
(CQED) 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 (EIT) 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 (OFG).
