  Superconducting cavities with high quality factors play an essential role in
circuit quantum electrodynamics and quantum computing. In measurements of the
the intrinsic loss rates of high frequency modes, it can be challenging to
design an appropriate coupling to the measurement circuit in such a way that
the resulting signal is sufficiently strong but also that this coupling does
not lead to unwanted loading circuit, obscuring the intrinsic internal loss
rates. Here, we propose and demonstrate a spectroscopic probe of high-Q
resonators based on the phenomena of electromagnetically-induced transparency
(EIT) between the resonator and qubit in the weak dispersive coupling regime.
Applying a sideband drive signal to the qubit, we observe an interference dip
originated from EIT in the qubit spectroscopy, originating from the quantum
interference between the qubit probe signal and sideband transition. From the
width and the depth of the dip, we are able to extract the single-photon
linewidth of the resonator from an analytical model. Working in a previously
unexplored regime in which the qubit has a larger linewidth than the resonator
reduces the technical challenge of making a high-coherence qubit and is
advantageous for remaining in the weakly-invasive limit of coupling to the
resonator. Furthermore, the sideband and the dispersive coupling between the
resonator and the qubit can be tuned $in~situ$ controlling the strength of the
sideband drive power. This $in-situ$ tuneability allows the technique to be
applied for efficient measurement of the resonator loss rate for any quality
factor below a fixed upper bound, on the order of $10^8$ for our device,
allowing a wide range of quality factors to probed using a single design.
