  Nanomechanical resonators (NMRs), as the quantum mechanical sensing probers,
have played the important roles for various high-precision quantum
measurements. Differing from the previous emission spectral probes (i.e., the
NMR modified the atomic emission), in this paper we propose an alternative
approach, i.e., by probing the scattering spectra of the quantum mechanical
prober coupled to the driving microwaves, to characterize the physical features
of the NMR embedded in a rf-SQUID based superconducting qubit. It is shown
that, from the observed specifical frequency points in the spectra, i.e.,
either the dips or the peaks, the vibrational features (i.e., they are
classical vibration or quantum mechanical one) and the physical parameters
(typically such as the vibrational frequency and displacements) of the NMR can
be determined effectively. The proposal is feasible with the current technique
and should be useful to design the desired NMRs for various quantum
metrological applications.
