  We present a hybrid system consisting of a superconducting coplanar waveguide
resonator coupled to a nanomechanical string and a transmon qubit acting as
nonlinear circuit element. We perform spectroscopy for both the transmon qubit
and the nanomechanical string. Measuring the ac-Stark shift on the transmon
qubit as well as the electromechanically induced absorption on the string
allows us to determine the average photon number in the microwave resonator in
both the low and high power regimes. In this way, we measure photon numbers
that are up to nine orders of magnitude apart. We find a quantitative agreement
between the calibration of photon numbers in the microwave resonator using the
two methods. Our experiments demonstrate the successful combination of
superconducting circuit quantum electrodynamics and nano-electromechanics on a
single chip.
