  Hybrid devices based on the superconducting qubits have emerged as a
promising platform for controlling the quantum states of macroscopic
resonators. The nonlinearity added by a qubit can be a valuable resource for
such control. Here we study a hybrid system consisting of a mechanical
resonator longitudinally coupled to a transmon qubit. The qubit readout can be
done by coupling to a readout mode like in c-QED setup. The coupling between
the mechanical resonator and transmon qubit can be implemented by modulation of
the SQUID inductance. In such a tri-partite system, we analyze the steady-state
occupation of the mechanical mode when all three modes are dispersively
coupled. We use the quantum-noise and the Lindblad formalism to show that the
sideband cooling of the mechanical mode to its ground state is achievable. We
further experimentally demonstrate that measurements of the thermomechanical
motion is possible in the dispersive limit, while maintaining a large coupling
between qubit and mechanical mode. Our theoretical calculations suggest that
single-photon strong coupling is within the experimental reach in such hybrid
devices.
