  The fields of opto- and electromechanics have facilitated numerous advances
in the areas of precision measurement and sensing, ultimately driving the
studies of mechanical systems into the quantum regime. To date, however, the
quantization of the mechanical motion and the associated quantum jumps between
phonon states remains elusive. For optomechanical systems, the coupling to the
environment was shown to preclude the detection of the mechanical mode
occupation, unless strong single photon optomechanical coupling is achieved.
Here, we propose and analyse an electromechanical setup, which allows to
overcome this limitation and resolve the energy levels of a mechanical
oscillator. We find that the heating of the membrane, caused by the interaction
with the environment and unwanted couplings, can be suppressed for carefully
designed electromechanical systems. The results suggest that phonon number
measurement is within reach for modern electromechanical setups.
