  The effects of a turnstile operation on the current-induced vibron dynamics
in nanoelectromechanical systems (NEMS) are analyzed in the framework of the
generalized master equation. In our simulations each turnstile cycle allows the
pumping of up to two interacting electrons across a biased mesoscopic subsystem
which is electrostatically coupled to the vibrational mode of a nanoresonator.
The time-dependent mean vibron number is very sensitive to the turnstile
driving, rapidly increasing/decreasing along the charging/discharging
sequences. This sequence of heating and cooling cycles experienced by the
nanoresonator is due to specific vibron-assisted sequential tunneling processes
along a turnstile period. At the end of each charging/discharging cycle the
nanoresonator is described by a linear combination of vibron-dressed states
$s_{\nu}$ associated to an electronic configuration $\nu$. If the turnstile
operation leads to complete electronic depletion the nanoresonator returns to
its equilibrium position, i.e.\,its displacement vanishes. It turns out that a
suitable bias applied on the NEMS leads to a slow but complete cooling at the
end of the turnstile cycle. Our calculations show that the quantum turnstile
regime switches the dynamics of the NEMS between vibron-dressed subspaces with
different electronic occupation numbers. We predict that the turnstile control
of the electron-vibron interaction induces measurable changes on the input and
output transient currents.
