  The dynamics of electrons in ac driven double quantum dots have been
extensively analyzed by means of Floquet theory. In these systems, coherent
destruction of tunneling has been shown to occur for certain ac field
parameters. In the present work we analyze, by means of Floquet theory, the
electron dynamics of a triple quantum dot in series attached to electric
contacts, where the central dot position oscillates. In particular, we analyze
the quasienergy spectrum of this ac driven nanoelectromechanical system, as a
function of the intensity and frequency of the ac field and of external dc
voltages. For strong driving fields, we derive, by means of perturbation
theory, analytical expressions for the quasienergies of the driven oscillator
system. From this analysis we discuss the conditions for coherent destruction
of tunneling (CDT) to occur as a function of detuning and field parameters. For
zero detuning, and from the invariance of the Floquet Hamiltonian under a
generalized parity transformation, we find analytical expressions describing
the symmetry properties of the Fourier components of the Floquet states under
such transformation. By using these expressions, we show that in the vicinity
of the CDT condition, the quasienergy spectrum exhibits exact crossings which
can be characterized by the parity properties of the corresponding
eigenvectors.
