  Motivated by the development of on-going optomechanical experiments aimed at
constraining non-local effects inspired by some quantum gravity scenarios, the
Hamiltonian formulation of a non-local harmonic oscillator, and its coupling to
a cavity field mode(s), is investigated. In particular, we consider the
previously studied model of non-local oscillators obtained as the
non-relativistic limit of a class of non-local Klein-Gordon operators,
$f(\Box)$, with $f$ an analytical function. The results of previous works, in
which the interaction was not included, are recovered and extended by way of
standard perturbation theory. At the same time, the perturbed energy spectrum
becomes available in this formulation, and we obtain the Langevin's equations
characterizing the interacting system.
