  We prove that a harmonic oscillator driven by Lindblad dynamics where the
typical drive and loss channels are two-photon processes instead of
single-photon ones, converges to a protected subspace spanned by two coherent
states of opposite amplitude. We then characterize the slow dynamics induced by
a perturbative single-photon loss on this protected subspace, by performing
adiabatic elimination in the Lindbladian dynamics.
