  By exploiting the nonlinear nature of the Jaynes Cumming's interaction, one
can get photon population trapping in cavity-QED arrays. However, the
unavoidable dissipative effects in a realistic system would destroy the
self-trapped state by continuous photon leakage. To circumvent this issue, we
show that a careful engineering of drive, dissipation and Hamiltonian results
in achieving indefinitely sustained self-trapping. We show that the intricate
interplay between drive, dissipation, and light-matter interaction results in
requiring an optimal window of drive strengths in order to achieve such
non-trivial steady states. We treat the two-cavity and four-cavity cases using
exact open quantum many-body calculations. Additionally, in the semiclassical
limit we scale up the system to a long 1-D chain and demonstrate localization
de-localization transition in a driven-dissipative system. Although, our
analysis is performed keeping cavity-QED systems in mind, our work is
applicable to other driven-dissipative systems where nonlinearity plays a
defining role.
