  We consider photons strongly coupled to the excitonic excitations of a
coupled quantum well, in the presence of an electric field. We show how under a
field increase, the hybrid polariton made of photon coupled to hybrid carriers
lying in the two wells, transforms into a dipolariton made of photon coupled to
direct and indirect excitons. We also show how the cavity photon lifetime and
the coherence time of the carrier wave vectors, that we analytically handle
through non-hermitian Hamiltonians, affect these polaritonic states. While the
hybrid polaritons display a spectral singularity, where the eigenvalues
coalesce and known as exceptional point, that depends on detuning and
lifetimes, we find that the three dipolaritonic states display an anti-crossing
without exceptional point, due to interaction between photons, direct and
indirect excitons.
