  A driven-dissipative nonlinear photonic system (e.g. exciton-polaritons) can
operate in a gapped superfluid regime. We theoretically demonstrate that the
reflection of a linear wave on this superfluid is an analogue of the Andreev
reflection of an electron on a superconductor. A normal region surrounded by
two superfluids is found to host Andreev-like bound states. These bound states
form topological synthetic bands versus the phase difference between the two
superfluids. Changing the width of the normal region allows to invert the band
topology and to create "interface" states. Instead of demonstrating a linear
crossing, synthetic bands are attracted by the non-linear non-Hermitian
coupling of bosonic systems which gives rise to a self-amplified strongly
occupied topological state.
