  We consider quantum phase transitions in a system of bright dipolar excitons
which can form bound pairs (dipolar biexcitons). We assume a narrow resonance
in the interaction of excitons with opposite spins. At sufficiently large
density a resonant exciton superfluid transforms into a superfluid of
biexcitons. The transition may be either of the first or the second kind. The
average relative momenta of excitons in the pairs being beyond the light cone,
the transition should be accompanied by reduction of the photoluminescence
intensity. Effective magnetic fields due to the long-range exchange splitting
of non-radiative exciton states induce broadening of the biexciton resonance.
The fields shift the position of the gap in the elementary excitation spectrum
to a circle of degenerate minima in the k-space. Closing the new gap defines a
second order phase transition into a mixture of counter-propagating plane-wave
excitonic condensates polarized linearly in the direction perpendicular to
their wavevectors. In the resonance energy vs density phase diagram the novel
phase intervenes between the dark biexciton and radiative exciton superfluids.
We conclude that formation of a BCS-like biexciton condensate induces
correlated alignment of the effective magnetic fields and excitonic spins. We
outline important differences of the emergent mechanism from the phenomenon of
spin-orbit (SO) coupled Bose-Einstein condensation. We expect existence of
analogous mechanisms in SO-coupled fermionic superfluids and superconductors.
