  Exceptional points describe the coalescence of the eigenmodes of a
non-Hermitian matrix. When an exceptional point occurs in the unitary evolution
of a many-body system, it generically leads to a dynamical instability with a
finite wavevector [N. Bernier \etal, Phys. Rev. Lett. 113, 065303 (2014)].
Here, we study exceptional points in the context of the counterflow instability
of colliding Bose-Einstein condensates. We show that the instability of this
system is due to an exceptional point in the Bogoliubov spectrum. We further
clarify the connection of this effect to the Landau criterion of superfluidity
and to the scattering of classical particles. We propose an experimental set-up
to directly probe this exceptional point, and demonstrate its feasibility with
the aid of numerical calculations. Our work fosters the observation of
exceptional points in nonequilibrium many-body quantum systems.
