  In Bose-Einstein condensates with an attractive contact interaction the
stable ground state and an unstable excited state emerge in a tangent
bifurcation at a critical value of the scattering length. At the bifurcation
point both the energies and the wave functions of the two states coalesce,
which is the characteristic of an exceptional point. In numerical simulations
signatures of the exceptional point can be observed by encircling the
bifurcation point in the complex extended space of the scattering length,
however, this method cannot be applied in an experiment. Here we show in which
way the exceptional point effects the collapse dynamics of the Bose-Einstein
condensate. The harmonic inversion analysis of the time signal given as the
spatial extension of the collapsing condensate wave function can provide clear
evidence for the existence of an exceptional point. This method can be used for
an experimental verification of exceptional points in Bose-Einstein
condensates.
