The N

Context. Deuterated ions, especially H2D+ and N2D+, are abundant in cold (~10 K), dense (~105 cm-3) regions, in which CO is frozen out onto dust grains. In such environments, the N2D+/N2H+ ratio can exceed the elemental abundance ratio of D/H by a factor of $\simeq$104. Aims. We use deuterium fractionation to investigate the evolutionary state of Class 0 protostars. In particular, we expect the N2D+/N2H+ ratio to decrease as temperature (a sign of the evolution of the protostar) increases. Methods. We observed N2H+ 1-0, N2D+ 1-0, 2-1 and 3-2, C18O 1-0 and HCO+ 3-2 in a sample of 20 Class 0 and borderline Class 0/I protostars. We determined the deuteration fraction and searched for correlations between the N2D+/N2H+ ratio and well-established evolutionary tracers, such as TDust and the CO depletion factor. In addition, we compared the observational result with a chemical model. Results. In our protostellar sample, the N2H+ 1-0 optical depths are significantly lower than those found in prestellar cores, but the N2H+ column densities are comparable, which can be explained by the higher temperature and larger line width in protostellar cores. The deuterium fractionation of N2H+ in protostellar cores is also similar to that in prestellar cores. We found a clear correlation between the N2D+/N2H+ ratio and evolutionary tracers. As expected, the coolest, i.e. the youngest, objects show the largest deuterium fractionation. Furthermore, we find that sources with a high N2D+/N2H+ ratio show clear indications of infall (e.g. $ \delta v$ 0.15 even in the most evolved objects. Conclusions. The N2D+/N2H+ ratio is known to trace the evolution of prestellar cores. We show that this ratio can be used to trace core evolution even after star formation. Protostars with an N2D+/N2H+ ratio above 0.15 are in a stage shortly after the beginning of collapse. Later on, deuterium fractionation decreases until it reaches a value of ~0.03 at the Class 0/I borderline