Two submm/mm sources in the Barnard 1b (B1-b) core, B1-bN and B1-bS, have been observed with the Submillimeter Array (SMA) and the Submillimeter Telescope (SMT). The 1.1 mm continuum map obtained with the SMA reveals that the two sources contain spatially compact components, suggesting that they harbor protostars. The N2D+ and N2H+ J=3-2 maps were obtained by combining the SMA and SMT data. The N2D+ map clearly shows two peaks at the continuum positions. The N2H+ map also peaks at the continuum positions, but is more dominated by the spatially extended component. The N2D+/N2H+ ratio was estimated to be ~ 0.2 at the positions of both B1-bN and B1-bS. The derived N2D+/N2H+ ratio is comparable to those of the prestellar cores in the late evolutionary stage and the class 0 protostars in the early evolutionary stage. Although B1-bN is bright in N2H+ and N2D+, this source was barely seen in H13CO+. This implies that the depletion of carbon-bearing molecules is significant in B1-bN. The chemical property suggests that B1-bN is in the earlier evolutionary stage as compared to B1-bS with the H13CO+ counterpart. The N2H+ and N2D+ lines show that the radial velocities of the two sources are different by ~ 0.9 km s-1. However, the velocity pattern along the line through B1-bN and B1-bS suggests that these two sources were not formed out of a single rotating cloud. It is likely that the B1-b core consists of two velocity components, each of which harbors a very young source.