  We study the full-fledged microscopic dynamics of two interacting, ultracold
bosons in a one- dimensional double-well potential, through the numerically
exact diagonalization of the many-body Hamiltonian. With the particles
initially prepared in the left well, we increase the width of the right well in
subsequent trap realizations and witness how the tunneling oscillations evolve
into particle loss. In this closed system, we analyze the spectral signatures
of single- and two-particle tunneling for the entire range of repulsive
interactions. We conclude that for comparable widths of the two wells,
pair-wise tunneling of the bosons may be realized for specific system
parameters. In contrast, the decay process (corresponding to a broad right
well) is dominated by uncorrelated single-particle decay.
