  We present one-dimensional simulation results for the cold atom tunneling
experiments by the Heidelberg group [G. Z\"urn {\em{et al.}}, Phys. Rev. Lett.
{\bf{108}}, 075303 (2012) and G. Z\"urn {\em{et al.}}, Phys. Rev. Lett.
{\bf{111}}, 175302 (2013)] on one or two $^6$Li atoms confined by a potential
that consists of an approximately harmonic optical trap plus a linear magnetic
field gradient. At the non-interacting particle level, we find that the WKB
(Wentzel-Kramers-Brillouin) approximation may not be used as a reliable tool to
extract the trapping potential parameters from the experimentally measured
tunneling data. We use our numerical calculations along with the experimental
tunneling rates for the non-interacting system to reparameterize the trapping
potential. The reparameterized trapping potentials serve as input for our
simulations of two interacting particles. For two interacting (distinguishable)
atoms on the upper branch, we reproduce the experimentally measured tunneling
rates, which vary over several orders of magnitude, fairly well. For infinitely
strong interaction strength, we compare the time dynamics with that of two
identical fermions and discuss the implications of fermionization on the
dynamics. For two attractively-interacting atoms on the molecular branch, we
find that single-particle tunneling dominates for weakly-attractive
interactions while pair tunneling dominates for strongly-attractive
interactions. Our first set of calculations yields qualitative but not
quantitative agreement with the experimentally measured tunneling rates. We
obtain quantitative agreement with the experimentally measured tunneling rates
if we allow for a weakened radial confinement.
