  While the zero-temperature properties of harmonically trapped cold few-atom
systems have been discussed fairly extensively over the past decade, much less
is known about the finite-temperature properties. Working in the canonical
ensemble, we characterize small harmonically trapped atomic systems as a
function of the temperature using analytical and numerical techniques. We
present results for the energetics, structural properties, condensate fraction,
superfluid fraction, and superfluid density. Our calculations for the two-body
system underline that the condensate and superfluid fractions are distinctly
different quantities. Our work demonstrates that the path integral Monte Carlo
method yields reliable results for bosonic and fermionic systems over a wide
temperature range, including the regime where the de Broglie wave length is
large, i.e., where the statistics plays an important role. The regime where the
Fermi sign problem leads to reasonably large signal to noise ratios is mapped
out for selected parameter combinations. Our calculations for bosons focus on
the unitary regime, where the physics is expected to be governed by the
three-body parameter. If the three-body parameter is large compared to the
inverse of the harmonic oscillator length, we find that the bosons form a
droplet at low temperature and behave approximately like a non-interacting Bose
and eventually Boltzmann gas at high temperature. The change of the behavior
occurs over a fairly narrow temperature range. A simple model that reproduces
the key aspects of the phase transition like feature, which can potentially be
observed in cold atom Bose gas experiments, is presented.
