  In the quest to reach lower temperatures of ultra-cold gases in optical
lattice experiments, non-adiabaticites during lattice loading are one of the
limiting factors that prevent the same low temperatures to be reached as in
experiments without lattice. Simulating the loading of a bosonic quantum gas
into a one-dimensional optical lattice with and without a trap, we find that
the redistribution of atomic density inside a global confining potential is by
far the dominant source of heating. Based on these results we propose to adjust
the trapping potential during loading to minimize changes to the density
distribution. Our simulations confirm that a very simple linear interpolation
of the trapping potential during loading already significantly decreases the
heating of a quantum gas and we discuss how loading protocols minimizing
density redistributions can be designed.
