  In a recent letter [Phys. Rev. Lett. 104, 167201 (2010)] we proposed a new
confining method for ultracold atoms on optical lattices, based on off-diagonal
confinement (ODC). This method was shown to have distinct advantages over the
conventional diagonal confinement (DC) that makes use of a trapping potential,
including the existence of pure Mott phases and highly populated condensates.
In this paper we show that the ODC method can also lead to temperatures that
are smaller than with the conventional DC method, depending on the control
parameters. We determine these parameters using exact diagonalizations for the
hard-core case, then we extend our results to the soft-core case by performing
quantum Monte Carlo (QMC) simulations for both DC and ODC systems at fixed
temperatures, and analysing the corresponding entropies. We also propose a
method for measuring the entropy in QMC simulations.
