Using off-diagonal confinement as a cooling method

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.