Temperature changes when adiabatically ramping up an optical lattice

When atoms are loaded into an optical lattice, the process of gradually turning on the lattice is almost adiabatic. In this paper we investigate how the temperature changes when going from the gapless superfluid phase to the gapped Mott phase along isentropic lines. To do so we calculate the entropy in the single-band Bose-Hubbard model for various densities, interaction strengths and temperatures in one and two dimensions for homogeneous and trapped systems. Our theory is able to reproduce the experimentally observed visibilities and therefore strongly supports that current experiments remain in the quantum regime for all considered lattice depths with low temperatures and minimal heating.