Thermodynamics of Adiabatically Loaded Cold Bosons in the Mott Insulating Phase of One-Dimensional Optical Lattices

In this work we give a consistent picture of the thermodynamic properties of bosons in the Mott insulating phase when loaded adiabatically into one-dimensional optical lattices. We find a crucial dependence of the temperature in the optical lattice on the doping level of the Mott insulator. In the undoped case, the temperature is of the order of the large onsite Hubbard interaction. In contrast, at a finite doping level the temperature jumps almost immediately to the order of the small hopping parameter. These two situations are investigated on the one hand by considering limiting cases like the atomic limit and the case of free fermions. On the other hand, they are examined using a quasi-particle conserving continuous unitary transformation extended by an approximate thermodynamics for hardcore particles.