Thermometry and refrigeration in a two-component Mott insulator of ultracold atoms

Interesting spin Hamiltonians can be realized with ultracold atoms in a two-component Mott insulator (2CMI) [Adv. Phys. 56, 243 (2007); Rev. Mod. Phys. 80, 885 (2008)]. It was recently demonstrated that the application of a magnetic field gradient to the 2CMI enables new techniques of thermometry [Phys. Rev. Lett. 103, 245301 (2009)] and adiabatic cooling [e-print arXiv:1006.4674]. Here we present a theoretical description which provides quantitative analysis of these two techniques. We show that adiabatic reduction of the field gradient is capable of cooling below the Curie or Neel temperature of certain spin-ordered phases.