Effects of finite temperature on the Mott insulator state

We investigate the effects of finite temperature on ultracold Bose atoms
confined in an optical lattice plus a parabolic potential in the Mott insulator
state. In particular, we analyze the temperature dependence of the density
distribution of atomic pairs in the lattice, by means of exact Monte-Carlo
simulations. We introduce a simple model that quantitatively accounts for the
computed pair density distributions at low enough temperatures. We suggest that
the temperature dependence of the atomic pair statistics may be used to
estimate the system's temperature at energies of the order of the atoms'
interaction energy.