Phase Identification and Thermometry of Condensates in 2D Optical Lattices*

Definitive identification of the phases in a periodic optical lattice and an overall confining potential continues to present difficulties. By direct comparison of density images from experiments\footnote{N. Gemelke, et al., \emph{Nature} \textbf{460}, 995-998 (2009).} of bosons on 2D optical lattices to QMC density profile calculations,\footnote{Y. Kato, et al., \emph{Nature Physics} \textbf{4}, 617 (2008).} we differentiate between Mott insulator, superfluid and normal phases. Kinks in the compressibility spatially locate the emergence of superfluid order.\footnote{Q. Zhou, et al., \emph{Phys. Rev. Lett.} \textbf{103}, 085701 (2009).} The temperature is estimated by examining the deviations from integer density of the Mott plateaus as well as from the tails of the density profiles.