The Bogoliubov approach to number squeezing of atoms in an optical lattice

We describe an approach for finding the number squeezing for arrays of atoms in an optical lattice. It is based on a straightforward extension of the Bogoliubov method. We discuss the conditions for optimizing squeezing and how to predict what will be obtained in a given experiment. We consider using the method to deal with finite temperatures. The method also appears to be extensible to inhomogeneous and time-dependent systems.