Recent experimental advances have promoted the simple, ideal lattice systems appearing in condensed-matter textbooks from rough toy models to actual laboratory toolboxes. One prominent example in this respect is provided by ultracold atomic gases loaded in “crystals of light”, i.e. the optical lattices formed by counterpropagating lattice beams.
A long-standing issue in this context is the measure of temperature. Adding to the interest of this problem is the fact that lattice systems are thought to support negative temperature states, in view of the effective boundedness of the energy spectrum. Ideed, a proposal for creating negative-temperature metastable states with ultracold gases has been recently realized at the University of Munich, Germany. Further zest is added to this subject by the ongoing lively debate about the well-posedness of the concept of negative absolute temperatures, spurred by a very recent article published in Nature Physics.
We investigate these issues from the theoretical (analytical and numerical) point of view, focusing on nonlinear lattice models describing lattice boson systems under suitable conditions.
Other than for the measure of temperature in ultracold lattice gases, our study is relevant also for light propagating into optically induced nonlinear photonic lattices.