Compressibility Measures of Ultracold Atomic Gases in Optical Lattices

Synopsis

Ultracold atomic gases confined to optical lattices can be put into strongly correlated regimes where an energy gap makes the system incompressible.  Examples of incompressible states include Mott and quantum Hall states.  Measures of compressibility are therefore advantageous for the identification of robust many-body physics-archive in optical lattices.  Unfortunately, compressible edges in most trapping geometries render global measures of compressibility difficult to implement or interpret.  I will discuss methods to use double occupancies in optical lattices as routes to measure core compressibility.  Core compressibility implicitly excludes edge effects and measures compressibility near the trap center.  I will also discuss recent measurements of core compressibility of disordered bosons in an optical lattice.  Our theory-experiment comparison shows that the core compressibility signals a disorder-driven transition from an incompressible Mott regime to a compressible regime.   These measurements demonstrate that core compressibility offers a useful observable that can identify incompressible phases and phase transitions with disordered atoms in optical lattices.