Spatially resolved compressibility measurements in the disordered Bose-Hubbard model

Direct comparison between our recent disordered optical lattice measurements and theoretical predictions for the disordered Bose-Hubbard model have been complicated by the inhomogeneous density profile of the trapped gas. We propose to study a narrow range of densities by exclusively imaging atoms at the center of the trap. To achieve this, microwave-frequency magnetic fields will be used to transfer atoms into a hyperfine state that is selectively imaged. Spatial discrimination will be realized using hyperfine-state-sensitive AC Stark shifts induced by crossed laser beams. We will couple this imaging technique with transport and compressibility measurements to directly determine the disordered Bose-Hubbard phase diagram.