Resonant Dynamics of Interacting Cold Atoms in a Constant Field

We propose to study the dynamics of strongly interacting ultracold bosons loaded at commensurate and incommensurate fillings in an optical lattice driven by a constant force field. The field is tuned resonantly with the interaction parameters providing a reduced Hilbert space for analysis at sufficiently short times. In addition, we investigate a possible non-destructive detection scheme for the atomic motion by coupling the atoms to a small-intensity cavity field and show how the dynamics in our system is reflected in the probe field.