Quantum quenches of cold-atom gases in optical lattices: the influence of Anderson localization

We consider the following kind of non-equilibrium experiment. An ultracold fluid of fermions is prepared in a potential consisting of three parts: an optical lattice; a short-range-correlated disorder potential of finite strength; and a shallow harmonic trapping potential. After the fluid has equilibrated, the minimum of the harmonic potential is suddenly ``jumped'' to the side by a finite distance, $d$. The observables of interest are the subsequent evolution of the density distribution and phase correlations in the fluid. This kind of experiment is theoretically interesting because it contains two energy-dependent length scales: the localization length of the single-particle orbitals due to the disorder potential, $\xi$; and the ``Bragg localization length'' of the single-particle orbitals due to the combined effect of the harmonic trap and optical lattice, $l_B$. We present numerical results on the evolution of the density distributions and phase correlations in such cases, for a range of strengths of the disorder. In addition, we provide an approximate analytical framework for understanding our results in terms of the relative size of the length scales $\xi$ and $l_B$ at the Fermi energy. Possibilities for further work are also discussed.