  Quantum degenerate gases trapped in optical lattices are ideal testbeds for
fundamental physics because these systems are tunable, well characterized, and
isolated from the environment. Controlled disorder can be introduced to explore
suppression of quantum diffusion in the absence of conventional dephasing
mechanisms such as phonons, which are unavoidable in experiments on electronic
solids. Recent experiments use transport of degenerate Fermi gases in optical
lattices (Kondov et al. Phys. Rev. Lett. 114, 083002 (2015)) to probe a
particularly extreme regime of strong interaction in what can be modeled as an
Anderson-Hubbard model. These experiments find evidence for an intriguing
insulating phase where quantum diffusion is completely suppressed by strong
disorder. Quantitative interpretation of these experiments remains an open
problem that requires inclusion of non-zero entropy, strong interaction, and
trapping. We argue that the suppression of transport can be thought of as
localization of Hubbard-band quasiparticles. We construct a theory of transport
of Hubbard-band quasiparticles tailored to trapped optical lattice experiments.
We compare the theory directly with center-of-mass transport experiments of
Kondov et al. with no fitting parameters. The close agreement between theory
and experiments shows that the suppression of transport is only partly due to
finite entropy effects. We argue that the complete suppression of transport is
consistent with Anderson localization of Hubbard-band quasiparticles. The
combination of our theoretical framework and optical lattice experiments offers
an important platform for studying localization in isolated many-body quantum
systems.
