  Many-body effects are at the very heart of diverse phenomena found in
condensed-matter physics. One striking example is the Mott insulator phase
where conductivity is suppressed as a result of a strong repulsive interaction.
Advances in cold atom physics have led to the realization of the Mott
insulating phases of atoms in an optical lattice, mimicking the corresponding
condensed matter systems. Here, we explore an exotic strongly-correlated system
of Interacting Dual Mott Insulators of bosons and fermions. We reveal that an
inter-species interaction between bosons and fermions drastically modifies each
Mott insulator, causing effects that include melting, generation of composite
particles, an anti-correlated phase, and complete phase-separation. Comparisons
between the experimental results and numerical simulations indicate intrinsic
adiabatic heating and cooling for the attractively and repulsively interacting
dual Mott Insulators, respectively.
