  Hanbury-Brown-Twiss interferometry (HBTI) is used to study integer and
fractionally filled Mott Insulator (MI) phases in period-2 optical
superlattices. In contrast to the quasimomentum distribution, this second order
interferometry pattern exhibits high contrast fringes in the it insulating
phases. Our detailed study of HBTI suggests that this interference pattern
signals the various superfluid-insulator transitions and therefore can be used
as a practical method to determine the phase diagram of the system. We find
that in the presence of a confining potential the insulating phases become
robust as they exist for a finite range of atom numbers. Furthermore, we show
that in the trapped case the HBTI interferogram signals the formation of the MI
domains and probes the shell structure of the system.
