Correlations of Pairs in Bichromatic Optical Lattices

Correlation functions of two interacting bosons in bound states confined in a quasi-periodic 1D optical lattice are investigated. This two-body problem is exactly solvable, and therefore, various correlation functions can be directly calculated. The first-order correlation and the resulting momentum distribution behave smoothly across the phase boundary and exhibit a strong dependence on the sign of on-site interactions. We demonstrate that this special signature of momentum distribution exists for both the extended phase and the localized phase. In addition to the dependence on the sign of on-site interactions, the second-order quantum coherence reveals complementary information about the quasi-periodic order of the system, the underling structure of the bound states and the characterization of the different phases of the bound states. We also study the second-order correlation in momentum space of the bound states in both the weak and strong coupling regimes and demonstrate different correlation patterns in these two regimes.