Non-trivial Pairing Separated by a Mott Core on the t-J Ladder

We investigate the ground state properties of the t-J ladder by using the large-scale density matrix renormalization group method. Applying a strong chemical potential to the inner legs of the lattice, to emulate the effects of a confining trap, the central part of the system behaves as a Mott insulator, while on the outer legs the system is in a metallic-like phase. In this case, we demonstrate a real-space separated super-conducting pairing, with two paired-particles being split by the Mott insulator core. By examining the corresponding pairing correlation functions for both the singlet and the triplet channels, we find a regime where the singlet pairing dominates and decays as a power-law when the Mott core has an even number of legs. Therefore, there is a non-trivial singlet superconducting pairing displaying quasi-long-range order on this ladder in the presence of a Mott core. We expect that our findings can be confirmed by the cold atoms/molecules in optical lattices experiments.