Checkerboard Bose Hubbard Ladders using Transmon Arrays

Adding a sublattice bias to the two dimensional Bose Hubbard model greatly enriches the available physics, and introduces knobs which can be used to control and interrogate the quantum state. We describe the physics of this checkerboard Bose Hubbard model and how it can be explored using transmon arrays. We show that the sublattice bias brings the commensurate superfluid phase into an experimentally accessible regime, and gives new probes. We characterize the superfluid and insulating phases, with careful attention to finite size effects.