Realizing and adiabatically preparing bosonic integer and fractional quantum Hall states in optical lattices

We study the ground states of two-dimensional lattice bosons in an artificial gauge field. Using state-of-the-art density matrix renormalization group (DMRG) simulations we obtain the zero-temperature phase diagram for hard-core bosons at densities n(b) with flux n(phi) per unit cell, which determines a filling nu = n(b)/n(phi). We find the bosonic Jain sequence [nu = p/(p + 1)] states, in particular, a bosonic integer quantum Hall phase at nu = 2, are fairly robust in the hard-core boson limit, In addition to identifying Hamiltonians whose ground states realize these phases, we discuss their preparation, beginning from independent chains, and ramping up interchain couplings. Using time-dependent DMRG simulations, these are shown to reliably produce states close to the ground state for experimentally relevant system sizes. Our proposal only utilizes existing experimental capabilities.