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We theoretically study the adiabatic preparation of an antiferromagneticphase in a mixed Mott insulator of two bosonic atom species in aone-dimensional optical lattice. In such a system one can engineer a tunableparabolic inhomogeneity by controlling the difference of the trappingpotentials felt by the two species. Using numerical simulations we predict thata finite parabolic potential can assist the adiabatic preparation of theantiferromagnet. The optimal strength of the parabolic inhomogeneity dependssensitively on the number imbalance between the two species. We also find thatduring the preparation finite size effects will play a crucial role for asystem of realistic size. The experiment that we propose can be realized, forexample, using atomic mixtures of Rubidium 87 with Potassium 41 or Ytterbium168 with Ytterbium 174.

Quantum crystal growing: Adiabatic preparation of a bosonic antiferromagnet in the presence of a parabolic inhomogeneity