  We analyze a scheme for preparation of magnetically ordered states of
two-component bosonic atoms in optical lattices. We compute the dynamics during
adiabatic and optimized time-dependent ramps to produce ground states of
effective spin Hamiltonians, and determine the robustness to decoherence for
realistic experimental system sizes and timescales. Ramping parameters near a
phase transition point in both effective spin-1/2 and spin-1 models produces
entangled spin-symmetric states that have potential future applications in
quantum enhanced measurement. The preparation of these states and their
robustness to decoherence is quantified by computing the Quantum Fisher
Information of final states. We identify that the generation of useful
entanglement should in general be more robust to heating than it would be
implied by the state fidelity, with corresponding implications for practical
applications.

Quantum Gases;Quantum Physics