  Strongly-correlated polaritons in Jaynes-Cummings (JC) lattices can exhibit
quantum phase transitions between the Mott-insulating and superfluid phases at
integer fillings. The prerequisite to observe such phase transitions is to pump
polariton excitations into a JC lattice and prepare them into appropriate
ground states. Despite previous efforts, it is still challenging to generate
many-body states with high accuracy. Here we present an approach for the robust
preparation of many-body ground states of polaritons in finite-sized JC
lattices by optimized nonlinear ramping. We apply a Landau-Zener type of
estimation to this finite-sized system and derive the optimal ramping index for
selected ramping trajectories, which can greatly improve the fidelity of the
prepared states. With numerical simulation, we show that by choosing an
appropriate ramping trajectory, the fidelity in this approach can remain close
to unity in almost the entire parameter space. This approach can shed light on
high-fidelity state preparation in quantum simulators and advance the
implementation of quantum simulation with practical devices.
