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In recent years, due to unprecedented success in controlling and manipulating an individual quantum system, simulation of quantum systems using quantum simulators or a quantum computer is becoming reality. In this thesis, the main goal is to study many-body correlations in quantum simulators and their impact on quantum information science. In particular, we focus on high fidelity many-body ground state preparation in Jaynes-cummings lattices in coupled cavity arrays. In the first work, we show that by combining quantum engineering and nonlinear adiabatic ramping, high fidelity many-body ground state can be prepared in a targeted region either in the Mott insulating phase or in the Superfluid phase. In the second project, we use the shortcuts to adiabaticity (STA) method for the fast and efficient many-body state preparation. We compare the fidelity obtained by using the simple adiabatic method and the STA method to show the advantage of the STA method over the adiabatic method. In the third project, we apply the quantum optimal control (QOC) technique with a chopped random basis (CRAB) algorithm to prepare high fidelity many-body ground states in minimal time in the Jaynes-Cummings lattices. The methods we used are general and can be used for state preparation in other quantum simulators or quantum computers.