Abstract
We propose a scheme to simulate a one-dimensional Bose–Hubbard model with a coupled cavity optomechanical system. By eliminating the cavity field under the condition of large detuning, an effective Bose–Hubbard model can be achieved. By adiabatically adjusting the classical pumping, we show that the effective Hamiltonian can fully explain transitions from the Mott-insulating phase to the superfluid phase. In addition, we show that the system allows the quantum state transfer after including the dissipation of the oscillators.
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