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Non-Gaussian states (NGSs) with higher-order correlation properties havewide-range applications in quantum information processing. However, thegeneration of such states with high quality still faces practical challenges.Here, we propose a protocol to faithfully generate two types of mechanicalNGSs, i.e., Schr\"{o}dinger cat states and Fock states, in open optomechanicalsystems, even when the cooperativity is smaller than one($g^2/\kappa\gamma<1$). In contrast to the usual scheme, a short squeezed fieldis pumped to rapidly entangle with a mechanical resonator via abeam-splitter-like optomechanical interaction, effectively reducing themechanical decoherence. Furthermore, by performing an additional amplifier anda following multi photon subtraction on the entangled optical field, one canselectively obtain the high-fidelity mechanical cat and Fock states. Thisprotocol is robust to various imperfections, allowing it to be implemented withstate-of-the-art experimental systems with close to unit fidelity. Moreover, itcan be extended to generate a four-component cat state and providepossibilities for future quantum applications of NGSs.

Fast Generation of High-Fidelity Mechanical Non-Gaussian States via Additional Amplifier and Photon Subtraction