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The realization of multimode optomechanical interactions in the single-photonstrong-coupling regime is a desired task in cavity optomechanics, but itremains a challenge in realistic physical systems. In this work, we propose areliable scheme to simulate a three-mode optomechanical system working in thesingle-photon strong-coupling regime based on the Fredkin-type interaction.This is achieved by utilizing two strong drivings to the two exchangly-coupledmodes in the Fredkin-type coupling involving one optical mode and twomechanical-like modes. As an application of this enhanced three-mode nonlinearoptomechanical coupling, we show how to generate entangled-cat states of themechanical-like modes using the conditional displacement mechanism. The quantumcoherence effects in the generated states are investigated by calculatingtwo-mode joint Wigner function and quantum entanglement. The influence of thedissipation effect on the state generation is considered in the open-systemcase.

Quantum simulation of a three-mode optomechanical system based on the Fredkin-type interaction