We consider an optomechanical cavity made by two moving mirrors which contains a Kerr-down conversion nonlinear crystal. We show that the coherent oscillations of the two mechanical oscillators can lead to splitting in the electromagnetically induced transparency (EIT) resonance, and appearance of an absorption peak within the transparency window. In this configuration the coherent induced splitting of EIT is similar to driving a hyperfine transition in an atomic Lambda-type three-level system by a radio-frequency or microwave field. Also, we show that the presence of nonlinearity provides an additional flexibility for adjusting the width of the transparency windows. The combination of an additional mechanical mode and the nonlinear crystal suggests new possibilities for adjusting the resonance frequency, the width and the spectral positions of the EIT windows as well as the enhancement of the absorption peak within the transparency window.

The interaction of a single-mode field with both a weak Kerr medium and a parametric nonlinearity in an intrinsically nonlinear optomechanical system is studied. The nonlinearities due to the optomechanical coupling and Kerr-down conversion lead to the bistability and tristability in the mean intracavity photon number. Also, our work demonstrates that the lower bound of the resolved sideband regime and the minimum attainable phonon number can be less than that of a bare cavity by controlling the parametric nonlinearity and the phase of the driving field. Moreover, we find that in the system under consideration the degree of entanglement between the mechanical and optical modes is dependent on the two stability parameters of the system. For both cooling and entanglement, while parametric nonlinearity increases the optomechanical coupling , the weak Kerr nonlinearity is very useful for extending the domain of the stability region to the desired range in which the minimum effective temperature and maximal entanglement are attainable. Also, as shown in this paper, the present scheme allows to have significant entanglement in the tristable regime for the lower and middle branches which makes the current scheme distinct from the bare optomechanical system.

In this Letter we describe a new two-mode system, which consists of Kerr-like medium and down conversion process, called the Kerr-down conversion system. Under a certain condition we can obtain an exact solution of the dynamical equations of motion. For this system we investigate different kinds of quadrature squeezing, e.g., single-mode, two-mode and sum-squeezing. Also we give a more general definition of the principal squeezing. We show that the amounts of nonclassical effects produced by the Kerr-like and down-conversion processes separately are greater than those obtained from the Kerr-down conversion system where both the processes are in competition.

In this paper, we theoretically investigate the displacement and momentum fluctuations spectra of the movable mirror in a standard optomechanical system driven by a finite-bandwidth squeezed vacuum light accompanying a coherent laser field. Two cases in which the squeezed vacuum is generated by degenerated and non-degenerate parametric oscillators (DPO and NDPO) are considered. We find that for the case of finite-bandwidth squeezed vacuum injection, the two spectra exhibit unique features, which strongly differ from those of broadband squeezing excitation. In particular, the spectra exhibit a three-peaked and a four-peaked structure, respectively, for the squeezing injection from DPO and NDPO. Besides, some anomalous characteristics of the spectra such as squeezing-induced pimple, hole burning, and dispersive profile are found to be highly sensitive to the squeezing parameters and the temperature of the mirror. We also evaluate the mean-square fluctuations in position and momentum quadratures of the movable mirror and analyze the influence of the squeezing parameters of the input field on the mechanical squeezing. It will be shown that the parameters of driven squeezed vacuum affects the squeezing. We find the optimal mechanical squeezing is achievable via finite-bandwidth squeezed vacuum injection which is affected by the intensity of squeezed vacuum. We also show that the phase of incident squeezed vacuum determines whether position or momentum squeezing occurs. Our proposed scheme not only provides a feasible experimental method to detect and characterize squeezed light by optomechanical systems, but also suggests a way for controllable transfer of squeezing from an optical field to a mechanical oscillator.

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