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We theoretically study the nonlinear optical phenomena including optical stability state and four-wave mixing (FWM) process in a hybrid opto-electromechanical system with the cross-Kerr (CK) effect. The hybrid system consists of an optomechanical cavity in which the cross-Kerr (CK) effect and Coulomb interaction are simultaneously introduced by the CK medium and the mechanical resonator capacitively coupling to an external circuit, respectively. The CK interaction induces a tristability behavior of the mean intracavity photon number, which can be modulated by the strength of the CK effect and electrically controlled by the voltage on the capacitor. In addition, we give the effects of the optomechanical, CK, and Coulomb coupling strengths on the FWM of the output field. The results show that the voltage can be employed to electrically engineer the optical nonlinear phenomena. [ABSTRACT FROM AUTHOR]

The future quantum networks will require reversible coherent conversion and modulation between microwave and optical photons to link the quantum information-processing ability of microwave and long-distance distribution ability of optical photons. Here, we present a scheme of bi-directional phase controllable four-wave mixing (FWM) between microwave and optical fields in the hybrid opto-electromechanical system. As an intermediate interface, a nanomechanical resonator optomechanically couples both optomechanical cavities in the optical and microwave frequency domains by the radiation pressure forces. We can find the four peaks of FWM, study the effects of the phases of the driven fields on the total, absolute, and cross correlation FWMs, and achieve the laws of phase control FWM based on quantum interference. In particular, we believe that such a hybrid opto- and electro-mechanical device incorporating highly coherent and compact mechanical elements on a chip has some potential functions for electro-optic modulation. We expect that such a modulator will have a broad range of applications including in optical communications and further quantum networks. [ABSTRACT FROM AUTHOR]

We present a scheme of reversible waveform conversion between microwave and optical fields in the hybrid opto-electromechanical system. As an intermediate interface, nanomechanical resonator optomechanically couples both optomechanical cavities in the optical and microwave frequency domains. We find the double-optomechanically induced transparency and achieve coherent signal waveform bi-directional transfer between microwave and optical fields based on quantum interference. In addition, we give an analytical expression of one-to-one correspondence between the microwave field and the optical output field, which intuitively shows the reversible waveform conversion relationship. In particular, by numerical simulations and approximate expression, we demonstrate the conversion effects of the three waveforms and discuss the bi-directional conversion efficiency and the bandwidth. such a hybrid opto- and electro-mechanical device has significant potential functions for electro-optic modulation and waveform conversion of quantum microwave-optical field in optical communications and further quantum networks. [ABSTRACT FROM AUTHOR]

We theoretically investigate the Doppler effect on optical bistability in an N-type active Raman gain atomic system inside an optical ring cavity. It is shown that the Doppler effect can greatly enhance the dispersion and thus create the bistable behaviour or greatly increase the bistable region, which has been known as the positive Doppler effect on optical bistability. In addition, we find that a positive Doppler effect can change optical bistability from the hybrid dispersion-gain type to a dispersive type. [ABSTRACT FROM AUTHOR]