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arXiv:1511.04518 · Physical Review A

Cross-Kerr effect on an optomechanical system

Wei Xiong, Da-Yu Jin, Yueyin Qiu, Chi‐Hang Lam, J. Q. You

Published Feb 26, 2016• 101 citations
arXivHTMLPDF

Abstract

We study the cross-Kerr (CK) effect on an optomechanical system driven by two-tone fields. We show that in the presence of the CK effect, a bistable behavior of the mean photon number in the cavity becomes more robust against the fluctuations of the frequency detuning between the cavity mode and the control field. The bistability can also be turned into a tristability within the experimentally accessible range of the system parameters. Also, we find that the symmetric profile of the optomechanically induced transparency is broken and the zero-absorption point is shifted in the presence of the CK effect. This shift can be used to measure the strength of the CK effect and the asymmetric absorption profiles can be employed to engineer a high quality factor of the cavity.

DOI
10.1103/physreva.93.023844

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We study the cross-Kerr (CK) effect on an optomechanical system driven by two-tone fields. We show that in the presence of the CK effect, a bistable behavior of the mean photon number in the cavity becomes more robust against the fluctuations of the frequency detuning between the cavity mode and the control field. The bistability can also be turned into a tristability within the experimentally accessible range of the system parameters. Also, we find that the symmetric profile of the optomechanically induced transparency is broken and the zero-absorption point is shifted in the presence of the CK effect. This shift can be used to measure the strength of the CK effect and the asymmetric absorption profiles can be employed to engineer a high quality factor of the cavity.
We theoretically study the effect of Kerr effect on the second-order nonlinearity induced transparency in a double-resonant optical cavity system. We show that in the presence of the Kerr effect, as the strength of the Kerr effect increases, the absorption curve exhibits an asymmetric-symmetric-asymmetric transition, and the zero absorption point shifts with the increase of the Kerr effect. Furthermore, by changing the strength of the Kerr effect, we can control the width of the transparent window, and the position of the zero-absorption point and meanwhile change the left and right width of the absorption peak. The asymmetry absorption curve can be employed to improve the quality factor of the cavity when the frequency detuning is tuned to be around the right peak. The simple dependence of the zero-absorption point on the strength of Kerr effect suggests that the strength of Kerr effect can be measured by measuring the position of the zero-absorption point in a possible application.
We examine the effect of cavity field fluctuations on Kerr nonlinearity in an atom-assisted optomechanical system. It is found that a new self-Kerr (SK) nonlinearity term, which can greatly surpass that of a classical Λ type atomic system when the hybrid system has numerous atoms, is generated based on cavity field fluctuations by atom-cavity interactions. A strong photon-phonon cross-Kerr (CK) nonlinearity is also produced based on cavity field fluctuations. These nonlinearity features can be modified by atom-cavity and optomechanical interactions. This work may provide a new method to enhance the SK nonlinearity and generate the photon-phonon CK nonlinearity.
We investigate the effect of Kerr nonlinearity and optomechanical couplings on cavity field spectra in an optomechanical system driven by a pump field. In the mean-field approximation, the system exhibits optical bistability for a wide range of parameters. The spectra are numerically calculated for different initial states, which show that a single peak in the spectrum splits because of the presence of the optomechanical coupling and the increase of the number of phonon. In addition, the peak position in the cavity field spectra changes due to the Kerr nonlinearity, while the cavity detuning is modified. The strength of spectra determines the size of the photon-phonon conversion capabilities. These results provides a theoretical basis for optical communication.
We theoretically investigate the optomechanically induced transparency (OMIT) phenomenon and the fast and slow light effects of a four-mode optomechanical system with the Kerr medium. The optomechanical system is composed of an array of three single-mode cavities and a mechanical oscillator. The three cavities are a passive cavity, a no-loss-gain cavity and a gain optical cavity, respectively. A Kerr medium is inserted in the passive cavity. We study the influence of the Kerr medium on the stability of the optomechanical system, and find that the stable regime of the optomechanical system can be adjusted by changing the Kerr coefficient. We demonstrate that the phenomenon of optomechanically induced transparency will appear when the Kerr medium exists in the optomechanical system and find that the frequency position of the absorption peak on the left increases linearly with the Kerr coefficient. In addition, we also investigate the fast and slow light effects in this system. The results show that we can control the fast and slow light by adjusting the Kerr coefficient, tunneling strength, and driving field strength. This study has potential application prospects in the fields of quantum optical devices and quantum information processing.
We study the optical bistability of an optomechanical system in which the position of a mechanical oscillator modulates the cavity frequency. The steady-state mean-field equation of the optical mode is identical to the one for a Kerr medium, and thus we expect it to have the same characteristic behavior with a lower, a middle, and an upper branch. However, the presence of position fluctuations of the mechanical resonator leads to a new feature: the upper branch will become unstable at sufficiently strong driving in certain parameter regimes. We identify the appropriate parameter regime for the upper branch to be stable, and we confirm, by numerical investigation of the quantum steady state, that the mechanical mode indeed acts as a Kerr nonlinearity for the optical mode in the low-temperature limit. This equivalence of the optomechanical system and the Kerr medium will be important for future applications of cavity optomechanics in quantum nonlinear optics and quantum information science.
We investigate a hybrid optomechanical system consisting of two coupled cavities, one of them is composed of two-end fixed mirrors (called the traditional cavity), and the other has a one-end oscillating mirror (named as the optomechanical cavity). A Kerr medium is inside the traditional cavity to enhance the nonlinearity due to the fact that it can cause observing of bistable behavior in intracavity intensity for the optomechanical cavity. The Hamiltonian of the system is written in a rotating frame and its dynamics is described by quantum Langevin equations of motion. Our proposed system exhibits unconventional plots for the mean photon number of the optomechanical cavity which are not observed in previous works. The present results show a deep effect of the Kerr medium on optical bistability of intracavity intensity for the optomechanical cavity. Also, coupling strength of the cavities can effectively change the stability of the system.