In this article we study tunable optically induced transparency and photon blockade in an optomechanical system comprising a suspended single-layer graphene sheet above a one-dimensional photonic crystal nanobeam cavity above which a single layer graphene sheet is suspended where optomechanical coupling exist not only between photonic and mechanical modes of nanobeam, but also between the photonic cavity field and graphene resonator and the photonic cavity exhibits Kerr type nonlinearity. We develop a Hamiltonian for the system and analytically solve for the photon transmission rate in Hamilton-Langevin formulation. It is found that we can manipulate the absorption window by varying both the nanobeam photon-nanobeam phonon coupling and nanobeam photon-graphene phonon coupling. We also theoretically and numerically analyze the photon statistics of the system. We analytically determine the optimal conditions of unconventional photon blockade due to destructive interference between different transition pathways in weak Kerr nonlinear regime. We also numerically evaluate the second order photon correlation function and plot it against different system parameters to find that the numerical results are in agreement with analytical optimal conditions.

中文翻译：

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基于石墨烯耦合非线性光子晶体纳米束腔的光机械系统中的光机械诱导透明度和光子阻挡

在本文中，我们研究了光机械系统中的可调光诱导透明度和光子阻挡，该系统包括一维光子晶体纳米束腔上方悬浮的单层石墨烯片，单层石墨烯片悬浮在其上方，其中光机械耦合不仅存在于光子之间和纳米束的机械模式，而且光子腔场和石墨烯谐振器之间以及光子腔表现出克尔型非线性。我们为该系统开发了一个哈密顿量，并分析求解了 Hamilton-Langevin 公式中的光子传输率。研究发现，我们可以通过改变纳米束光子-纳米束声子耦合和纳米束光子-石墨烯声子耦合来操纵吸收窗。我们还从理论上和数值上分析了系统的光子统计。我们通过分析确定了由于弱克尔非线性状态下不同跃迁路径之间的相消干涉而导致的非常规光子封锁的最佳条件。我们还对二阶光子相关函数进行了数值评估，并将其针对不同的系统参数进行绘制，发现数值结果与分析的最佳条件一致。