Sala Kamila, Tufarelli Tommaso
Centre for the Mathematics and Theoretical Physics of Quantum Non-Equilibrium Systems, School of Mathematical Sciences, University of Nottingham, University Park, Nottingham, NG7 2RD, United Kingdom.
Sci Rep. 2018 Jun 14;8(1):9157. doi: 10.1038/s41598-018-26739-0.
We compare two approaches for deriving corrections to the "linear model" of cavity optomechanics, in order to describe effects that are beyond first order in the radiation pressure coupling. In the regime where the mechanical frequency is much lower than the cavity one, we compare: (I) a widely used phenomenological Hamiltonian conserving the photon number; (II) a two-mode truncation of C. K. Law's microscopic model, which we take as the "true" system Hamiltonian. While these approaches agree at first order, the latter model does not conserve the photon number, resulting in challenging computations. We find that approach (I) allows for several analytical predictions, and significantly outperforms the linear model in our numerical examples. Yet, we also find that the phenomenological Hamiltonian cannot fully capture all high-order corrections arising from the C. K. Law model.
我们比较了两种用于推导对腔光力学“线性模型”进行修正的方法，以描述辐射压力耦合中超出一阶的效应。在机械频率远低于腔频率的 regime 中，我们比较：（I）一种广泛使用的守恒光子数的唯象哈密顿量；（II）C.K.劳的微观模型的双模截断，我们将其视为“真实”的系统哈密顿量。虽然这些方法在一阶时是一致的，但后一种模型不守恒光子数，导致计算具有挑战性。我们发现方法（I）允许进行几个解析预测，并且在我们的数值示例中明显优于线性模型。然而，我们也发现唯象哈密顿量不能完全捕捉C.K.劳模型产生的所有高阶修正。
