论文标题
部分可观测时空混沌系统的无模型预测
Quadratic Zeeman Spectral Diffusion of Thulium Ion Population in a Yttrium Gallium Garnet Crystal
论文作者
论文摘要
储层计算是预测湍流的有力工具,其简单的架构具有处理大型系统的计算效率。然而,其实现通常需要完整的状态向量测量和系统非线性知识。我们使用非线性投影函数将系统测量扩展到高维空间,然后将其输入到储层中以获得预测。我们展示了这种储层计算网络在时空混沌系统上的应用,该系统模拟了湍流的若干特征。我们表明,使用径向基函数作为非线性投影器,即使只有部分观测并且不知道控制方程,也能稳健地捕捉复杂的系统非线性。最后,我们表明,当测量稀疏、不完整且带有噪声,甚至控制方程变得不准确时,我们的网络仍然可以产生相当准确的预测,从而为实际湍流系统的无模型预测铺平了道路。
The creation of well understood structures using spectral hole burning is an important task in the use of technologies based on rare earth ion doped crystals. We apply a series of different techniques to model and improve the frequency dependent population change in the atomic level structure of Thulium Yttrium Gallium Garnet (Tm:YGG). In particular we demonstrate that at zero applied magnetic field, numerical solutions to frequency dependent three-level rate equations show good agreement with spectral hole burning results. This allows predicting spectral structures given a specific hole burning sequence, the underpinning spectroscopic material properties, and the relevant laser parameters. This enables us to largely eliminate power dependent hole broadening through the use of adiabatic hole-burning pulses. Though this system of rate equations shows good agreement at zero field, the addition of a magnetic field results in unexpected spectral diffusion proportional to the induced Tm ion magnetic dipole moment and average magnetic field strength, which, through the quadratic Zeeman effect, dominates the optical spectrum over long time scales. Our results allow optimization of the preparation process for spectral structures in a large variety of rare earth ion doped materials for quantum memories and other applications.