Hartmann Richard, Strunz Walter T
Institut für Theoretische Physik, Technische Universität Dresden, Dresden, D-01062, Germany.
J Phys Chem A. 2021 Aug 19;125(32):7066-7079. doi: 10.1021/acs.jpca.1c03339. Epub 2021 Aug 5.
The spectral properties of a quantum system are essential when probing theoretical predictions against experimental data. For an open quantum system strongly interacting with its environment, spectral features are challenging to calculate. Here we demonstrate that the stochastic Hierarchy of Pure States (HOPS) approach is well suited to calculate the response of an to a, possibly strong, coherent probe driving. For weak driving, where Kubo's linear response theory is applicable, it turns out that the HOPS method is highly efficient since fluctuations inherent to the stochastic dynamics cancel for the response function and, thus, allow us to obtain the susceptibility easily. Our results are in agreement with experimental data for a strongly damped spin system showing that the transition from oscillatory to overdamped motion is also reflected by the transmission spectrum. As a further application we demonstrate that the susceptibility, quantifying the amplitude of the response, as a function of temperature exhibits a maximum which is the hallmark of stochastic resonance. Beyond the linear regime, the exact open system dynamics shows the asymptotic Floquet state. We use the topic of probe driving and response to present the HOPS approach in a novel and self-contained way. This includes the importance sampling scheme which yields the nonlinear HOPS as well as the stochastic treatment of a thermal initial environmental state within the zero temperature formalism. Special attention is given to the exponential representation of the algebraic Ohmic bath correlation function and the truncation condition for the hierarchy.
在将理论预测与实验数据进行对比时，量子系统的光谱特性至关重要。对于一个与其环境强烈相互作用的开放量子系统，光谱特征的计算颇具挑战性。在此，我们证明随机纯态层级（HOPS）方法非常适合计算一个量子系统对一个可能很强的相干探测驱动的响应。对于弱驱动情况，即久保线性响应理论适用时，结果表明HOPS方法效率极高，因为随机动力学固有的涨落在响应函数中相互抵消，从而使我们能够轻松获得磁化率。我们的结果与一个强阻尼自旋系统的实验数据相符，表明从振荡运动到过阻尼运动的转变也反映在透射光谱中。作为进一步的应用，我们证明，作为温度函数的、量化响应幅度的磁化率呈现出一个最大值，这是随机共振的标志。在线性区域之外，精确的开放系统动力学呈现出渐近弗洛凯态。我们利用探测驱动和响应这一主题，以一种新颖且自成体系的方式介绍HOPS方法。这包括产生非线性HOPS的重要性抽样方案，以及在零温度形式体系内热初始环境态的随机处理。特别关注代数欧姆浴关联函数的指数表示以及层级的截断条件。
