Université Paris-Sud, Institut des Sciences Moléculaires d'Orsay, ISMO, CNRS, F-91405 Orsay, France.
J Chem Phys. 2013 Jan 14;138(2):024108. doi: 10.1063/1.4774056.
We introduce a non-Hermitian approximation of Bloch optical equations. This approximation provides a complete description of the excitation, relaxation, and decoherence dynamics of ensembles of coupled quantum systems in weak laser fields, taking into account collective effects and dephasing. In the proposed method, one propagates the wave function of the system instead of a complete density matrix. Relaxation and dephasing are taken into account via automatically adjusted time-dependent gain and decay rates. As an application, we compute the numerical wave packet solution of a time-dependent non-Hermitian Schrödinger equation describing the interaction of electromagnetic radiation with a quantum nano-structure, and compare the calculated transmission, reflection, and absorption spectra with those obtained from the numerical solution of the Liouville-von Neumann equation. It is shown that the proposed wave packet scheme is significantly faster than the propagation of the full density matrix while maintaining small error. We provide the key ingredients for easy-to-use implementation of the proposed scheme and identify the limits and error scaling of this approximation.
我们引入了 Bloch 光学方程的非厄米近似。该近似考虑了集体效应和退相位，提供了弱激光场中耦合量子系统集合的激发、弛豫和退相干动力学的完整描述。在提出的方法中，传播的是系统的波函数而不是完整的密度矩阵。通过自动调整的时变增益和衰减率来考虑弛豫和退相位。作为应用，我们计算了描述电磁辐射与量子纳米结构相互作用的时变非厄米薛定谔方程的数值波包解，并将计算出的透射、反射和吸收谱与从刘维尔-冯·诺依曼方程的数值解获得的谱进行了比较。结果表明，与传播完整密度矩阵相比，所提出的波包方案速度显著提高，同时保持较小的误差。我们提供了易于实现所提出方案的关键要素，并确定了该近似的限制和误差缩放。
