We describe a generalized algorithm for evaluating the steady-state solution of the density matrix equation of motion, for the pump-probe scheme, when two fields oscillating at different frequencies couple the same set of atomic transitions involving an arbitrary number of energy levels, to an arbitrary order of the harmonics of the pump-probe frequency difference. We developed a numerical approach and a symbolic approach for this algorithm. We have verified that both approaches yield the same result for all cases studied, but require different computation time. The results are further validated by comparing them with the analytical solution of a two-level system to first order. We have also used both models to produce results up to the third order in the pump-probe frequency difference, for two-, three- and four-level systems. In addition, we have used this model to determine accurately, for the first time, the gain profile for a self-pumped Raman laser, for a system involving 16 Zeeman sublevels in the D1 manifold of 87Rb atoms. We have also used this model to determine the behavior of a single-pumped superluminal laser. In many situations involving the applications of multiple laser fields to atoms with many energy levels, one often makes the approximation that each field couples only one transition, because of the difficulty encountered in accounting for the effect of another field coupling the same transition but with a large detuning. The use of the algorithm presented here would eliminate the need for making such approximations, thus improving the accuracy of numerical calculations for such schemes.
Calculations of Nonlinear Wave-Packet Interferometry Signals in the Pump-Probe Limit as Tests for Vibrational Control over Electronic Excitation Transfer
Single-photon-level sub-Doppler pump-probe spectroscopy of rubidium
我们提出并证明了铷吸收的泵浦探测光谱，它揭示了$^{5}$ S $_{1/2} \leftrightarrow$ $^{5}$ P $_{3/2}$（D2）跃迁的亚多普勒超精细结构。反向传播的泵浦和探测激光器的频率是独立可调的，探测器工作在单光子水平。扫描激光频率时测得的二维光谱显示出荧光、多普勒展宽吸收下降和亚多普勒特征。泵浦和探测激光器之间的失谐允许补偿室温蒸气中所有原子速度的多普勒频移，这意味着我们观察到光束中所有原子的亚多普勒特征。我们详细介绍了一个理论模型的系统，其中包括荧光，饱和效应和光泵，并与测量光谱进行比较，发现平均绝对百分比误差为4.17%。在未来，这种技术可以帮助激光器的频率稳定，单光子探测器可以被单光子源取代。
Addressing intramolecular vibrational redistribution in a single molecule through pump and probe surface-enhanced vibrational spectroscopy
Centro de Física de Materiales (CFM-MPC), CSIC-EHU（材料物理中心）；Donostia International Physics Center (DIPC)（多诺西亚国际物理中心）；Department of Electricity and Electronics, FCT-ZTF, UPV-EHU（巴斯克国立大学电气与电子工程系）；Department of Polymers and Advanced Materials, Faculty of Chemistry, The University of the Basque Country, UPV/EHU（巴斯克国立大学化学学院高分子与先进材料系）；IKERBASQUE, Basque Foundation for Science（伊克尔巴斯基克科学基金会）
