Dynamical origin of near- and below-threshold harmonic generation of Cs in an intense mid-infrared laser field

Near- and below-threshold harmonic generation provides a potential approach to generate vacuum-ultraviolet frequency comb. However, the dynamical origin of in these lower harmonics is less understood and largely unexplored. Here we perform an ab initio quantum study of the near- and below-threshold harmonic generation of caesium (Cs) atoms in an intense 3,600-nm mid-infrared laser field. Combining with a synchrosqueezing transform of the quantum time-frequency spectrum and an extended semiclassical analysis, the roles of multiphoton and multiple rescattering trajectories on the near- and below-threshold harmonic generation processes are clarified. We find that the multiphoton-dominated trajectories only involve the electrons scattered off the higher part of the combined atom-field potential followed by the absorption of many photons in near- and below-threshold regime. Furthermore, only the near-resonant below-threshold harmonic is exclusive to exhibit phase locked features. Our results shed light on the dynamic origin of the near- and below-threshold harmonic generation.This work was partially supported by the Chemical Sciences, Geosciences and Biosciences Division, Office of Basic Energy Sciences, Office of Science, US Department of Energy. P.-C.L. is partially supported by the National Natural Science Foundation of China (grants nos. 11364039 and 11465016), the Natural Science Foundation of Gansu Province (grant no. 1308RJZA195) and the Education Department of Gansu Province (grant no. 2014A-010). We also would like to acknowledge the partial support of the Ministry of Science and Technology and the National Taiwan University (grants nos NTU-104R104021 and NTU-ERP-104R8700-2). We would also like to thank Dr Tak-San Ho and Liang-Yan Hsu (Princeton University) and Dr Dmitry A. Telnov (St Petersburg State University) for helpful discussions and suggestions