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Chin. Phys. B, 2020, Vol. 29(2): 023204    DOI: 10.1088/1674-1056/ab610c

Comparative study on atomic ionization in bicircular laser fields by length and velocity gauges S-matrix theory

Hong Xia(夏宏)1, Xin-Yan Jia(贾欣燕)1, Xiao-Lei Hao(郝小雷)2, Li Guo(郭丽)3, Dai-He Fan(樊代和)1, Gen-Bai Chu(储根柏)4, Jing Chen(陈京)5,6
1 School of Physical Science and Technology, Southwest Jiaotong University, Chengdu 610031, China;
2 Institute of Theoretical Physics and Department of Physics, Shanxi University, Taiyuan 030006, China;
3 State Key Laboratory for Quantum Optics and Center for Cold Atom Physics, Shanghai Institute of Optics and Fine Mechanics, Chinese Academy of Sciences, Shanghai 201800, China;
4 Science and Technology on Plasma Physics Laboratory, Laser Fusion Research Center, China Academy of Engineering Physics, Mianyang 621900, China;
5 HEDPS, Center for Applied Physics and Technology, Peking University, Beijing 100871, China;
6 Institute of Applied Physics and Computational Mathematics, Beijing 100088, China
Abstract  Ionization of atoms in counter-rotating and co-rotating bicircular laser fields is studied using the S-matrix theory in both length and velocity gauges. We show that for both the bicircular fields, ionization rates are enhanced when the two circularly polarized lights have comparable intensities. In addition, the curves of ionization rate versus the field amplitude ratio of the two colors for counter-rotating and co-rotating fields coincide with each other in the length gauge case at the total laser intensity 5×1014 W/cm2, which agrees with the experimental observation. Moreover, the degree of the coincidence between the ionization rate curves of the two bicircular fields decreases with the increasing field amplitude ratio and decreasing total laser intensity. With the help of the ADK theory, the above characteristics of the ionization rate curves can be well interpreted, which is related to the transition from the tunneling to multiphoton ionization mechanism.
Keywords:  above-threshold ionization (ATI)      bicircular laser fields      length gauge      velocity gauge      S-matrix theory  
Received:  09 November 2019      Revised:  09 December 2019      Accepted manuscript online: 
PACS:  32.80.Rm (Multiphoton ionization and excitation to highly excited states)  
  42.50.Hz (Strong-field excitation of optical transitions in quantum systems; multiphoton processes; dynamic Stark shift)  
Fund: Project supported by the Key Laboratory Project of Computational Physics of National Defense Science and Technology of China (Grant No. 6142A05180401), the National Key Program for S&T Research and Development of China (Grant Nos. 2019YFA0307700 and 2016YFA0401100), and the National Natural Science Foundation of China (Grant Nos. 11847307, 11425414, 11504215, 11774361, and 11874246).
Corresponding Authors:  Xin-Yan Jia, Jing Chen     E-mail:;

Cite this article: 

Hong Xia(夏宏), Xin-Yan Jia(贾欣燕), Xiao-Lei Hao(郝小雷), Li Guo(郭丽), Dai-He Fan(樊代和), Gen-Bai Chu(储根柏), Jing Chen(陈京) Comparative study on atomic ionization in bicircular laser fields by length and velocity gauges S-matrix theory 2020 Chin. Phys. B 29 023204

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