A theoretical study on achieving the generalized binomial states with second harmonic generation processes

  • Yuzhe Zhang
  • Ziyang Ma
  • Li Li
  • Chuanxiang Sheng
  • Yishi Han


In this paper, the generalized binomial states (GBSs) are theoretical presented with second-harmonic generation (SHG) processes by utilizing the Schwinger–Bose operation realization. The GBSs are theoretically demonstrate by a combination of two fundamental-frequency light fields, which are incident upon a second-order nonlinear crystal under the type-II SHG configuration. One incident field is in the number state \(\left| M \right\rangle\), and the other is in coherent state of sufficiently strong intensity to be treated as a classical field. It is found that GBSs will eventually convert to the coherent states when the incident number-state field possess sufficiently large number of photons. The presented study provides an alternative and theoretically intriguing scheme to achieve the important GBSs.


Binomial state Coherent state Interaction picture Second-harmonic generation 



The authors would like to sincerely thank Mr. Liu Shilong from the University of Science and Technology of China for inspiring discussions. This work is supported by the High-Level Innovation and Entrepreneurship Talent Introduction Plan and the Educational Innovation Team Introduction Plan of Jiangsu Province, China, the National Natural Science Foundation of China (No. 61627802), and the Fundamental Research Funds for the Central Universities (No. 30916011103). This work is also supported by the National Science Foundation of China (No. 61471130), Science and Technology Planning Project of Guangdong Province, China (No. 2016B090918060) and Science and Technology Planning Project of Guangzhou City, China (No. 201604016079).


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© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  • Yuzhe Zhang
    • 1
  • Ziyang Ma
    • 2
  • Li Li
    • 1
    • 2
  • Chuanxiang Sheng
    • 1
  • Yishi Han
    • 3
  1. 1.College of Electronic and Optical EngineeringNanjing University of Science and TechnologyNanjingChina
  2. 2.Advanced Launching Cooperation and Innovation CenterNanjing University of Science and TechnologyNanjingChina
  3. 3.School of Information EngineeringGuangdong University of TechnologyGuangzhouChina

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