中国物理B ›› 2009, Vol. 18 ›› Issue (10): 4110-4116.doi: 10.1088/1674-1056/18/10/008

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Effects of periodic modulation on the nonlinear Landau--Zener tunneling

吴利华, 段文山   

  1. College of Physics and Electronic Engineering, Northwest Normal University, Lanzhou 730070, China
  • 收稿日期:2008-11-18 修回日期:2009-04-02 出版日期:2009-10-20 发布日期:2009-10-20
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant No 10875098). The Natural Science Foundation of Northwest Normal University (Grant No NWNU-KJCXGC 03-48,03-17).

Effects of periodic modulation on the nonlinear Landau--Zener tunneling

Wu Li-Hua(吴利华) and Duan Wen-Shan(段文山)†   

  1. College of Physics and Electronic Engineering, Northwest Normal University, Lanzhou 730070, China
  • Received:2008-11-18 Revised:2009-04-02 Online:2009-10-20 Published:2009-10-20
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant No 10875098). The Natural Science Foundation of Northwest Normal University (Grant No NWNU-KJCXGC 03-48,03-17).

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摘要： We study the Landau-Zener tunneling of a nonlinear two-level system by applying a periodic modulation on its energy bias. We find that the two levels are splitting at the zero points of the zero order Bessel function for high-frequency modulation. Moreover, we obtain the effective coupling constant between two levels at the zero points of the zero order Bessel function by calculating the final tunneling probability at these points. It seems that the effective coupling constant can be regarded as the approximation of the higher order Bessel function at these points. For the low-frequency modulation, we find that the final tunneling probability is a function of the interaction strength. For the weak inter-level coupling case, we find that the final tunneling probability is more disordered as the interaction strength becomes larger.

Abstract: We study the Landau-Zener tunneling of a nonlinear two-level system by applying a periodic modulation on its energy bias. We find that the two levels are splitting at the zero points of the zero order Bessel function for high-frequency modulation. Moreover, we obtain the effective coupling constant between two levels at the zero points of the zero order Bessel function by calculating the final tunneling probability at these points. It seems that the effective coupling constant can be regarded as the approximation of the higher order Bessel function at these points. For the low-frequency modulation, we find that the final tunneling probability is a function of the interaction strength. For the weak inter-level coupling case, we find that the final tunneling probability is more disordered as the interaction strength becomes larger.

Key words: nonlinear two-level system, Landau--Zener tunneling, tunneling probability, periodic modulation

中图分类号:  (Tunneling, traversal time, quantum Zeno dynamics)

  • 03.65.Xp
02.30.Gp (Special functions) 02.50.Cw (Probability theory)