1. Rosen-Zener Tunneling and Rosen- Zener Ramsey Interferometer Li-Bin Fu ( 傅立斌 ) Institute of applied physics and computational mathematics, Beijing Condensed matter physics of cold atoms KITPC Beijing, Sep 22 2009

2. Collaborators Beijing institute of applied physics and computational Mathematics Prof. Jie Liu DiFa Ye Sheng-Chang Li East China Normal University Prof. Weiping Zhang Australian National University Dr. Chaohong Lee

3. Outline Nonlinear Rosen-Zener tunneling Rosen-Zener interference with Double-Well BECs Ramsey Interferometer via nonlinear RZ process

4. S-G Rosen-Zener Tunneling Detector B=B(z) is a spatial dependent transversl field

5. The Model of Rosen-Zener tunneling For γ=0, the problem is solvable. The transition probability is defined as the population of (0,1)

6. Nonlinear Rosen-Zener Model Two components BECs

7. Transition Probability of adiabatic case (T>>1) for γ=0 For the linear case, we can obtain the transition probability (see fig.a) For weak nonlinear case, we find the interesting case that the transition probablity is rectangular oscillation. (seeing fig. b and c) For strong nonliear case, transition probability is zero in adiabatic regime.

8. Eigen Levels Nonliearity leads to extra egien levels. The configurations of new levels play important role in adiabatic process.

9. The bifurcation of fixed points gives rise to rectangular oscillation |b| 2 θ=θa-θbθ=θa-θb

10. The period of rectangular oscillation The small oscillation around fixed piont The phase at the bifurcation point determine the evoluton direction Then we obtain the period as

11. Analytic results for sudden limits With the transformation One gets

12. RZT for nondegenerated case γ≠0

13. Nonlinear Rosen-Zener Rosen-Zener interference with Double-Well BECs Ramsey Interferometer via nonlinear RZ process

14. Rosen-Zener interference with Double-Well BECs

15. Coherent Transition of atoms in Double Well

16. Simple model

18. Results of the Simple model Phase locking effect plays the key role of the coherent tran- sition.

19. Interference Pattern Phase sensitive around the first excited state.

20. Nonlinear Rosen-Zener Rosen-Zener interference with Double-Well BECs Ramsey Interferometer via nonlinear RZ process

22. Various Interference Pattern

23. Theoretical Prediction of frequencies of Fringes The fringers frequencies determined by the accumulated phase during the second stage, which is where s is the population difference of the first RZ process, then the frequencies are

24. Theoretical prediction of frequencies of Fringes The transition probability of the first stage Then the frequencies of Ramsey fringes For sudden limit For adiabatic limit The population difference of the first stage The frequncies of Ramsey fringes

25. Theoretical prediction of frequencies of Fringes The transition probability of the first stage Then the frequencies of Ramsey fringes For sudden limit For adiabatic limit The population difference of the first stage The frequncies of Ramsey fringes

26. Frequencies of Fringes Sudden limit Adiabatic limit General case

27. The oscillation near c=0 is due to breakdown of adiabatic evolution The oscillation near c=0 Adiabatic condition

28. Summary Nonlinear Rosen-Zener Tunneling The nonlinearity could dramatically affect the transition dynamics leading to many interesting phenomena Realization RZ interferences in Double-Well BECs Ramsy interference with Rosen-Zener Process The frequency of Ramsey pattern is dependent both on nonliearity and energy bias. 1.DiFa Ye, Li-Bin Fu, and Jie Liu, Phys. Rev. A 77 013402 (2008) 2.Li-Bin Fu, Di-Fa Ye, Chaohong Lee, Weiping Zhang, Jie Liu, Phys. Rev. A 80 13619 (2009) 3.Sheng-Chang Li, Li-Bin Fu, Wen-Shan Duan, Jie Liu, Phys. Rev. A 78 063621 (2008)