周小计 School of Electronic Engineering and Computer Science Peking University, Beijing

1. 第六届全国冷原子物理和量子信息 青年学者学术讨论会—浙江金华 Manipulation of Ultracold Bose Gasesby Pulsed Standing Wave 周小计 School of Electronic Engineering and Computer Science Peking University, Beijing 北京大学信息科学技术学院

2. Outline • Background • Interaction between a BEC and standing wave pulses • Observation of critical correlation • Discussion and Summary

3. Motivation of coherent amplification--- precise measurement • Coherent amplification of a weak signal • Coherent manipulate quantum states BEC in space ; Science328,1540(2010) BEC : Heisenberg uncertainty limit Nature 464 ,1165(2010); 1170(2010) Vacuum fluctuation: PRL104,195303(2010)

4. Typical cooperative scattering process A cigar-shaped BEC + GHz off-resonant pump laser + Time of flight (Science 285,571(1999); Science 300,475(2003))

5. Matter wave Grating and Spatial distribution intensity; duration; detuning L. Deng, E.W. Hagley, Q. Cao, Xiaorui Wang, Xinyu Luo, R.Q Wang, M. G. L. Payne, Fan Yang, Xiaoji Zhou, X.Z. Chen, and Mingsheng Zhan, Phys. Rev. Lett. 105, 220404 (2010).

6. Cooperative scattering by traveling wave pulses for new parameters : Angle, Frequencies, Phase, Linewidth, Lattice • Bo Lu, Xiaoji Zhou*,T. Vogt, Zhen Fang, Xuzong Chen,Phys. Rev. A83, 033620 (2011) . • X. Liu, Xiaoji Zhou*, Wei Xiong, T. Vogt, and Xuzong Chen, Phys. Rev. A 83, 063402 (2011). • T. Vogt, Bo Lu, X. Liu, Xu Xu, Xiaoji Zhou*, and Xuzong Chen, Phys. Rev. A 83 053603 (2011). • Bo Lu, T. Vogt, X. Liu, Xu Xu, Xiaoji Zhou*, Xuzong Chen, Phys. Rev. A 83, 051608(R) (2011). • Xiaoji Zhou* , F. Yang, X.G. Yue, T. Vogt, Xuzong Chen, Phys. Rev. A 81, 013615 (2010). • Zhen Fang, Rui Guo, Xiaoji Zhou*, Xuzong Chen, Phys. Rev. A 82, 015601 (2010). • L. Deng et al, Phys. Rev. Lett. 105, 220404 (2010). • Xiaoji Zhou*, Phys. Rev. A 80, 023818 (2009)； • Xiaoji Zhou*, Jiageng Fu, Xuzong Chen, Phys. Rev. A 80, 063608 (2009)； • F. Yang, Xiaoji Zhou*, J Li, Y. K. Chen, L. Xia, X. Z. Chen, Phys. Rev. A 78, 043611 (2008)；

7. Several pumping frequencies Mechanism for Resonant Superradiant Scattering Fan Yang, Xiaoji Zhou *, J. Li, Y. Chen, Lin Xia, and X. Z. Chen, Phys. Rev. A 78, 043611 (2008). X.J. Zhou*,J. Fu, X.Z.Chen, Phys. Rev. A 80, 063608 (2009).

8. Relative phase of pump beams • Duration equals to periods, usual models do not predict. • The light relative initial phase is imprinted into two matter wave gratings. Xiaoji Zhou* , F. Yang, X.G. Yue, T. Vogt, Xuzong Chen, Phys. Rev. A 81, 013615 (2010).

9. Scattering Gain from an array of condensates Superradiant gain and direction of coherent radiant 850nm 780nm Xu Xu, Xiaoji Zhou*, and Xuzong Chen, Phys. Rev. A 79,033605 (2009);

10. Competition between superradiance and wave amplification T. Vogt, Bo Lu, X. Liu, Xu Xu, Xiaoji Zhou*, and Xuzong Chen, Phys. Rev. A 83 053603 (2011)

11. Cooperative scattering measurement of coherence Effects of the interaction between atoms on band gap Bo Lu, T. Vogt, X. Liu, Xu Xu, Xiaoji Zhou*, Xuzong Chen, Phys. Rev. A 83, 051608(R) (2011). X. X. Liu, Xiaoji Zhou*, W. Zhang, T. Vogt, Bo Lu, X.G. Yue, X.Z Chen,Phys. Rev. A 83, 063604 (2011).

12. Outline • Background • Interaction between a BEC and standing wave pulses • Observation of critical correlation • Discussion and Summary

13. Manipulation of BEC by Standing Wave Pulses

14. Beyond Raman–Nathregime • High intensity and short pulse • the momentum representation

15. Projection theory in the Bloch band • Raman-Nath regime High intensity and short pulse • Bragg regime low intensity and long pulse • Tunneling regime

16. 2.1 Design Atomic interferometry momentum states Wei Xiong, Xuguang Yue, Zhongkai Wang, , Xiaoji Zhou*, X.Z Chen, Phys. Rev. A 84, 043616 (2011)

17. 2.2 Rapid nonadiabatic loading in an optical lattice non-adiabatic loading: 40us, loss 10-3 adiabatic loading: 40ms X.X. Liu, Xiaoji Zhou*, W. Xiong, T. Vogt, and Xuzong Chen, Phys. Rev. A 83,063402 (2011)

18. 通过设计驻波脉冲序列，可以将原子激发到光晶格第二激发态通过设计驻波脉冲序列，可以将原子激发到光晶格第二激发态 四级线圈 驻波脉冲 第二激发态（d 带） Ioffe线圈 第一激发态（p带） x 基态 四级线圈 y z 驻波脉冲

19. 第二激发态占据大于95%情况下，实验测得0动量态原子占总原子比例。时间单位us。第二激发态占据大于95%情况下，实验测得0动量态原子占总原子比例。时间单位us。

20. 第二激发态与基态各占50%情况下，实验测得0动量态原子占总原子比例。时间单位us。第二激发态与基态各占50%情况下，实验测得0动量态原子占总原子比例。时间单位us。 可以看出，第二激发态与基态各占一半时，0动量态原子震荡比率明显更大。

21. 2.3 Effects of the velocity of condensate 入射光功率Pin Z X 四级线圈 Y Ioffe线圈 衰减片 反射镜 探测光 反射光功率Pr 四级线圈 动量空间的凝聚 + 质心运动

23. QUIC阱 QUIC阱 τ 驻波脉冲 驻波脉冲 28ms 28ms 探测光 探测光

25. 动量空间的凝聚+质心运动+不对称的脉冲驻波光动量空间的凝聚+质心运动+不对称的脉冲驻波光

26. 阱内脉冲 Pin=38mW, Pr=31mW Pin=38mW, Pr=9mW Pin=38mW, Pr=2.3mW

27. 阱外脉冲 Pin=38mW, Pr=31mW Pin=38mW, Pr=9mW Pin=38mW, Pr=2.3mW

29. 2.4 Two standing wave pulses and interference

31. 实验结果 从实验结果可以看到随着脉冲间时间间隔 tf 的变化，在上升沿会出现明显的拐点，而下降沿却不是很明显

32. 理论曲线 单色平面波 高斯波包 高斯波包 GP方程，N0=1E5

34. Temporal Talbot-Lau Interferometer(TLI)

36. Outline • Background • Interaction between a BEC and standing wave pulses • Observation of critical correlation • Discussion and Summary

37. 一个基本的物理问题：物态以及物态之间的相变一个基本的物理问题：物态以及物态之间的相变

38. Critical correlation Transition Textbooks tell us the correlation length diverges near the critical temperature Science315, 1556,(2007): the interference of two released beams with a high-finesse optical cavity

39. Revelation of critical phase transition area under the broad peak; the total area in the bi-modal structure

40. The fraction of the filtered atoms as temperature Wei Xiong, Xiaoji Zhou*, Xuguang Yue, Xuzong Chen, Biao Wu, Hongwei Xiong*, submitted

41. The results based on the data fitting • Critical exponents: ν’ = 0.70±0.08, ν =0 .70±0.11 • universality XY Model: 0.67 • 2) Amplitude ratio: • field theory in 3D: 0.50; ǫ-expansion method:0.33 • 3) Critical temperature: • interaction correction:0.05; finite-size correction:0.03

42. Outline • Background • Interaction between a BEC and standing wave pulses • Observation of critical correlation • Discussion and Summary

43. Discussion: How about more pulses? Four pluses– collisions between different momentum 不打后两个脉冲，前面两个脉冲的效果为： 由于t_d的改变是以一个Talbot时间为单位改变的，因此在第二和第三个脉冲间动能演化的相位为2pi的整数倍。

45. Summary • An efficient coherent control for the momentum states based on a sequence of standing wave pulses are given. • Effects of velocity of condensate and diffraction phases induced temporal asymmetry are discussed. • Observation of Critical Correlation Across Superfluid Lambda Transition in an Ultra-cold Bose Gas

46. Acknowledgement Collaborator Hongwei Xiong, Biao Wu Hui Zhai, Guangjiong Dong Wei Zhang, Lan Yin Helpful discusser Li You, Cheng Chin, Han Pu , Ying Wu , Jie Liu, Su Yi, Baolong Lu, Chaohong Lee, Vincent Liu, Guangjiong Dong, Jing Zhang, Tiancai Zhang, Shougang Zhang, Mingsheng Zhan, Ruquan Wang, Supeng Kou, Shuai Chen, Libing Fu, Junpeng Cao,Weidong Li, Yubo Zhang ………

47. 忠心感谢很多同行对我的帮助和支持。 谢谢大家！