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

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 Gases by Pulsed Standing Wave

Outline

1 Background

2 Interaction between a BEC and standing wave pulses

3 Observation of critical correlation

4 Discussion and Summary

2

Motivation of coherent amplification--- precise measurement

3

BEC : Heisenberg uncertainty limitNature 464 ,1165(2010); 1170(2010)

BEC in space ; Science328,1540(2010)

Vacuum fluctuation: PRL104,195303(2010)

Coherent amplification of a weak signal

Coherent manipulate quantum states

Typical cooperative scattering process

4

A cigar-shaped BEC + GHz off-resonant pump laser + Time of flight

(Science 285,571(1999); Science 300,475(2003))

Matter wave Grating and Spatial distribution

5

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. A 83, 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)；

Several pumping frequencies Mechanism for Resonant Superradiant Scattering

7

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).

Relative phase of pump beams

8Xiaoji Zhou* , F. Yang, X.G. Yue, T. Vogt, Xuzong Chen, Phys. Rev. A 81, 013615 (2010).

Duration equals to periods, usual models do not predict. The light relative initial phase is imprinted into two matter wave gratings.

Scattering Gain from an array of condensates

9

780nm

850nm

Xu Xu, Xiaoji Zhou *, and Xuzong Chen, Phys. Rev. A 79,033605 (2009);

Superradiant gain and direction of coherent radiant

Competition between superradiance and wave amplification

10

T. Vogt, Bo Lu, X. Liu, Xu Xu, Xiaoji Zhou*, and Xuzong Chen, Phys. Rev. A 83 053603 (2011)

Cooperative scattering measurement of coherence Effects of the interaction between atoms on band gap

11

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).

Outline

1 Background

2 Interaction between a BEC and standing wave pulses

3 Observation of critical correlation

4 Discussion and Summary

12

Manipulation of BEC by Standing Wave Pulses

13

Beyond Raman–Nath regime

• High intensity and short pulse• the momentum representation

2 22

02( , ) ( , ) co ((

2s ) , )i kzp t p t U p t

t M z

20 ( ) /( , ) ( ,0) ( 2 0) , )(kiU cos

nt izp t e p e p nJ k

0 / 2U t

Projection theory in the Bloch band

15

• Raman-Nath regime

High intensity and short pulse

• Bragg regime

low intensity and long pulse• Tunneling regime

1 21f s fs1s

( )a

( )b

( )c RF Cooling in MT

BEC achieved

Lattice sequence

MT off, BEC released

absorptionimaging

( )d

2 k 0 k 2 k 4 k8 k 6 k 4 k 6 k 8 k

( )

1 2

21/( 1)

, , , 11 1

( , , )mi

fi

s

s siEs

m m m m i i ii i

P b m m e

, /

, 00

| ( ) ( ) | ,n qiE t

n qn

t c m e n q

, 1 /

0 1 , 0 ,0

( , , ) ( ) ( ) n qiE

n q n qn

b m m c m c m e

0U

2.1 Design Atomic interferometry momentum states

16

Wei Xiong, Xuguang Yue, Zhongkai Wang, , Xiaoji Zhou*, X.Z Chen, Phys. Rev. A 84, 043616 (2011)

17

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)

2.2 Rapid nonadiabatic loading in an optical lattice

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

基态

第一激发态（ p 带 ）

第二激发态（ d 带）

四级线圈

四级线圈

Ioffe 线圈

驻波脉冲

x

zy

驻波脉冲

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。

入射光功率 Pin

反射光功率 Pr

四级线圈

四级线圈

Ioffe 线圈

探测光

Z

X

Y

衰减片

反射镜

2.3 Effects of the velocity of condensate

动量空间的凝聚 + 质心运动

28ms

驻波脉冲

QUIC 阱

探测光

τ

28ms

驻波脉冲

QUIC 阱

探测光

动量空间的凝聚 + 质心运动 + 不对称的脉冲驻波光

Pin=38mW, Pr=9mW

Pin=38mW, Pr=31mW

Pin=38mW, Pr=2.3mW

阱内脉冲

Pin=38mW, Pr=9mW

Pin=38mW, Pr=31mW

Pin=38mW, Pr=2.3mW

阱外脉冲

2.4 Two standing wave pulses and interference

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

理论曲线

单色平面波

高斯波包

高斯波包

GP 方程， N0=1E50.05p k

0.08p k

Temporal Talbot-Lau Interferometer(TLI)

34

Outline

1 Background

2 Interaction between a BEC and standing wave pulses

3 Observation of critical correlation

4 Discussion and Summary

36

一个基本的物理问题：物态以及物态之间的相变

Critical correlation Transition

38

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

Revelation of critical phase transition

39

1 /r Tbf A A area under the broad peak; the total area in the bi-modal structure

The fraction of the filtered atoms as temperature

40 Wei Xiong, Xiaoji Zhou*, Xuguang Yue, Xuzong Chen, Biao Wu, Hongwei Xiong*, submitted

The results based on the data fitting

41

1) 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

0 0( / / )rC C CT

fT T

a

Tb

0 00 0 '

'' ( / /

( / /' )

) C C CC C C

r

af b T T T T

T T T Tc

0 0.92 0 1/ .0C CT T

0.59 .1/ 0' 2a a

Outline

1 Background

2 Interaction between a BEC and standing wave pulses

3 Observation of critical correlation

4 Discussion and Summary

42

1 26 , 57f fs t t s

dt

1ft 2ft0 35 RU E

不打后两个脉冲，前面两个脉冲的效果为：

79 stepd T st T 的改变以 为一个

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。

Discussion: How about more pulses? Four pluses– collisions between different momentum

Summary

45

Observation of Critical Correlation Across Superfluid

Lambda Transition in an Ultra-cold Bose Gas

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.

Acknowledgement

46

Collaborator

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 ………

Hongwei Xiong, Biao Wu

Hui Zhai, Guangjiong Dong

Wei Zhang, Lan Yin

谢谢大家！

忠心感谢很多同行对我的帮助和支持。