Transcript Observation of critical correlation across superfluid Lambda

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
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
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
 Coherent amplification of a weak signal
 Coherent manipulate quantum states
BEC in space ;
Science328,1540(2010)
Vacuum fluctuation:
PRL104,195303(2010)
BEC : Heisenberg uncertainty limit
Nature 464 ,1165(2010); 1170(2010)
3
Typical cooperative scattering process
A cigar-shaped BEC + GHz off-resonant pump laser +
Time of flight
(Science 285,571(1999); Science 300,475(2003))
4
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).
5
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)；
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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).
7
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).
8
Scattering Gain from an array of condensates
Superradiant gain and direction of coherent radiant
850nm
Xu Xu, Xiaoji Zhou *, and Xuzong Chen, Phys. Rev. A 79,033605 (2009);
9
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)
10
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).
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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

2
2
i
 ( p, t )  

(
p
,
t
)

U
co
s
(kz ) ( p, t )
0
2
t
2M z
 ( p, t )  e
iU0cos2 ( kz ) t /
i
 ( p,0)  e J n ( ) ( p  2n k , 0)
  U0t / 2
Projection theory in the Bloch band
(a)

U0
1
(b)
 f1
 fs
s
2
 s 1
absorption
imaging
RF Cooling in MT
(c )
Lattice sequence
MT off, BEC released
BEC achieved
•
•
•
Raman-Nath regime
High intensity and short
pulse
Bragg regime
low intensity and long pulse
Tunneling regime
(d )
8 k
6 k
4 k
2 k
0 k

2 k
| (t )   cn , q (m0 )e
n 0
4 k
 iEn ,q t /
6 k
8 k
| n, q

b(m0 , m, 1 )   cn,q (m0 )cn,q (m)e
 iEn ,q1 /
n 0
( s 1)
m
P


s 1
m1 , m2 , , ms
 b( m
i 1
i 1
s
, mi , i ) e
 iE ( mi ) fi /
2
i 1
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2.1 Design Atomic interferometry momentum states
Wei Xiong, Xuguang Yue, Zhongkai Wang, , Xiaoji Zhou*, X.Z Chen, Phys. Rev. A 84, 043616 (2011)
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2.2 Rapid nonadiabatic loading in an optical lattice
adiabatic loading: 40ms
non-adiabatic loading: 40us, loss 10-3
X.X. Liu, Xiaoji Zhou*, W. Xiong, T. Vogt, and Xuzong Chen, Phys. Rev. A 83,063402 (2011)
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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
第二激发态（d 带）
第一激发态（p带 ）
基态
四级线圈
驻波脉冲
驻波脉冲
Ioffe线圈
x
四级线圈
y
z
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。
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
QUIC阱
τ
驻波脉冲
28ms
探测光
QUIC阱
驻波脉冲
28ms
探测光
动量空间的凝聚+质心运动+不对称的脉冲驻波光
阱内脉冲
Pin=38mW,
Pr=31mW
Pin=38mW,
Pr=9mW
Pin=38mW,
Pr=2.3mW
阱外脉冲
Pin=38mW,
Pr=31mW
Pin=38mW,
Pr=9mW
Pin=38mW,
Pr=2.3mW
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
p  0.05 k
高斯波包
p  0.08 k
GP方程，N0=1E5
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
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
38
Revelation of critical phase transition
f r  1  Ab / AT
area under the broad peak; the total area in the bi-modal
structure
39
The fraction of the filtered atoms as temperature
Wei Xiong, Xiaoji Zhou*, Xuguang Yue, Xuzong Chen, Biao Wu, Hongwei Xiong*, submitted
40
The results based on the data fitting
fr 
a'
0
0

b
'

c
'
(
T
/
T

T
/
T
C
C
C )
(TC / TC 0  T / TC 0 ) '
1) Critical exponents:
fr 
a
b
(T / TC 0  TC / TC 0 )
ν’ = 0.70±0.08, ν =0 .70±0.11
universality XY Model: 0.67
2) Amplitude ratio:
a / a '  0.59  0.12
field theory in 3D: 0.50;
ǫ-expansion method: 0.33
3) Critical temperature:
TC / TC 0  0.92  0.01
interaction correction:0.05;
finite-size correction:0.03
41
Outline
1
Background
2
Interaction between a BEC and standing wave pulses
3
Observation of critical correlation
4
Discussion and Summary
42
Discussion: How about more pulses?
Four pluses– collisions between different momentum

tf1



td
tf 2
U 0  35ER
  6 s, t f 1  t f 2  57 s
td 的改变以 TT  79 s 为一个step
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。
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
45
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 ………
46
忠心感谢很多同行对我的帮助和支持。
谢谢大家！