Transcript 光和超冷原子气体相互作用中的局域场效应

光和超冷原子气体相互作用中的
局域场效应
董光炯
精密光谱科学与技术国家重点实验室
物理系，华东师范大学
第五届冷原子和量子信息青年物理会议，
兰州大学
2011年8月4日
Theory
Experiment
张卫平
Group leader
董光炯
袁春华
周鲁
钱静
张可烨
Z. Y. Ou
区泽宇
荆杰泰
胡瑞安
陈丽清
Outline
1.前言
2.光和相干原子分子气体相互作用中的局域场效应
3. 非对称衍射和局域场效应引起的光晶格形变
4. 原子在光晶格中的动力学与光晶格产生方式有关
5. 原子晶格的超辐射
6.总结
2005年诺贝尔
物理学奖
Atom optics
Quantum simulation
Quantum information
Ultracold chemistry
Quantum metrology
Lasers play an important role in atom optics
经
典
原
子
光
学
Diffraction
Optical lens
Interferometers
量子原子光学
Optical mirror
Quantum Simulation
Photoassociation
The theory of interaction between light and a
cold atomic gas
Interaction processes between light and a condensate
Dipole potential
Light induced atom-atom interaction
Atom density
Refraction index of the condensate
Local field effect
Light propagation
𝜙2


ˆ1
ˆ2  e
i   i /2 t
t
 2 2
 ˆ  i i /2t '
i   i /2 t
 i   i /2 t '
2
†
()
dt ' e
dt '
0   2m  V2  kd ˆ1 ˆ1 2e
0 ( 2  ˆ1  Gˆ 2 )e
t


d   (  )ˆ1  Gˆ 2 
 2

t
t
 (  )ˆ1  Gˆ 2
2 2

dt '
ˆ2  ei i /2t  (
 V2  kd 2ˆ1†ˆ1 )ˆ2 e  i i /2t ' dt ' 2
(1  ei  i /2 t )  
e  i  i /2 t ' dt '
2m
i (  i / 2)
i (  i / 2)
0
0
 (  )ˆ1  Gˆ 2
ˆ2  2
(1  ei ( i /2)t )
i (  i / 2)
当时间足够长，括号中第二项可忽略，
得到通常的绝热近似结果
在上述近似基础上，采用迭代计算，可以证明余下的误差
~
可见在大失谐的情况下，余项可抛，
绝热近似成立与否与快光/慢光无关！
1
(  i / 2) 2
绝热消去
The light induced interaction between atoms have been emphasized in early
research.
It’s now widely accepeted that back influence of atomic density
modification on the light propagation can be neglected in free space!
So far, two approaches have been applied to enhance the back influence effect.
One approach is to
increase the density
n 
2
Another approach is to
put an atomic gas in a cavity
Quantum optics with quantum gases
APS March Meeting, Dallas, 2011
Strong local field effect on dynamics of a dilute atomic gas
irradiated by two counter-propagating optical fields:
beyond standard optical lattices
Optical lattice: formed by counterpropagating beams.
Splitting, reflecting and diffracting matter waves.
decelerating a supersonic molecular beam
Bose-/Fermi- Hubbard model (Quantum simulation
of strongly correlated many-body systems)
Precision measurement
...
One of the hottest topics on cold atoms is quantum simulation of
strongly correlated many-body systems with optical lattices .
We need precision analysis of current optical lattice
experiments for strictly testing strong-correlation theories.
We can improve precision by improving numerical and analytical
technologies.
But,
good understanding of optical lattices could be one
essential step, which has not been discussed before.
Coherent quantum matter
I  I1  I 2  2 I1 I 2 cos(2kx)
𝐼1 𝐼2 matters!
I1  I 2 or I1  I 2 makes no difference!?
Intensity difference of the two beams matters!
I  I1  I 2  2 I1I 2 cos(2kx)
The concept of Widely accepted optical lattice
cannot be applied!
Interaction processes between light and a condensate
Dipole potential
Light induced atom-atom interaction
Modified atom density
Modified refraction index of the condensate
Local field effect
Light propagation
Intensity
balance
Intensity
imbalance
Theoretic approach
Boundary conditions
+ for results without local field effect.
E1  E3  E (0, t )
E2  E4  E ( L, t )
E1 E3 E (0, t )


x
x
x
E2 E4 E ( L, t )


x
x
x
Boundary condition
E1  E3  E (0, t )
E2  E4  E ( L, t )
E1 E3 E (0, t )


x
x
x
E2 E4 E ( L, t )


x
x
x
Atoms riding a seesaw!
The difference of the calculated intensity
with that of the stand optical lattice
Intensity balance
Intensity imbalance
I st =I1  I 2 +2 I1 I 2 cos(2kx) The intensity of the standard optical lattice
Intensity imbalance
Intensity balance
Atoms riding a seesaw!
Modified coupled mode method
E   A ei ( x ,t )  A e  i ( x ,t )  /  1/4    n( x, t )dxk0 ,   n( x, t )
A
 S A
x
2 i
dn
e

S 
dx 2n
 ( x, t )    n (t )e 2inkL x
n
i  n  J1e  i t  n 1  J 0  n  J 1ei t  n 1
J l    E ( x ', t ) ei 2lkL x ' dx '
2
l  0, 1
When there is an intensity difference of two optical fields
The present manuscript focuses on a feature of
the experiment which
was noted but explained away by Li et al,
namely an asymmetry of the
momentum distribution. The authors attribute
this to the backcoupling
of the atomic motion to the light field. My
view is that if this is
the case, the paper should be a PRL as there
Butterfly effect
are many matter wave
experiments where this is not
taken into account and where
such
assumptions might have to be
re-examined.
Dynamics of an atomic gas
within an optical lattice could depend on
how the lattice is created
Breakdown of superradiance
of an atomic grating with a large number of atom
N  105 I  100 mw / cm 2
N  106 I  100 mw / cm 2
N  106 I  0.1 mw / cm 2
总结：
1.介绍了光和超冷原子分子气体相互作用的理论，引
入了局域场效应。
2.我们解释了非对称衍射,由此发现局域场效应引起光
晶格形变，在精确分析光晶格中原子气体的动力学时
可能是一个不可忽略的因素。
3.当局域场效应不可忽略时，原子气体在光晶格中的
动力学与光晶格的产生方式有关。用镜子反射产生的
光晶格会引起非对称衍射。
4.超冷原子气体的辐射场强与原子气体中原子的数目
有复杂的函数关系，只有在原子数目很小时才有超辐
射现象。
Thanks.
国家自然科学基金
科技部973“量子调控”
精密光谱科学技术国家重点实验室
上海市科委