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

张卫平Group leader

Z. Y. Ou

董光炯 周鲁 荆杰泰 陈丽清

袁春华 钱静 张可烨

Theory Experiment

胡瑞安

区泽宇

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

Outline

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

Diffraction Optical lens Optical mirror

Interferometers

量子原子光学

经典原子光学

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

Refraction index of the condensate

Light propagation

Atom density

Local field effect

2 2

/2 /2 ' /2 /2 '2 † ( )2 2 1 1 2 1 2

0 0

ˆ ˆ ˆˆ ˆ ˆ' ( ) '2 2

t ti i t i i t i i t i i te V kd e dt e G e dt

m

( )1 2

( )2 2 1 2

/2 /2 ' /2 /2 '2 †2 2 1 1 2

0 0

ˆˆ2ˆˆ

'2ˆ ˆˆ ˆ( ) ' (1 ) '2 ( / 2) ( / 2)

t ti i t i i t i i t i i t

d GG

dte V kd e dt e e dtm i i i i

( )1 2

( /2)2

ˆˆ2ˆ (1 )

( / 2)i i t

Ge

i i

在上述近似基础上，采用迭代计算，可以证明余下的误差 2

1~( / 2)i

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

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！

1̂

�̂�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!

2n

So far, two approaches have been applied to enhance the back influence effect.

One approach is to increase the density

Another approach is to put an atomic gas in a cavity

Quantum optics with quantum gases

Strong local field effect on dynamics of a dilute atomic gas irradiated by two counter-propagating optical fields:

beyond standard optical lattices

APS March Meeting, Dallas, 2011

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.

good understanding of optical lattices could be one essential step, which has not been discussed before.

We can improve precision by improving numerical and analytical technologies. But,

1 2 1 22 cos(2 )I I I I I kx

1 2 1 2 or makes no difference!?I I I I

Coherent quantum matter

matters!

Intensity difference of the two beams matters!1 2 1 22 cos(2 )I I I I I kx 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 refraction index of the condensate

Light propagation

Modified atom density

Local field effect

1 3

31

(0, )

(0, )

E E E t

EE E tx x x

2 4

2 4

( , )

( , )

E E E L t

E E E L tx x x

Boundary conditions+ for results without local field effect.

Theoretic approach

Intensity balance

Intensity imbalance

1 3

31

(0, )

(0, )

E E E t

EE E tx x x

2 4

2 4

( , )

( , )

E E E L t

E E E L tx x x

Boundary condition

Atoms riding a seesaw!

Intensity balance Intensity imbalance

1 2 1 2= +2 cos(2 ) The intensity of the standard optical latticestI I I I I kx

The difference of the calculated intensity with that of the stand optical lattice

Intensity balance

Intensity imbalance

Atoms riding a seesaw!

( , ) ( , ) 1/4/i x t i x tE A e A e

A S Ax

2

2

idn eSdx n

Modified coupled mode method

0( , ) , ( , )n x t dxk n x t

When there is an intensity difference of two optical fields

2( , ) ( ) Link xn

n

x t t e

1 1 0 1 1i t i t

n n n ni J e J J e

2 2 '( ', ) ' 0, 1Li lk xlJ E x t e dx l

Butterfly effect

The present manuscript focuses on a feature of the experiment whichwas noted but explained away by Li et al, namely an asymmetry of themomentum distribution. The authors attribute this to the backcouplingof the atomic motion to the light field. My view is that if this is

the case, the paper should be a PRL as there are many matter waveexperiments where this is not taken into account and where suchassumptions 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

5 210 100 mw / cmN I

6 210 100 mw / cmN I

6 210 0.1 mw / cmN I

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