Study on Correlation Length at Lambda Critical Point in an Ultracold Bose Gas

Xuzong Chen () Institute of Quantum Electronics (, Peking University, ChinaJoint Workshop on Bose Einstein Condensation and Ultracold Phenomena September 25-27 2013,Beijing,China

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School of Electronics Engineering and Computer Science, Peking University

Institute of Quantum Electronics

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Research Cold atom and Precision Measurement(Prof. Xuzong Chen, Xiaoji Zhou) Quantum Optics and Quantum Information (Prof. Hong Guo)Optical Clock(Prof. Jingbiao Chen )Ultra Laser(Prof. Zhigang Zhang)Magnetic Resonant Imaging ,(Asso. Prof. Weiming Wang)professors. 5, assoc. professors. 4, Assistant Prof. 3,staff 3, PhD students 34, master students 30

Outline

BackgroundMeasurement of phase transition and correlation between atoms in 1Doptical LatticeMeasurement of critical exponent at Lambda point in quantum gasFuture ultracold atom experiments in space

Cooling Roadmap and Phase TransitionT(K)

Quantum Phase Transitionnormal liquidquantum liquidquantum gasnormal gasT/TcCv/R

Many body systemExist critical temp: TcSuperfluid while T

Evidence (1) of superfluid in quantum gasvortexhelium-4Bose Einstein CondensateScience 292, 476 (2001)

Evidence (2) of superfluid in quantum gasquantum phase transition in optical lattice

1 D2 D3 D

3 DPhase Transition in 3D Optical LatticesuperfluidMott insulator

superfluidMott insulator Quantum Phase Transition M. Greiner et al. Nature 415, p38 (2002)

Outline

BackgroundMeasurement of phase transition and correlation between atoms in 1Doptical LatticeMeasurement of critical exponent at Lambda point in quantum gasFuture ultracold atom experiments in space

Upper MOTLow MOTApparatus for Rb BECThank for Prof. Joerg Schmiedmayer

1D Optical LatticeSuperfluid phase U > J1 DBECPancake BECBose-Hubbard model

Primary phase transition between SF and MI

Lattice Depth: 0, 5.6Er, 11.2Er, 16.9Er, 22.4Er, 28ErFan Yang, Xiaoji Zhou, Juntao Li, Yuankai Chen, Lin Xia, and Xuzong Chen, Phys. Rev. A 78, 043611(2008)

123Correlation vs optical potential in 1D optical lattice 1,21,3Spatial correlation functionxd

(2) Measurement on the Coherence of optical lattice (-1,0)(-1,0)

Superradiation scattering in optical lattice Xu Xu, Xiaoji Zhou, and Xuzong Chen, Phys. Rev. A 79, 033605(2009)Thibault Vogt, Bo Lu, XinXing Liu, Xu Xu, Xiaoji Zhou, and Xuzong Chen, Phys. Rev. A 83, 053603 (2011)

Superradiant scattering in 1D optical latticepure BEC, V=0Er pure Optical Lattice (OL) , V=11Er MWA in Optical Lattice, V=11Er, MWA in Optical Lattice, V=34Er, superfluidMott insulator

Matter wave amplification VS delay timePower=4 mWpulse= 5 sRed Detuning = 1.3 GHz V= 11.44 Er

0 s10 s35 s30 s70 s60 s40 s5 s15 s20 s25 s50 s80 s

Matter wave amplification VS delay timePower=4 mWpulse= 5 sRed Detuning = 1.3 GHz V= 11.44 Er

0 s10 s35 s30 s70 s60 s40 s5 s15 s20 s25 s50 s80 s

1231,2Bo Lu, Thibault Vogt, Xinxing Liu, Xu Xu, Xiaoji Zhou, and Xuzong Chen, Phys. Rev. A 83, 051608(R) (2011)Thibault Vogt, Bo Lu, XinXing Liu, Xu Xu, Xiaoji Zhou, and Xuzong Chen, Phys. Rev. A 83, 053603 (2011)

Scattering light enhanced while matter wave grating in t = 2n/rScattering light cancelled while matter wave grating in t = 2(n+1)/r

Coherence of matter wave grating will be decreased while t increased, so that the visibility will be deceasedtVmax1,12,23,31122331,02,13,2

Correlation decay in Mott insulator casePower=4 mWpulse= 5 sRed Detuning = 1.3 GHz V=36 Er

0 s10 s35 s30 s70 s60 s40 s5 s15 s20 s25 s50 s80 sBo Lu, Thibault Vogt, Xinxing Liu, Xu Xu, Xiaoji Zhou, and Xuzong Chen, Phys. Rev. A 83, 051608(R) (2011)

Outline

BackgroundMeasurement of phase transition and correlation between atoms in 1Doptical LatticeMeasurement of critical exponent at Lambda point in quantum gasFuture ultracold atom experiments in space

Critical behavior around phase transition pointAlexei A. AbrikosovVitaly L. GinzburgAnthony J. Leggett"for pioneering contributions to the theory of superconductors and super fluids"

The correlated length of gas around phase transition point is satisfied:critical temperatureCritical factorKenneth G. Wilson"for his theory for critical phenomena in connection with phase transitions"

Critical exponentsuniversal description on phase transitionthe dimension of the system,the range of the interaction,the spin dimension.Correlation functioncorrelated length

A

The correlated length vs temperature M. Khl, T. Donner, S. Ritter, T. Bourdel, A. ttl, F. Brennecke, and T. Esslinger: Advances in Solid State Physics, 79-88 (2008)Critical exponentphase transition in quantum gascorrelated lengthcorrelated functionCritical exponent

A

A

Measurement of the critical exponent at critical point in quantum gasCorrelation function:Correlated length:

A

Momentum filterTalbot EffectHenry Fox Talbot 1836 Grating 2Grating 1

Matter Wave momentum filterBy means of Talbot-Lau EffectXiong, Wei; Zhou, Xiaoji; Yue, Xuguang; XuzongChen, NEW JOURNAL OF PHYSICSVol.15, 063025 (2013 )

Momentum width compressed by momentum filter

Correlated length:Signal to noise ratio:

Critical behavior of Bose gas

Bimode fitting approachFixed momentum window fitting approach

Outline

BackgroundMeasurement of phase transition and correlation between atoms in 1Doptical LatticeMeasurement of critical exponent at Lambda point in quantum gasFuture ultracold atom experiments in space

Cooling in SpaceSisyphus coolingCooling in spaceT(K)

Technique challenge for cooling in spaceOn the groundCritical temperature for phase transition:groundspaceOperation time is needed103 seconds

Scheme for cooling in spacePhase space distribution functionOptical potential Temperature for the systemTotal energy for the system

Procedure for cooling28000 Rb atomswith temperature of ~7 pK

Procedure for cooling28000 Rb atomswith temperature of ~7 pKUltracold CollisionFeshbach ResonanceMotivation: Increase the collision rate and reduce cooling time

Science ChanmberApparatus for Cs\Rb\K BECThank for Prof. Cheng Chin

Chinese Space station

Core cabin launch in 2018, Science cabin launch in 2020

The rack for cold atom physics

Science chamber for experimentsRb+K

Advantages for cold atom in spaceLow temperature: 10-12 KpK,three order lower than on the earth (nK)Longer observation time (20s) , three order longer than on the earth (20ms)Space uniform, no gravity potential.

Ideal place for quantum gas research space uniform

Research based on Space Cold Atoms Four types of experiments

(1) Quantum StateaQuantum gasbExotic materialcBose-Fermi mixturedPolar molecules;(2) celestial body:eAcoustic black hole Bose explosion(3) Quantum Computation: fTopologic computation(4) Frontier Explorationgtest of quantum measurement theoryhrelation between quantum mechanics and gravityitest of standard model

CAP Publications for Bose Gas 1

Phase Transition and Exotic materials

1Zhang, Huirong; Guo, Qiuyi; Ma, Zhaoyuan; ; XuzongChen, PHYSICAL REVIEW A, Vol. 87, No.4 , 043625 (20132Huirong Zhang, Qiuyi Guo, Zhaoyuan Ma, Xuzong Chen. Physical Review A, 86(5): 053622(1-5) (2012)3Xiong, Wei; Zhou, Xiaoji; Yue, Xuguang;; XuzongChen, NEW JOURNAL OF PHYSICSVol.15, 063025(2013 )

Optical Lattice and Strong Correlation:

4Xinxing Liu, Xiaoji Zhou, Wei Zhang, Thibault Vogt, Bo Lu, Xuguang Yue, and Xuzong Chen, Phys. Rev. A 83, 063604 (2011)5Xinxing Liu, Xiaoji Zhou, Wei Xiong, Thibault Vogt, and Xuzong Chen, Phys. Rev. A 83, 063402 (20116Bo Lu, Thibault Vogt, Xinxing Liu, Xu Xu, Xiaoji Zhou, and Xuzong Chen, Phys. Rev. A 83, 051608(R) (2011)7Thibault Vogt, Bo Lu, XinXing Liu, Xu Xu, Xiaoji Zhou, and Xuzong Chen, Phys. Rev. A 83, 053603 (2011)8Xiaoji Zhou, Xu Xu, Lan Yin, Wuming Liu, and Xuzong ChenOptics Express 18, 15664(2010)9Muzhi Wu, Xiaoji Zhou, Wuming Liu, and Xuzong Chen, Phys. Rev. A 81, 033625(2010)10Xu Xu, Xiaoji Zhou, and Xuzong Chen, Phys. Rev. A 79, 033605(2009)21Xiaofei Zhang, Qin Yang, Jiefang Zhang, Xuzong Chen, and Wuming Liu, Phys. Rev. A 77, 023613(2008)11Guanqiang Li, Libin Fu, Jukui Xue, Xuzong Chen, and Jie Liu, Phys. Rev. A 74, 055601(2006)12Guanfang Wang, Difa Ye, Libin Fu, Xuzong Chen, and Jie Liu, Phys. Rev. A 74, 033414(2006)

CAP Publications for Bose Gas 2

Superradiant Scattering:

13Bo Lu, Xiaoji Zhou, Thibault Vogt, Zhen Fang, and Xuzong Chen Phys. Rev. A 83, 033620 (2011)14L. Deng, E. W. Hagley, Qiang Cao, Xiaorui Wang, Xinyu Luo, Ruquan Wang, M. G. Payne, Fan Yang, Xiaoji Zhou, Xuzong Chen, and Mingsheng Zhan. Phys. Rev. Lett. 105, 220404 (2010)15Xiaoji Zhou, Fan Yang, Xuguang Yue, Thibault Vogt, and Xuzong Chen, Phys. Rev. A 81, 013615 (2010)16Zhen Fang, Rui Guo, Xiaoji Zhou, and Xuzong Chen, Phys. Rev. A 82, 015601(2010)17Xiaoji Zhou, Jiageng Fu, and Xuzong Chen, Phys. Rev. A 80, 063608(2009)18Xiaoji Zhou, Phys. Rev. A 80, 023818(2009)19Rui Guo, Xiaoji Zhou, and Xuzong Chen, Phys. Rev. A 78, 052107(2008)20Fan Yang, Xiaoji Zhou, Juntao Li, Yuankai Chen, Lin Xia, and Xuzong Chen, Phys. Rev. A 78, 043611(2008)21Xuguang; Zhai, Yueyang; Wang, Zhongkai; Xizoji Zhou, XuzongChen, PHYSICAL REVIEW A Vol. 88, No. 1 ,013603 (2013 )22Zhai, Yueyang; Yue, Xuguang; Wu, Yanjiang;; Xizoji Zhou, XuzongChen, PHYSICAL REVIEW AVol. 87,No.6 , 063638( 2013 ) 23Wang, Zhongkai; Niu, Linxiao; Zhang, Peng; ; Xizoji Zhou, XuzongChen, OPTICS EXPRESSVol. 21 No. 12 ,14377-14387 (2013 )

Atom Lasers24Lin Xia, Xu Xu, Rui Guo, Fan Yang, Wei Xiong, Juntao Li, Qianli Ma, Xiaoji Zhou, Hong Guo, and Xuzong Chen, Phys. Rev. A 77, 043622(2008). 25Xiuquan Ma, Lin Xia, Fan Yang, Xiaoji Zhou, Yiqiu Wang, Hong Guo, and Xuzong Chen, Phys. Rev. A 73, 013624 (2006)

CAP group (Cold Atom and Precision Measurement)) http://iqe.pku.edu.cn

Faculty:Xuzong Chen(), Xiaoji Zhou(), Xianghui Qi,Yin Zhang ( Yiqiu Wang (), Donghai Yang ()Zhaoyuan Ma (, Shanghai Institute of Optics and Fine Mechanics,CAS

BEC1Post Doctor: Tilbault Vigot, Ph D students:Cheng Li (, Tian Ran(, Tianwei Zhou()Qiuyu Guo(Master stududents: Longyi Zhang(), Shizhe Li(),Jianbo Zhou(),Bo Fan(), Haitao Xue(), Lu Wang(), Yaozhang Wang()

BEC2:Ph D students: Weixiong (Yueyang Zhai), Xuguang Yue(Zheng Fang ( Zhongkai Wang ()Baoguo Yang(),Master Students: Mingxuan Wen(),Dong Hu(),Lingxiao Niu(),Huajia Zhang ()

Optical Comb: Ph D students: Daiwei Zhou(), Shangyang Dai(),Master students: Liyang Liu(),Xinbo Liu(),

Atomic Clock: Ph D students: Qing Wang(), Master students: Zhenhua Zhang (),Lan Jin(), Qijun Shan(),Pingan Liu()

Collaboration:BEC: Prof. Zhaoyuan Ma(SIOM), Prof. Wuming Liu (IOP), Prof. Baolong Liu(PMIW), Prof. P. Bouyuer( Optical Institute, France)Optical Comb: Dr. Fenglei Hong (NIMJ), Dr. Inaba (NIMJ), Atomic Clock: Dr. Lianshan Gao (203), Mingwei He (4404)

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Theoretical group:Post Doctor: Huirong Zhang(Ph. D students: Xueguang Yue, Qiuyu Guo, Xia Xu (Zheng Fang (Master Students: Muzhi Wu)

Formal students: Shuai Chen(USTC), Lin Yi(Paris Observatory), Lin Xia (JILA), Fan Yang( GE Inc.), Rui Guo (Phillips Inc.), Jie Yuan (Wuxi, Huishan) , Bo Lu Nortinghan Univ.), Xinxin Liu(Rice Univ.), Wei Xiong (Tisnghua Univ.)

Thanks

Thanks

**To achieve the BEC, it needs very low temperature, different cooling methods were invented.*Liquid helium is similar to quantum gas*To find the surperfluid evidence in quantum gas is interesting work for scientists, there are different approach to demonstrate the superfluid in quantum gas. The first one is vortex.*The second one is BEC in optical lattice. there are different types of lattice.

*For three D, *Standing wave laser will form a sine cure potential, while the lattice depth is low, the tuneling is great, the BEC is in the state of superfluid, while the lattice depth is high, the tunneling is small, the BEC is in the state of Mott insulate, *To measure the correlation between BEC in each lattice, we use the superradiant scattering method.**In quantum gas, there is similar phenomena,there is correlated function. And correlated length is, the critical exponnent is univeral, equal to 0.67.*To measure this critical exponnent, esslinger group did nice experimental by interfermtery.but only half part is meaured.

*But how to measure the another part, we use the Talbot interfermeter method. *B*But the experimental result shoud be improved by decrease temperature. One way is to do this experiment in space.*On the ground, we have use deep trap to sustain gravity, **