Coherence, Dynamics, Coherence, Dynamics, Transport and Phase Transport and Phase

Transition of Cold AtomsTransition of Cold Atoms

Wu-Ming Liu （刘伍明） (Institute of Physics, Chinese Academy of Sciences)

http://www.iphy.ac.cnEmail: wmliu@aphy.iphy.ac.cn

CollaboratorsCollaboratorsS.T. Chui (Delaware Univ.)J.Q. Liang (Shanxi Univ.)B.A. Malomed (Telviv Univ.)Q. Niu (Texas Univ. at Austin)S.Q. Shen (HongKong Univ.)B. Wu (IOP, CAS)Z.D. Zhang (IMR, CAS)

OutlineOutline

1. Coherence

2. Dynamics

3. Quantum transport

4. Quantum phase transition

5. Spinor BEC

6. Boson - Fermion mixture

1. Coherence (decoherence)1. Coherence (decoherence)

1.1. Atom-molecule coherence

1.2. Atom-molecule coherence

1.3. Molecule-molecule coherence 1.4. Decoherence

1.1. Atomic BEC coherence1.1. Atomic BEC coherence

W. Ketterle, Science 275, 637 (1997).

W.M. Liu, B. Wu, Q. Niu,

Nonlinear effects in interference of Bose-Einstein condensates,

Phys. Rev. Lett. 84, 2294 (2000).

Gross-Pitaevskii equationGross-Pitaevskii equation

2 2 2

24

2 ext

ai V rt m m

Long time solutionLong time solution

22

2 ( ) log(4 )12

2 2

( )( , ) ( log )

1( ) log(1 ( ) )

2

x xi i tt t

xtx t e O t tt

k r kg

Theoretical explanationTheoretical explanation

1 2

''0 0

12 2 2

2n nk E V n V

Fringe positionFringe position

Central fringeCentral fringe

1 2"

0 1 1 0 04 2k k k V V

Experimental prediction:Experimental prediction:1. Energy level 2. Many wave packets1. Energy level 2. Many wave packets

Ratio of level width to level spacingRatio of level width to level spacing 22 n ng E w En n

n n

k Ee

k E

Two component BECTwo component BEC

PRL 81, 1539, 1543 (1998).PRL 81, 1539, 1543 (1998).

W.D. Li, X.J. Zhou, Y.Q. Wang, J.Q. Liang, W.M. LiuW.D. Li, X.J. Zhou, Y.Q. Wang, J.Q. Liang, W.M. Liu,,

Time evolution of relative phase Time evolution of relative phase in two-component Bose-Einstein cin two-component Bose-Einstein condensates with a coupling drive,ondensates with a coupling drive,

Phys. Rev. A64, 015602 (2001).Phys. Rev. A64, 015602 (2001).

1.2. Atom-molecule coherence (1.2. Atom-molecule coherence (8787RbRb22))E.A. Donley et al., Nature 417, 529 (2002).E.A. Donley et al., Nature 417, 529 (2002).

1.3. Molecule-molecule coherence1.3. Molecule-molecule coherenceR.H. Wynar et al., Science 287, 1016 (2000).R.H. Wynar et al., Science 287, 1016 (2000).

1.4. Decoherence1.4. DecoherenceM.K. Kasevich, Science 298, 1363 (2002).M.K. Kasevich, Science 298, 1363 (2002).

2. Dynamics2. Dynamics

2.1. BEC near Feshbach resonance

2.2. Soliton

2.3. Vortex

S. Inouye et al., Nature 392, 151 (1998).S. Inouye et al., Nature 392, 151 (1998).

2.1. BEC near Feshbach resonance2.1. BEC near Feshbach resonance

Z. X. Liang, Z. D. Zhang, W. M. Liu,Z. X. Liang, Z. D. Zhang, W. M. Liu,

Dynamics of a bright soliton in Bose-Einstein condensates

with time-dependent atomic scattering length in an expulsive parabolic potential,

Phys. Rev. Lett. 74, 050402 (2005).Phys. Rev. Lett. 74, 050402 (2005).

L. Khaykovich et al., Science 296, 1290 (2002).

2.2. Soliton2.2. Soliton

Z.W. Xie, Z.X. Cao, E.I. Kats, W.M. LiuZ.W. Xie, Z.X. Cao, E.I. Kats, W.M. Liu,,

Nonlinear dynamics Nonlinear dynamics of of dipolardipolar Bose-Einstein condensate Bose-Einstein condensate

in optical lattice,in optical lattice,

Phys. Rev. A 71, 025601 (2005).Phys. Rev. A 71, 025601 (2005).

L. Li, B.A. Malomed, D. Mihalache, W.M. Liu,L. Li, B.A. Malomed, D. Mihalache, W.M. Liu,

Exact soliton-on-plane-wave soluExact soliton-on-plane-wave solutions for two-component Bose-Eitions for two-component Bose-Ei

nstein condensates,nstein condensates,

Phys. Phys. Rev. E 73, 066610 (2006).Rev. E 73, 066610 (2006).

3. Quantum transport3. Quantum transport

W.M. Liu, W.B. Fan, W.M. Zheng, J.Q. Liang, S.T. Chui,

Quantum tunneling of Bose-Einstein condensates

in optical lattices under gravity,

Phys. Rev. Lett. 88, 170408 (2002).

Landau-Zener tunnelingLandau-Zener tunneling Barrier between lattices is low Localized level between lattices is coupling Miniband Adiabatic approximation Tunneling between delocalized states in different Bloch bands

Potential energy and Bloch bandsPotential energy and Bloch bands

Tilted bands and WS laddersTilted bands and WS ladders

Wannier-Stark tunnelingWannier-Stark tunneling An external field Wavefunction of miniband is localization Miniband is divided into discrete level Wannier-Stark ladder Tunneling between localized states in different individual wells

—Wannier-Stark localized states

At high temperature:At high temperature:Arrhenius lawArrhenius law

max /0

2BV k T

AR e

Temperature dependenceTemperature dependence

0max0

0

432

0( ) (1 )

w

k TB

B

Vwe

wk TT e e

Crossover temperatureCrossover temperature

0

2

257

( , ) 2.1

crB

cr

l R

hwT

k

T nK

U x y E

At low temperature:At low temperature:Pure quantum tunnelingPure quantum tunneling

At intermediate temperature:At intermediate temperature:Thermally assisted tunnelingThermally assisted tunneling

4. Quantum phase transition

Superfluid Mott insulator

Insulator + disorder = Bose glassInsulator + weak disorder = Anderson glass

Berezinskii–Kosterlitz–Thouless transation

Magnetic phase transition

M. Greiner et al., Nature 415, 39 (2002)M. Greiner et al., Nature 415, 39 (2002)

J.J. Liang, J.Q. Liang, W.M. Liu,

Quantum phase transition of condensed bosons in optical lattices,

Phys. Rev. A68, 043605 (2003).

Z.W. Xie, W.M. Liu,Z.W. Xie, W.M. Liu,

Superfluid–Mott insulator transition Superfluid–Mott insulator transition of of dipolardipolar bosons in an optical lattice, bosons in an optical lattice,

Phys. Rev. A70, 045602 (200Phys. Rev. A70, 045602 (2004).4).

G.P. Zheng, J.Q. Liang, W.M. Liu,G.P. Zheng, J.Q. Liang, W.M. Liu,

Phase diagram of two-species Bose-Einstein condensate

s in an optical lattice ，

Phys. Rev. A71, 053608 (2005)Phys. Rev. A71, 053608 (2005)

P.B. He, Q. Sun, S.Q. Shen, W. M. Liu,

Magnetic quantum phase transition of cold atoms in optical lattice,

Phys. Rev. A 76, 043618 (2007).

A.C. Ji, X.C. Xie, W. M. Liu,

Magnetic dynamics of polarized light in arrays of microcavities,

Phys. Rev. Lett. 99, 183602 (2007).

2.5. Spinor BEC2.5. Spinor BEC J. Stenger, Nature 396, 345 (1998).

Z.W. Xie, W.P. Zhang, S.T. Chui, W.M. Liu,

Magnetic solitons of

spinor Bose-Einstein condensates

in optical lattice,

Phys. Rev. A69, 053609 (2004).

Z.D. Li, P.B. He, L.Li, J.Q. Liang, W.M. LiZ.D. Li, P.B. He, L.Li, J.Q. Liang, W.M. Liu,u,

Soliton collision of spinor Bose-Einstein condensates

in optical lattice,

Phys. Rev. A71, 053608 (2005).

L. Li, Z.D. Li, B. A. Malomed, D. Mihalache, W. M. Liu,L. Li, Z.D. Li, B. A. Malomed, D. Mihalache, W. M. Liu,

Exact soliton solutions and Exact soliton solutions and

nonlinear nonlinear modulation instabilitymodulation instability

in spinor Bose-Einstein condensates,in spinor Bose-Einstein condensates,

Phys. Rev. A 72, 033611 (2005).Phys. Rev. A 72, 033611 (2005).

2.6. Boson - Fermion mixture2.6. Boson - Fermion mixtureR.G. Hulet, Science 291, 2570 (2001).R.G. Hulet, Science 291, 2570 (2001).

SummarySummary

1. Coherence

2. Dynamics

3. Quantum transport

4. Quantum phase transition

5. Spinor BEC

6. Boson - Fermion mixture

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