coherence, dynamics, transport and phase transition of cold atoms wu-ming liu (刘伍明)...
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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: [email protected]
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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