non-abelian josephson effect and fractionalized vortices
DESCRIPTION
Non-Abelian Josephson effect and fractionalized vortices. Wu-Ming Liu (刘伍明) ( Institute of Physics, CAS ) Email: [email protected]. Supported by NSFC, MOST, CAS. Collaborators. Jiang-Ping Hu (Purdue Univ) An-Chun Ji Zhi-Bing Li (Zhongshan Univ) Ran Qi Qing Sun - PowerPoint PPT PresentationTRANSCRIPT
Non-Abelian Josephson effect Non-Abelian Josephson effect and fractionalized vorticesand fractionalized vortices
Wu-Ming Liu(刘伍明)( Institute of Physics, CAS)
Email: [email protected]
Supported by NSFC, MOST, CAS
CollaboratorsCollaboratorsJiang-Ping Hu (Purdue Univ)An-Chun JiZhi-Bing Li (Zhongshan Univ)Ran QiQing SunXin-Cheng Xie (Oklahoma State Univ)Xiao-Lu YuYan-Yang ZhangFei Zhou (British Columbia Univ)
1. Introduction2. Non-Abelian Josephson effect3. Josephson effect of photons4. Localization5. Fractionalized vortex6. Outlook
Outline
1.1. BEC of ideal gas 7Li 6Li
1. Introduction1. Introduction
1.2. BEC in dilute gas1.2. BEC in dilute gas
1.3. BEC near Feshbach resonance1.3. BEC near Feshbach resonance
1.4. BEC in optical lattices1.4. BEC in optical lattices
1.5. Fermionic condensation
1.6. Molecule condensation?J.G. Danzl et al. Science 321, 1062 (2008)
R. Qi, X.L. Yu, Z.B. Li, W.M. Liu,
Non-Abelian Josephson effect between two F=2 spinor Bose-Einstein
condensates in double optical traps,
Phys. Rev. Lett. 102, 185301 (2009)
2. Non-Abelian Jesephson effect2. Non-Abelian Jesephson effect
Abelian case:U(1) × U(1) U(1) diagonaltwo goldstone modes one gapless
mode (goldstone mode) and one gapped mode (pseudo goldstone mode)
Non-Abelian case:Non-Abelian case:SO(N), U(1) SO(N), U(1) × SO(N)…SO(N)…Multiple Multiple pseudo goldstone modes
No Josephson effect
U(1)XU(1)Nambu-Goldstone modes
Josephson effect
Single mode:U(1)XU(1)Nambu-Goldstone modesMany modes:S=1, U(1)XS(2);S=2, U(1)XSO(3)Pseudo Nambu-Goldstone modes
Ground states of S=2 boson
Ferromagnetic phaseAntiferromagnetic phaseCyclic phase
Ferromagnetic phase
U(1)XU(1)Nambu-Goldstone modes
Antiferromagnetic phase
U(1)XSO(3)Pseudo Nambu-Goldstone modes
Cyclic phase
U(1)XSO(3)Pseudo Nambu-Goldstone modes
Antiferromagnetic phase
m=0
m=±2
Fig. 2 The frequencies of pseudo Goldstone modes as a function of coupling parameter J in the case of antiferromagnetic phase.
Cyclic phasem=±1
m=0,±2
Fig. 3 The frequencies of pseudo Goldstone modes as a function of coupling parameter J in the case of cyclic phase.
Experimental parameter
Rb-87, F=2AFM: c2<0, c1-c2/20>0Cyclic: c1>0, c2>0c1:0-10nK, c2:0-0.2nK, c0:150nKfluctuation time scale-10mspseudo Goldstone modes:1-10nk
Experimental signatures
Initiate a density oscillationDetect time dependence of atom numbers in different spin component◆Measure density oscillation in each of spin componentsNon-Abelian Josephson effect
A.C. Ji, Q. Sun, X. C. Xie, W. M. Liu,
Josephson effects of photons in two weakly-inked microcavities,
Phys. Rev. Lett. 102, 023602 (2009)
3. Jesephson effect of photons3. Jesephson effect of photons
Fig. 1 Experimental setup and control of coupling along resonator axis
Fig. 2 Excitations of a polariton condensate
Fig. 3 Chemical potential-current relation in polariton condensates
4. Localization4. LocalizationJ. Billy et al., Nature 453, 891 (2008).J. Billy et al., Nature 453, 891 (2008).
G. Roati et al., Nature 453, 895 (2008)
Y.Y. Zhang, J.P. Hu, B.A. Bernevig, X.R. Wang, X.C. Xie, W.M. Liu,
Localization and Kosterlitz-Thouless transition in disordered graphene,
Phys. Rev. Lett. 102, 106401 (2009)
ABAA
B
B
Fig. 1 The scaling function
Fig. 2 Typical configurations of local currents In (red arrows)and potential Vn (color contour) on two sides of K-T type MIT with N=56X32 sites, \xi=1:73a, nI=1% and EF=0:1t. (a) W=1:1t (delocalized); (b) W=2:9t (localized).
A.C. Ji, W.M. Liu, J.L. Song, F. Zhou,
Dynamical creation of fractionalized vortices and vortex lattices,
Phys. Rev. Lett. 101, 010402 (2008)
5. Half vortex5. Half vortex
Dynamical creation of fractionalized vortices and vortex lattices
Fig.1 Density and spin density of an individual half vortex
Fig. 2 Interaction potentials between two half vortex
220
0
_
2 1 1 0 2 1 1 0
( ) [2
( )] 2
tr zi V L ct m
c c
hh
221
_2
0 2 1 0 1 1 2 0 1
( ) [2
( ) ]
tr zi V Lt m
c c W c
m m
hh m
2
2 21 12
2 250 Hz
trmV r x y
2
2 2
2mW r x y
m
Fig. 3 Creation of a half-quantum vortex. The bottom panel shows that a single half vortex is formed at t=600 ms after magnetic trap has been adiabatically switched off.
(a) Creation of a triangular integer vortex lattice
(b) A square half vortex lattice formation at t=1600 ms
6. Outlook6. Outlook
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