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Transcript of Wu-Ming Liu (刘伍明) Institute of Physics, Chinese Academy of Sciences e-mail:...
Wu-Ming Liu (刘伍明)Institute of Physics, Chinese Academy of Sciences
e-mail: [email protected]
Novel states of cold atoms in
gauge field and optical lattices
Critical behavior of lattice models in atomic and molecular, condensed matter and particle
Collaborators
Yao-Hua Chen (陈耀桦)Ren-Yuan Liao (廖任远)Chao-Fei Liu (刘超飞)Hong-Shuai Tao (陶红帅)Wei Wu (吴为)Yi-Xiang Yu (喻益湘)Dao-Xin Yao (姚道新,中山大学)
Outline
1. Introduction
2. Cold atoms in gauge field:
Half-skyrmion
3. Cold atoms in optical lattices:
Bose metal
4. Cold atoms in gauge field and optical lattices:
Spin Hall effect, Topological insulator
5. Summary
Bose-Einstein condensation
Bose-Einstein statistics (1924)
Bose enhancement
(0 .83 N )1/3= T C k B
h
Fermi-Dirac statistics (1926)
E F
Fermi sea
Pauli Exclusion
T << T = (6 N )F 1/3
k B
h
1 、 Introduction : Bose-Einstein condensate
1 、 Introduction : Cold atoms
1924 1987
Nobel Prize (1997)
. . . . . .1995
Nobel Prize (2001)
Cold atoms and molecules are nano- or micro-kelvin temperature laboratory
Cold atoms and molecules are nano- or micro-kelvin temperature laboratory
New quantum
states
Quantum simulation
Quantum information
Nonequilibrium dynamics
Application in high technology
1 、 Introduction : Low temperature laboratory
High technology
Space clock
Gyroscope Interferometer
Optical clock
1 、 Introduction : Application
1 、 Introduction : 200 Experiment group
JILA,NIST,Harvard,Rice,Duke,MIT,PurdeUSA ( 60 )
ANU,UQ,SwinburneAustralia ( 10 )
Toronta,UBC,York Univ
Canada ( 15)
TUD,LMU,MPQ,US,UD,UH
Germany ( 25)
SIOM,PKU,WIPM,SXU,IOP,USTCChina ( 15)
Come from :
CNRS,LCAR,ENS Paris, PhLAM
France ( 20)
Niels Bohr, Aarhus Univ
Danmark( 5)
Oxford,Cambridge,Imperial,U
CL,DurhamEngland ( 1
5 )
JST,Tokyo,NTTJapan ( 15 )
IITK,SSMRV,ARSDIndia ( 10 )
2.1. Spin polarized fermi gas in gauge field:
Magnetized superfluid
2.2. Spinor BEC in gauge field:
Half-skyrmion
2 、 Cold atoms in gauge field
Spielman, Nature 462, 628 (2009)
2 、 Cold atoms in gauge field
R.Y. Liao, Y.X. Yu, W.M. Liu, Phys. Rev. Lett. 108, 080406 (2012)
2. Cold atoms in gauge field : Phase diagram
FIG. 1. Isoenergy surface (Ek=0.8EF) for quasiparticle excitation spectrum at unitarity where 1/(kFas)=0 at T=0: (a) h=0,λ=0.125vF; (b) h=0,λ= 0.25vF; (c) h=0.1EF,λ=0.125vF; (d) h=0.1EF,λ=0.25vF. Red dashed line is plotted for Ek-, blue solid line is for Ek+, green dash-dotted circle is for a spherical isoenergy surface, plotted for comparison.
FIG. 2 Upper panel: Finite-temperature phase diagram as a function of T and h at 1/(kFas)= -1 (BCS side). There are four different phases: N state, PS state, SF state, magnetized superfluid (SFM). Above tricritical point, transition line separating broken-symmetry state (SFM) and symmetric state (N) is of second order. Below tricritical point (TP), it changes to first order. Lower panel: Evolution of tricritical point (Ttri/TF, htri/EF) as a function of SOC strength λ.
FIG. 3. Finite-temperature phase diagram in plane of T and P at 1/(kFas)=-1. The inset shows corresponding polarization Ptri for tricritical point as a function of SOC strength . The phase SF is along line of P=0. The notation is the same as in Fig. 2.
FIG. 4. Left: polarization P=(n↑-n↓)/ (n↑+n↓) as a function of magnetic field h for various SOC strength at zero temperature at unitarity. Right: The critical temperature for balanced superfluid at unitarity; Tc0 is calculated from mean field theory and Tcg is calculated by taking account of Nozieres–Schmitt-Rind correction.
FIG. 5. The momentum distribution nkσ and correlation function C↑↓(k) at
unitarity at zero temperature with SO coupling strength λ=0.2vF for two typical polarizations: P=0.7 (left) and P=0.9 (right).
C. F. Liu, W. M. Liu, Phys. Rev. A 86, in press (2012)
Combination SOC and rotation
2 、 Cold atoms in gauge field : Dynamics
C. F. Liu, W.M. Liu, Phys. Rev. A 86, in press (2012)
Densities and phases of spinor BEC of 87Rb with SOC when system reaches equilibrium state. (a) К=0.1; (b) К=0.2; (c) К=0.5; (d) К=0.7; (e) К=1.0. Ω=0.5ω.
2 、 Cold atoms in gauge field : SO effect
C.F. Liu, W.M. Liu, Phys. Rev. A 86, in press (2012)
(a) Spin texture, К=0.5, Ω=0.5ω. Color of each arrow indicates magnitude of Sz. Black pane points out a Skyrmion, blue pane indicates a half-Skyrmion. (b) Position of vortices and spin texture. Green, blue, red spots are center of vortices formed by mF=-1, mF=0, mF=1. (c) Topological charge density. (d) Position of vortices and spin texture, К=0.1, Ω=0.5ω. (e) Scheme of three vortices structure.
2. Cold atoms in gauge field : Half-skyrmion
C.F. Liu, W.M. Liu, Phys. Rev. A 86, in press (2012)
Effect of rotation frequency for spinor BEC of 23Na,К=1, (a) Ω=0; (b) Ω=0.2ω; (c) Ω=0.5ω. Fourth column shows corresponding spin textures and position of vortices in region of y>0.
2. Cold atoms in gauge field : Rotation effect
C.F. Liu, W.M. Liu, Phys. Rev. A 86, in press (2012)
Phase diagrams of products in spin-1 BEC with rotation frequency Ω and SOC strength К: (a) 87Rb; (b) 23Na.
2. Cold atoms in gauge field : Phase diagram
3.1. Quantum phase transition
3.2. Super-counter-fluidity
3.3 Spin liquid
3.4 Kondo metal and plaquette insulator
3 、 Cold atoms in optical lattices
Tuning : interaction, component, structure, dimension
v0
3/ 4
0s r
r
VU ka E
E
3.1. Superfluid-Mott insulator transition
one component
Superfluid-Mott insulator transition
( PRA03 )super-counter-fluidity
( PRL07 )Nematic phase
(PRA08)
Two component Three component
Tuning : interaction, component, structure, dimension
3.2. Super-counter-fluidity
Dirac fermion( PRB 2010 )
Frustrated system( PRA 2010 )
Supersolid(PRA 2011)
Triangular lattice Square latticeHoneycomb lattice
Tuning : interaction, component, structure, dimension
3.3. Spin liquid
Spin liquid
Y.H. Chen, H.S. Tao, D.X. Yao, W.M. Liu, Phys. Rev. Lett. 108, 246402 (2012)
†ij i j ii i
ij i i
H t c c U n n n
3.4. Kondo metal and plaquette insulator
FIG. 1: (a1) Unit cell of triangular Kagome lattice (TKL) without asymmetry (λ=1.0). Open circles denote A-sites and Solid circles denote B-sites. Blue lines represent hopping between A-sites and B-sites. Red lines denote hopping between B-sites. (a2) λ>1.0, TKL is similar with Kagome lattice. (a3) λ<1.0, TKL is transformed into a system composed of many triangular plaquettes. (b) Thick red lines show first Brillouin zone of triangular Kagome lattice. Thin black lines correspond to Fermi surface for non-interacting case. Γ, K, M, K’, M points denote points in first Brillouin zone with different symmetry.
FIG. 2: Phase diagram of triangular kagome lattice atλ=0.6. The black solid lines show transition line of A-sites, red dashed lines show transition line of B-sites. Two kinds of coexisting phases between red lines and black lines are plaquette insulator and Kondo metal. Inset: Phase diagram of symmetric triangular kagome lattice (λ=1), in which there are no coexisting phases.
FIG. 3: Momentum resolved spectrum Ak(ω) atλ=0.6. (a) Metallic phase at U =6, T=0.5. (b) Mott insulating phase at U=9, T=0.5. A visible single particle gap shows up around Fermi energy. (c) Plaquette insulating phase at U=7.6, T=0.5, A sites are insulating, B sites are metallic. A small gap shows up. (d) Kondo metallic phase at U=7, T=0.2, A sites are metallic, B sites are insulating. Single particle gap vanishes.
FIG. 4: Evolution of double occupancy D on A sites as a function of U with different temperatures at λ=0.6. The inset figure shows evolution of double occupancy on B sites. The arrows with different colors show phase transition points at different temperatures.
FIG. 5: The evolution of spectral function on Fermi surface. (a) λ=0:6. (b)λ=1. (c) λ=1:25.
FIG. 6: Single particle gap ΔE and ferrimagnetic order parameter m at λ=1.0, T=0.2, tbb=1.0. A paramagnetic metallic phase is found when interaction is weak with ΔE=0, m=0. As interaction U increases, a gap is opened and no magnetic order is formed with ΔE≠0, m=0. This paramagnetic insulating phase can be a short range RVB spin liquid. An obvious magnetic order is formed when interaction is strong enough withΔE≠0, m≠0. Insert picture shows evolution of E at λ=0.6, T=0.5. A plaquette insulator is found when A-sites are insulating, B-sites are metallic.
FIG. 7: Phase diagram represents competition between interaction U and asymmetry λfor T=0.2, tbb=1. Region between black lines with square points and red lines with circle points denotes coexisting zone which contains plaquette insulator and Kondo metal. A wide paramagnetic insulating region is found with an intermediate U. Blue lines with triangular points show transition point to ferrimagnetic insulator with a clear magnetic order. Insert: (a) Dimers formed in paramagnetic insulator, which is a candidate for short range RVB spin liquid, (b) Spin configuration of ferrimagnetic insulator.
4.1. Quantum spin Hall effect
4.2. Topological insulator
4 、 Cold atoms in gauge field and optical lattices
FIG. 1: (a) Illustration of honeycomb lattice. The dashed line sketches six-site cluster scheme. (b) The first Brillouin zone of honeycomb lattice. The linear low-energy dispersion relation displays conical shapes near Fermi level.
4.1. Quantum spin Hall effect
W. Wu, S. Rachel, W. M. Liu, K. Le Hur, Phys. Rev. B 85, 205102 (2012)
FIG. 2: Phase diagram of KMH model obtained within CDMFT, including four phases: (i) topological band insulator (TBI); (ii) magnetically ordered spin density wave (SDW); (iii) non-magnetic insulator (SL); (iv) semi-metal (SM) region which is shown (from right to left) for T=0.05, 0.025, 0.0125, 0.005.
† †
i
zi j ij i j i
ij iij
H t c c i c c U n n
4.1. Quantum spin Hall effect
FIG. 3: Temperature dependence of phase diagram at SOCλ=0.02. Inset: Single-particle gap Δsp and magnetization m vs. U is shown forλ=0.02 and T=0.025.
4.1. Quantum spin Hall effect
FIG. 4: α-λ phase diagram of plaquette honeycomb model at U=0. Theα=1 line corresponds to KM model. Spectra for armchair ribbons (L=96) are shown atλ=0.15,α=1.5 (top, QSH phase) andα=0.48 (bottom, entrance of PI phase). Blue lines correspond to SM.
4.2. Topological insulator
Summary
1. Cold atoms in gauge field:
Half-skyrmion
2. Cold atoms in optical lattices:
Bose metal
3. Cold atoms in gauge field and optical
lattices:
spin Hall effect, Topological insulator
Outlook
1. Fundamental physics:
Topological phase transition,
Quantum critical phenomena,
Strong correlated effect,
Non-equilibrium dynamics, …
2. Application in high technology:
Optics and interferometry,
Precision metrology, …