Post on 31-Dec-2015
description
Phase separation in optical lattices in spin-dependent external potentials
高 先龙
Aug 5, 2010Aug 5, 2010
第四届全国冷原子物理和量子信息青年学者学术讨论会
合作者:陈阿海
Outline
Introduction
Motivation: spin-dependent potential off-diagonal confinement
Some results
Conclusions
Tunabilities in quantum gases
Dimensionality
Interaction
External potential
Continuous/discrete systems
Disorder
Components/population imbalance
Static/dynamics
thanks to Markus GreinerN ~100-1000 atoms
Dimensionality
D. Jaksch et al., PRL81, 3108 (98)
Interaction
Directly by Feshbach resonance
Indirectly by lasers
d
External potential
External potential
confinement+interaction new methods demanded
zpotential along z
Observed by H. Moritz et al., PRL94, 210401 (2005)
Continuous/discrete systemsInhomogeneous 1D Gaudin/Yang model
Confinement-induced resonance
M. Olshanii, PRL81, 938 (98) G. Xianlong et al., PRA73, 033609 (06)
Inhomogeneous 1D Hubbard model
U
=
t
t
t
t
Continuous/discrete systems
To observe the optical peak density: absorption images of expanded clouds
i sp
eckl
e in
tens
ity
Billy et al., Nature 453, 891(2008)
Roati et al., Nature 453, 895 (2008)
Disorder
Components/population imbalance
Components/population imbalance
Quantum Newton’s cradle
Kinoshita, Nature 440, 900 (2006)
Static/dynamics
Spin-charge separation in 1D
GXL et al., PRL(2008); GXL, PRB(2010)
Outline
Introduction
Motivation: spin-dependent potential off-diagonal confinement
Some results
Conclusions
The Phase Diagram: Hubbard model
n=Nf /Ns
0
2
1
u=U/t
Luttinger Liquid
Luttinger Liquid
Mott insulator
Band insulator
E.H. Lieb and F.Y. Wu, Phys. Rev. Lett. 20, 1445 (1968)
Band insulator
Luther-Emery Liquid
Phases induced by spin-independent external potential
See M. Rigol et al., PRL91, 130403 (2003) GXL et al., PRL98, 030404 (2007)
U<0 U>0
To realize spin-dependent external potential
* Potassium 40, DeMarco and Jin, Science 285, 1703(99)
* Unequal masses
* Spin-dependent optical trap: asymmetrically detuning the laser frequencies with respect to the two hyperfine states
Blume, PRA78, 013613(08)
Iskin and Williams, PRA77, 013605(08)
Phase Separation induced by external potential
Outline
Introduction
Motivation: spin-dependent potential off-diagonal confinement
Some results
Conclusions
The effects of interaction on phase separationP=0
3D Plots for
Contour plot
The effects of spin-dependent trapping on PSP=0Weak interaction
Strong interaction
3D Plots for u=5
Contour plot
Phase diagram for P=0
1
cuu
Phase diagram for P=0.5
1
cuu
CAH & GXL, PRA81
The effects of trap ratio on Mott phase
Phase diagram for Mott phase
1
cuu
CAH & GXL, PRA81
Phase separation for mass imbalance
Diagonal confinement off-diagonal confinement
Fermi-Hubbard model with ODC
Density distribution with varying N
CAH, GXL, in preparation
Chemical potential
Outline
Introduction
Motivation: spin-dependent potential off-diagonal confinement
Some results
Conclusions
Conclusions:
* Fermions can be phase-separated in a spin-dependent external potential by repulsive interaction
* Increase the trap imbalance, Mott phase ferromagnetic insulating phase
* Critical U exists in the spin-dependent system
Thanks for your attention!
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