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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