Symmetry Breaking in Scalar, Spinor,

and Rotating Bose-Einstein condensates

Hiroki Saito

FB18 Aug. 24, 2006

Univ. of Electro-Communications, Japan

Tokyo Institute of Technology, Japan

Yuki KawaguchiMasahito Ueda

Univ. of Arizona, Tucson

Rina Kanamoto

Contents

Symmetry breaking in BEC

1. rotation symmetry breaking

in attractive BEC

2. clockwise-counterclockwise symmetry breaking

in ferromagnetic BEC

3. chiral symmetry breaking

in dipolar BEC

1D attractive BEC

1D infinite space

bright soliton

translation symmetry breaking

1D ring

rotation symmetry breaking

Critical localization on a ringd

ensi

ty

exc

ita

tio

ne

ner

gy

RK, HS, and MU, PRA 67 013608 (2003); PRA 68 043619 (2003); PRL 94 090904 (2005); PRA 73 033611 (2006)

zero pointenergy

attractiveinteraction

energy> localization

Goldstone mode

gN

Single vortex ------ ring geometry

axi-symmetric vortex state

topological defect

ringlike geometry

attractive interaction

rotation symmetry breaking

Symmetry breaking inrotating attractive BEC

HS and MU, PRL 89 190402 (2002); PRA 69 013604 (2004)

split-merge cycleex

cita

tio

n e

ner

gy

rotation symmetry breakingGoldstone mode

Magnetization of spinor BEC

Ferromagnetic interaction (e.g. spin-1 87Rb)

The initial state is prepared in non-magnetic state. (e.g. mF=0)

violation ofspin conservation

How does magnetization occur in isolated systems?

spin texture

e.g.domain structure

HS and MU, PRA 72, 023610 (2005)

Topological texture formation

polar-core vortex

energy costat domain walls

ferromagneticenergy>

spontaneous formation oftopological texture

HS, YK, and MU, PRL 96, 065302 (2006)

degenerate

Polar-core vortex formation

initial statem = 0

+ noise

m=1 component

clockwise-counterclockwise symmetry breaking

Energy of broken symmetry state

cos sina b

Recent experiment in Berkeley

Sadler et al., cond-mat/0605351

magnitude of spin

direction of spin

Dipolar interaction

dipolar interaction long range

anisotropic

52Cr dipolar BEC has been realized in Stuttgart.Griesmaier et al., PRL 94 10401 (2005)

dipolar magnetic field

YK, HS, and MU, PRL 96, 080405 (2006)

Ground state spin texture

spin-1 87Rb BEC ferromagnetic

dipoleenergy

kineticenergy<<

x-z plane

x-y plane

single domain

dipoleenergy

kineticenergy>>

magnetic closure

Chiral symmetry breaking

dipoleenergy

kineticenergy~

x-z plane

x-y plane

Chiral symmetry breaking

YK, HS, and MU, to appear in PRL

Spontaneous circulation

orb

ital

an

gu

lar

mo

men

tum

dipole interaction / kinetic energy

Nonzero circulation by chiral symmetry breaking

Summary

1. Rotation symmetry breaking

vortex split by attractive interaction

2. Clockwise-counterclockwisesymmetry breaking

topological spin texture formation

3. Chiral symmetry breaking

ground state with dipolar interaction