Hiroki Saito et al- Symmetry Breaking in Scalar, Spinor, and Rotating Bose-Einstein condensates

8/3/2019 Hiroki Saito et al- Symmetry Breaking in Scalar, Spinor, and Rotating Bose-Einstein condensates

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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 Kawaguchi

Masahito UedaUniv. 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 symmetrybreaking



Critical localization on a ring

d

e n s i t y

e x c i t a t

i o n

e n e r g

y

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 cycle

e x c

i t a t i o n e n e r g

y

rotation symmetry breaking Goldstone mode





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

θ ψ θ ψ Ψ = +



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

o r b i t a l

a n g u l a r m o

m e n t u m

dipole interaction / kinetic energy

Nonzero circulation by chiral symmetry breaking



Hiroki Saito et al- Symmetry Breaking in Scalar, Spinor, and Rotating Bose-Einstein condensates

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