symmetry breaking in scalar, spinor, and rotating bose-einstein condensates hiroki saito fb18 aug....
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![Page 1: Symmetry Breaking in Scalar, Spinor, and Rotating Bose-Einstein condensates Hiroki Saito FB18 Aug. 24, 2006 Univ. of Electro-Communications, Japan Tokyo](https://reader035.vdocument.in/reader035/viewer/2022081519/56649f145503460f94c28851/html5/thumbnails/1.jpg)
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
![Page 2: Symmetry Breaking in Scalar, Spinor, and Rotating Bose-Einstein condensates Hiroki Saito FB18 Aug. 24, 2006 Univ. of Electro-Communications, Japan Tokyo](https://reader035.vdocument.in/reader035/viewer/2022081519/56649f145503460f94c28851/html5/thumbnails/2.jpg)
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
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1D attractive BEC
1D infinite space
bright soliton
translation symmetry breaking
1D ring
rotation symmetry breaking
![Page 4: Symmetry Breaking in Scalar, Spinor, and Rotating Bose-Einstein condensates Hiroki Saito FB18 Aug. 24, 2006 Univ. of Electro-Communications, Japan Tokyo](https://reader035.vdocument.in/reader035/viewer/2022081519/56649f145503460f94c28851/html5/thumbnails/4.jpg)
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
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Single vortex ------ ring geometry
axi-symmetric vortex state
topological defect
ringlike geometry
attractive interaction
rotation symmetry breaking
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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
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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)
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Topological texture formation
polar-core vortex
energy costat domain walls
ferromagneticenergy>
spontaneous formation oftopological texture
HS, YK, and MU, PRL 96, 065302 (2006)
degenerate
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Polar-core vortex formation
initial statem = 0
+ noise
m=1 component
clockwise-counterclockwise symmetry breaking
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Energy of broken symmetry state
cos sina b
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Recent experiment in Berkeley
Sadler et al., cond-mat/0605351
magnitude of spin
direction of spin
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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)
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Ground state spin texture
spin-1 87Rb BEC ferromagnetic
dipoleenergy
kineticenergy<<
x-z plane
x-y plane
single domain
dipoleenergy
kineticenergy>>
magnetic closure
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Chiral symmetry breaking
dipoleenergy
kineticenergy~
x-z plane
x-y plane
Chiral symmetry breaking
YK, HS, and MU, to appear in PRL
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Spontaneous circulation
orb
ital
an
gu
lar
mo
men
tum
dipole interaction / kinetic energy
Nonzero circulation by chiral symmetry breaking
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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