Symmetry%20Breaking%20in%20Scalar,%20Spinor,

1
FB18 Aug. 24, 2006
Symmetry Breaking in Scalar, Spinor, and Rotating
Bose-Einstein condensates
Univ. of Electro-Communications, Japan
Hiroki Saito
Tokyo Institute of Technology, Japan
Yuki Kawaguchi Masahito Ueda
Univ. of Arizona, Tucson
Rina Kanamoto
2
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
3
1D attractive BEC
1D infinite space
bright soliton
translation symmetry breaking
1D ring
rotation symmetry breaking
4
Critical localization on a ring
density
excitation energy
gN
Goldstone mode
attractive interaction energy
gt
zero point energy
localization
RK, HS, and MU, PRA 67 013608 (2003) PRA 68
043619 (2003) PRL
94 090904 (2005) PRA 73 033611 (2006)
5
Single vortex ------ ring geometry
axi-symmetric vortex state
topological defect
ringlike geometry
attractive interaction
rotation symmetry breaking
6
Symmetry breaking in rotating attractive BEC
excitation energy
Goldstone mode
rotation symmetry breaking
split-merge cycle
HS and MU, PRL 89 190402 (2002) PRA 69 013604
(2004)
7
Magnetization of spinor BEC
Ferromagnetic interaction (e.g. spin-1 87Rb)
The initial state is prepared in non-magnetic
state. (e.g. mF0)
violation of spin conservation
How does magnetization occur in isolated systems?
spin texture
e.g. domain structure
HS and MU, PRA 72, 023610 (2005)
8
Topological texture formation
polar-core vortex
spontaneous formation of topological texture
degenerate
HS, YK, and MU, PRL 96, 065302 (2006)
9
Polar-core vortex formation
m1 component
initial state m 0 noise
clockwise-counterclockwise symmetry breaking
10
Energy of broken symmetry state
11
Recent experiment in Berkeley
magnitude of spin
direction of spin
Sadler et al., cond-mat/0605351
12
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)
13
Ground state spin texture
dipole energy
kinetic energy
dipole energy
kinetic energy
ltlt
gtgt
x-z plane
x-y plane
magnetic closure
single domain
14
Chiral symmetry breaking
dipole energy
kinetic energy

x-z plane
x-y plane
Chiral symmetry breaking
YK, HS, and MU, to appear in PRL
15
Spontaneous circulation
orbital angular momentum
dipole interaction / kinetic energy
Nonzero circulation by chiral symmetry breaking
16
Summary
1. Rotation symmetry breaking
vortex split by attractive interaction
2. Clockwise-counterclockwise symmetry breaking
topological spin texture formation
3. Chiral symmetry breaking
ground state with dipolar interaction