BEC in an Optical Potential
Post on 02-Jan-2016
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BEC in an Optical Potential. Optical Potential. Second order perturbation theory:. Scattering rate:. Many-Body Hamiltonian. Negligible Interactions. Bloch Theorem: periodic potential. Limiting Cases. Weak Lattice: Bandgap. Wave functions:. Near boundary:. - PowerPoint PPT Presentation
Transcript
Negligible Interactions
)()(),( ruRrurue nknknkikr
nk
G
iGrGeVrV )(
0,2VVV GG
Bloch Theorem: periodic potential
1',',
2
' 2/2
2 llllRll ssG
klEH
xklGilnk ecr )(
m
GER 2
2 22 REs /
'
''l
llll EccH
Limiting Cases
E
kk ,1
2/2/2/,1 GGG
Weak Lattice: Bandgap
Wave functions:
Near boundary:
Tight Binding: Harmonic potentialrr EE
E
m
G
8
22
Wannier functions )(1
)( ,
..0
redkv
Rrf kniRk
ZB
n Eigenstates
GPE
Bloch Wave with no linear counterpart:
c
vcV x 2
Im22
*
ixix eaaek 2/
2
1
Bloch waves are not only solutions!
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