Superfluidity and magnetism in multicomponent ultracold fermions

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Superfluidity and magnetism in multicomponent
ultracold fermions

• Robert Cherng - Harvard
• Gil Refael - Caltech
• Eugene Demler - Harvard

arXiv0705.0347
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Fermionic superfluidity and magnetization?
From Condensed Matter
To Cold Atoms
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Fermionic superfluidity and magnetization?

• Cold atoms multicomponent fermions
• Superfluidity pairing of different states
• Magnetization imbalance of different states
• This talk N2 vs. Ngt2, mean-field theory

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N2 BCS, FFLO, BP/Sarma

FS
FS

FS
FS
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N2 BCS, FFLO, BP/Sarma

FS
FS
BCS
FFLO

FS
FS
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N2 BCS, FFLO, BP/Sarma

• Bardeen, Cooper, Schreiffer
• Phys. Rev. 108, 1175 (1957)

BCS

• Fulde-Ferrel, Larkin-Ovchinnikov
• Breaks translational symmetry
• Phys. Rev. 135, A550 (1964)
• ZETP 47, 1136 (1964)

FFLO

• Liu-Wilczek (Breached-Pair), Sarma
• Phase separation in k space
• Gapless quasiparticles
• PRL 90, 047002 (2003)
• J. Phys. Chem. Solids 24, 1029 (1963)

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Three components using 6Li
6Li (I,L,S)(1,0,1/2)
E
B
Innsbruck group PRL 94, 103201 (2005)
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Pairing Three Components?
FS
FS
FS
Honerkamp and Hofstetter PRL 92, 170403 (2004)
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Pairing Three Components?
FS
FS
FS
FS
Honerkamp and Hofstetter PRL 92, 170403 (2004)
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Pairing Three Components?
FS
FS
FS
FS
FS
FS
Honerkamp and Hofstetter PRL 92, 170403 (2004)
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Model action
Imaginary Time Action
Coupling Constants
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Physical symmetries and symmetry breaking
U(N) Symmetric µaµ, ?aß?
U(1)N Normal State µa ? µß, ?aß ? ??d
U(1)N-P Superfluid State µa ? µß, ?aß ?
??d lt?a?ßgt?0
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Mean-field theory and Ward identities
Order Parameters
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Mean-field theory and Ward identities
Order Parameters
Constrained by Ward-Takahashi identity
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Mean-field theory and Ward identities
Order Parameters
Constrained by Ward-Takahashi identity
Solved by diagonalizing order parameters
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Mean-field theory and Ward identities
Order Parameters
Constrained by Ward-Takahashi identity
Solved by diagonalizing order parameters
And finding the eigenvectors
Diagonal Pairing States
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Microscopic Pairing Wavefunctions
N2 P1
N3 P1
N4 P1
N4 P2
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Ginzburg-Landau Free Energy
Coupling of magnetization and pairing
Quadratic symmetry breaking
U(N) symmetric superfluid transition
Ginzburg-Landau parameters a, b, c, d
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N3 Phase Diagrams
TgtTcSYM Fixed µ
TltTcSYM Fixed µ
TgtTcSYM Fixed n
TltTcSYM Fixed n
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N4 Phase Diagrams
TgtTcSYM, fixed µ
TltTcSYM, fixed µ
Legend
Global minimum
1st meta- stable
?, f parameterize anisotropies in µ
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Phase-contrast Imaging
MIT Group PRL 97, 030401 (2006)
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RF Spectroscopy
3
RF
1
2
Innsbruck Group Science 305, 1128 (2004)
BEC
BCS
Unitary
Higher T
Lower T
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Conclusions

• Ngt2 Superfluidity drives magnetization
• Classification via Ward-Takahashi identities
• Rich phase diagrams
• first/second order transitions
• metastability/phase separation
• multicritical points
• Direct signatures in cold atoms