Superfluidity and magnetism in multicomponent ultracold fermions

1
Superfluidity and magnetism in multicomponent
ultracold fermions

• Robert Cherng
• Gil Refael, Eugene Demler
• arxiv0705.0347

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Fermionic superfluidity and magnetization?

• 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
4
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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Three or more components

• Each component individually conserved
• N densities na, N(N-1)/2 scattering lengths aaß
• Limitations spin flips, inelastic losses

N2
Ngt2
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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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Field Redefinition Invariance
Start from
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Field Redefinition Invariance
Start from
Then redefine fields
15
Field Redefinition Invariance
Start from
Then redefine fields
But remember to redefine coupling constants
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Field Redefinition Invariance
Start from
Then redefine fields
But remember to redefine coupling constants
Leaving Z invariant
17
Field Redefinition Invariance
Start from
Then redefine fields
But remember to redefine coupling constants
Leaving Z invariant
Or infinitesimally (WT identity)
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Mean-field theory
Order Parameters
Gap Equations
Greens Functions
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Diagonal Pairing States
Solve WT Identity
By diagonalizing order parameters
And finding the eigenvectors
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Microscopic Pairing Wavefunctions
N2 P1
N3 P1
N4 P1
N4 P2
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Ginzburg-Landau Free Energy
Expansion from U(N) symmetric superfluid
transition
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Ginzburg-Landau Free Energy
Coupling of magnetization and pairing
Quadratic symmetry breaking
Expansion from U(N) symmetric superfluid
transition
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Ginzburg-Landau Free Energy
Coupling of magnetization and pairing
Quadratic symmetry breaking
Particle-hole symmetric
Expansion from U(N) symmetric superfluid
transition
Particle-hole symmetry breaking
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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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U(N) Symmetric Superfluid Transition
Ginzburg-Landau Action
Fields
Symmetric
Symmetry Breaking
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RG in e-Expansion
Crit. ? fields
Crit. ? fields, Mass. M fields integrated out
Crit. ? fields, Mass. M fields kept in
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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

• Superfluidity drives magnetization for
  multicomponent fermions
• Classification of microscopic pairing
  wavefunctions via Ward-Takahashi identities
• Rich phase diagrams first/second order
  transitions, metastability/phase separation,
  multicritical