Universal Fermi gas in mixed dimensions

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Universal Fermi gasin mixed dimensions
Yusuke Nishida (MIT)
2D
1D
3D
Dimensionality of space can be changedin cold
atom experiments !
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2D-3D mixed dimensions
A atoms are confined in 2D B atoms are in
3D
3D
2D
Imbalanced fermions in terms of dimensionality of
space Nontrivial phase structure
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Scattering property in 2D-3D
Free space scattering in 3D
Scattering in 2D-3D
l
B
aeff
a
A
Bare scattering length a tunable by Feshbach
resonance
Effective scattering length aeff depending on
a and l
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Effective scattering length
A Li6, B K40 m2D / m3D 0.15
A K40, B Li6 m2D / m3D 6.67
When l ltlt aeff, kF-1 Universal system in 2D-3D

• aeff kF ? -0 Weak attraction (BCS) limit
• aeff kF ? ? Resonant (unitarity) limit
• aeff kF ? 0 Strong attraction (BEC) limit
• with AB bound state

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Stability and Efimov effect
Stability of many-body system requires the
absence of Efimov effect

• Both atomic species A and B are fermionic
• Mass ratio 0.0351 lt mA2D / mB3D lt 6.35

When mA / mB lt 0.0351 When 6.35 lt mA / mB
ABB 3-body bound state AAB 3-body bound state
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Weak attraction (BCS) limit

• No pairing between A and B atoms due to
  mismatch in 2D and 3D Fermi surfaces

B atoms in 3D induces attraction between A atoms
in 2D 2D p-wave pairing
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Strong attraction (BEC) limit

• A atoms in 2D capture B atoms from 3D
• to form bound molecules

When aeff kF lt O(1), size of molecule lt mean
distance 2D BEC of localized molecules
aeff
kF-1
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Possible phase diagram
Universal 2-species Fermi gas in 2D-3D mixture
? ?

• BCS side (pxipy)-wave
  superfluidity in 2D
• Non-abelian statistics
• Topological quantum computation
• BEC side 2D BEC of s-wave molecules

For more details and 1D-3D mixture, see Refs Y.
Nishida S. Tan, Phys.Rev.Lett. 101, 170401
(2008) Y. Nishida, Ann. Phys. (2008)
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Possible phase diagram
? ?
2D BEC of localized molecules
2D-3D mixed gas with 2D p-wave pairing
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Brane world in cold atoms !?

• Brane world in cosmology
• Matter is confined in 3D
• Gravity is in higher D

• Our system in cold atoms
• A atoms are confined in 2D
• B atoms are in 3D

Extra dimension
2D
Brane world in cold atoms !?
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Summary

• Universal Fermi gas in 2D-3D mixture
• BCS side (pxipy)-wave
  superfluidity in 2D
• Non-abelian statistics
• Topological quantum computation
• BEC side 2D BEC of localized
  molecules
• Brane world in cold atoms
• Is it possible to simulate
• aspects of brane cosmology???

For more details and 1D-3D mixture, see Refs Y.
Nishida S. Tan, Phys.Rev.Lett. 101, 170401
(2008) Y. Nishida, Ann. Phys. (2008)