Title: Universal Fermi gas in mixed dimensions
1Universal Fermi gasin mixed dimensions
Yusuke Nishida (MIT)
2D
1D
3D
Dimensionality of space can be changedin cold
atom experiments !
22D-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
3Scattering 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
4Effective 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
5Stability 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
6Weak 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
7Strong 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
8Possible 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)
9Possible phase diagram
? ?
2D BEC of localized molecules
2D-3D mixed gas with 2D p-wave pairing
10Brane 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 !?
11Summary
- 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)