j. pei (utk/ornl) with: w. nazarewicz, j. dukelsky
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UNEDF workshop, Lansing, June 22, 2010
DFT Study of Exotic Pairing Phases in Imbalanced Fermi Condensates
J. Pei (UTK/ORNL)J. Pei (UTK/ORNL) With: W. Nazarewicz, J. Dukelsky With: W. Nazarewicz, J. Dukelsky
UNEDF workshop, Lansing, June 22, 2010
Expected exotic FFLO pairing In imbalanced Fermi systems, pairing with none-zero momentum can happ
en: Flude-Ferrell-Larkin-Ovchinnikov (FFLO)
Oscillation pairing gap is expected; Modulated densities (crystallized). It exists in many theoretical calculations, but difficult to find. Some signatures in heavy fermions systems. Radovan, et al. Nature 425, 51,
2003.
0( ) niq xn
n
x C e ⋅Δ =Δ ∑rrr
UNEDF workshop, Lansing, June 22, 2010
Some experiments Advantages of using cold atoms:
interaction is controllable; clear physics; High Tc; implications for other Fermi systems
Unitary limit: two body s-wave scattering length diverges: as→±∞
System is strongly correlated and its properties do not dependent on the value of scattering length as
Trapped by optical and magnetic potential
approximate HO potential:
Aspect ratio: η=wr/wz
2 22
2 2 2 / ( ) 200 0 02
1( , ) [1 ], ( ) [1 ( / ) ]
2 ( )r w z
B
wU r z m z U e w z w z z
w zω −= + − = −
834 G
2 22 20 0
1( , ) (1 exp( ( ) / ))
2 r zU r z U r zw Uw= − − +
highly elongate trap is of great interests! (good for looking FFLO pairing)
UNEDF workshop, Lansing, June 22, 2010
Experiments(Rice) Phase Separation Superfluid Core is deformed from th
e trap shape
and such deformation effects disappear at high temperatures
Trap aspect ratio ~ 50: highly elongate
Particle numbers ~ 105
G.B.Partridge, et al, PRL97,190407,2006
G.B.Partridge, et al, Science,311,503,2006
UNEDF workshop, Lansing, June 22, 2010
Experiments(MIT) Phase separation However, no superfluid core deformation
Clogston-Chandrasekhar limit of superfluidityTrap aspect ratio=5, particles=106
Y.Shin, et al, PRL 97,03401,2006
UNEDF workshop, Lansing, June 22, 2010
Experiments-others
• French group: 105 particles, aspect ratio=23 (agree with MIT)
C. Salomon, et al, PRL103, 18 (2009) 170402
No core deformation
Question???
1. different experimental conditions
2. or theory is not precise
UNEDF workshop, Lansing, June 22, 2010
Finite-size effect Finite-size effect of trap deformations and particle numbers
small deformation trap doesn't violate LDA solutions
Surface tension is important at large deformations
M.Ku, PRL 102, 255301, 2009
T.N. De Silva, et al, PRL 97, 070402(2006)
Non-equilibrium state observed in Rice experiment
Parish, et al. PRA 063305(2009)
Sensarma, et al. arxiv: 07061741
Tezuka, et al. arxiv: 0811.1650
UNEDF workshop, Lansing, June 22, 2010
Theoretics
Quantum Monte Carlo: QMC is very precise but limited to small systems Bogoliubov de-Genes equation: Mean Field approximation
Plenty of calculations, no Hartree potential, and not quantitatively accurate
A contest of computation: Tokyo U:30000 particles; Rice U: 105 particles
DFT: at the unitary limit, the physical properties only depends on the density. It is good for DFT descriptions. Superfluid Local Density Approximation (SLDA) is very precise.
PSBP
FFLO normal
TK Koponen, PRL 99,120403
UNEDF workshop, Lansing, June 22, 2010
Coexistence of difference phase?
SDLA calculations with different initials sin(qz)exp(-(z-zc)/a), why sensitive?
J.P, W. Nazarewicz, J. Dukelsky, arxiv:1005:3239
Quasi-continuum back ground
UNEDF workshop, Lansing, June 22, 2010
discussions
Is that Quantum fluctuations can be considered by a generator-coordinate DFT
FFLO is a superposition of different wavepackets
UNEDF workshop, Lansing, June 22, 2010
SLDA and ASLDA difference Very different Hartree potentials in ASLDA Related to different effective mass
Deformed core solution is washed out in ASLDA.
Because of their different Hartree potentials
BdG calculations are similar to SLDA calculations.
UNEDF workshop, Lansing, June 22, 2010
Propose to access LO states Pairing oscillations become remarkable as trap aspect ratio increase The oscillations are perpendicular to the long axis Oscillation periods are almost the same. Periods are related to the qLO
Numerical: evolve the trap from a ground-state solution at a moderately elongated trap to reach an excited state
Experiments: can be accessible by elongate the trap adiabatically.
UNEDF workshop, Lansing, June 22, 2010
Conclusions Phase separation is demonstrated in trapped system both by SLDA and AS
LDA
Energy structures of coexistent phases are shown.
Superfluid Core deformation is not shown in ASLDA.
The FFLO is predicted in highly elongated trap, both by SLDA and ASLDA. However, It has a higher energy than LDA solution. Could be access by experiments, need very low temperature.
Thanks: A. Bulgac, M.M. Forbes
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