Download UNEDF workshop, Lansing, June 22, 2010

DFT Study of Exotic Pairing Phases in
Imbalanced Fermi Condensates
J. Pei (UTK/ORNL)
With: W. Nazarewicz, J. Dukelsky
UNEDF workshop, Lansing, June 22, 2010
Expected exotic FFLO pairing
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In imbalanced Fermi systems, pairing with none-zero momentum can
happen: 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.
r r
r
iqn  x
( x )   0  Cn e
n
UNEDF workshop, Lansing, June 22, 2010
Some experiments
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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→±∞
834 G
System is strongly correlated and its
properties do not dependent on the
value of scattering length as
Trapped by optical and magnetic potential
w02 2 r 2 / w2 ( z )
1
2 2
U (r , z )  mB z  U 0 [1  2 e
], w( z )  w0[1  ( z / z0 ) 2 ]
2
w ( z)
approximate HO potential:
Aspect ratio: η=wr/wz U (r , z )  U (1  exp(  1 ( w2 r 2  w2 z 2 ) / U ))
0
r
z
0
2
highly elongate trap is of great interests! (good for looking FFLO pairing)
UNEDF workshop, Lansing, June 22, 2010
Experiments(Rice)
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Phase Separation
Superfluid Core is deformed from
the 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)
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Phase separation
However, no superfluid core deformation
Y.Shin, et al, PRL 97,03401,2006
Clogston-Chandrasekhar limit of
superfluidity
Trap aspect ratio=5, particles=106
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UNEDF workshop, Lansing, June 22, 2010
Experiments-others
•
French group: 105 particles, aspect ratio=23 (agree with MIT)
No core deformation
Question???
1. different experimental
conditions
2. or theory is not precise
C. Salomon, et al, PRL103, 18 (2009) 170402
UNEDF workshop, Lansing, June 22, 2010
Finite-size effect
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Finite-size effect of trap deformations and particle numbers
small deformation trap doesn't violate LDA solutions
M.Ku, PRL 102, 255301, 2009
Sensarma, et al. arxiv: 07061741
Tezuka, et al. arxiv: 0811.1650
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Non-equilibrium state observed
in Rice experiment
Parish, et al. PRA 063305(2009)
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Surface tension is important at large deformations
T.N. De Silva, et al, PRL 97, 070402(2006)
UNEDF workshop, Lansing, June 22, 2010
Theoretics
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Quantum Monte Carlo: QMC is very precise but limited to small systems
Bogoliubov de-Genes equation: Mean Field approximation
FFLO
normal
PS
BP
TK Koponen, PRL 99,120403
Plenty of calculations, no Hartree potential, and not quantitatively accurate
A contest of computation: Tokyo U:30000 particles; Rice U: 105 particles
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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.
UNEDF workshop, Lansing, June 22, 2010
Coexistence of difference phase?
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SDLA calculations with different initials sin(qz)exp(-(z-zc)/a), why sensitive?
J.P, W. Nazarewicz, J. Dukelsky, arxiv:1005:3239
UNEDF workshop, Lansing, June 22, 2010
Quasi-continuum
back ground
discussions
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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
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Very different Hartree potentials in ASLDA
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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
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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
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Phase separation is demonstrated in trapped system both by SLDA and
ASLDA
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Energy structures of coexistent phases are shown.
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Superfluid Core deformation is not shown in ASLDA.
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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
UNEDF workshop, Lansing, June 22, 2010