J. Pei (UTK/ORNL) With: W. Nazarewicz, J. Dukelsky

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