Correlation Effect in the Normal State of a Dipolar Fermi Gas

Lan Yin

School of Physics, Peking University

Collaborator: Bo Liu

Outline

(1) Introduction

(2) Correlation energy

(3) Lifetime of quasi-particles

(4) Conclusion

Creating 87Rb40K polar molecules (JILA)

(1) Introduction

Stimulated Raman adiabatic passage

Electric dipole:

0.052(2) Debye (Triplet ground state)0.566(17) Debye (Singlet)

Density~1012 cm-3

Temperature~2TF

Dipole-Dipole interaction( Long-range and anisotropic )

Consequences:

(1) Anisotropic self-energy and Fermi surface

Variational result

Low-density limit

(T. Miyakawa, T. sogo, H. Pu; S. Ronen, J. Bohn; J.-N. Zhang, S. Yi…)

(2) Critical density of mechanical collapse

(3) P-wave superfluid and other novel states…

(T. Miyakawa, T. sogo, H. Pu) (J.-N. Zhang, S. Yi)

Motivation:

In low density limit, the first-order Fock energy is

zero. Therefore Fock and correlation energies are

of the same order and importance.

(2) Correlation Energy

(S. Ronen, J. Bohn)

Hartree-Fock ground state energy

Perturbation theory

Hamiltonian

3 31' ( ') ( ) ( ') ( ') ( ),

2H d r d rV r r r r r r

Unperturbed ground state (0)0 0 ,

Fk

kk

(0)0

3

5 FE N

2 23

0 0, ( ) ( ),2

H H H H d rm

r r

First-order perturbation

(1) (0) (0)0 0 int 0 0E H

(0) (0)0(1) (0)

0 (0) (0)0 0

,m

mm m

H

E E

Second-order perturbation

(2) (0) (0) (0) (0)0 0 0(0) (0)

0 0

1,m m

m m

E H HE E

Collision process

1 2 2 1

(0) (0)0 ,m

k Q k Q k k

2 1

1 2 1 2

1 2 1 2 1 2

2(2)0 2

, ,

1(1 )(1 ),

2

V V VE n n n n

V

Q Q k k Qk k k Q k Q

k k Q k k k Q k Q

1 2 1 2 1 2

1 2 1 2 2 1

( , ) ( , ) ( , )

( , ) ( , ) ( , )

k k k Q k Q k k

k k k Q k Q k k

2(2) 2 2 70 3

20.66 ,

E mdn

V m

22 2 7Cor 3

20.31 ,

E mdn

V m

22 2 7Fock 3

20.35 ,

E mdn

V m

Mechanical collapse with high density

32 20 /n md

6

0 3 4m d

Chemical potential

Critical density 32 23.87 /Cn md

( in H-F approximation; by zero sound)

32 233.7 /Cn md 32 21.07 /Cn md

Proposed energy-density-functional in a trap

(Including kinetic, trap, Hartree-Fock, and correlation energies)

Critical molecule number under exp. conditions

Singlet Triplet

Beyond Hatree-Fock approximation, lifetime of

quasi-particles is infinite only at Fermi surface.

Decay rate of quasi-particles can be obtained from

2nd-order self-energy diagrams

(3) Lifetime of quasi-particles

(a)

(b)

Decay rate of quasi-particles

Anisotropic decay rate

Decay rate is smaller in dipole direction, and larger in perpendicular direction.

• Correlation and Fock energies of the same order.

• Critical density of mechanical collapse.

• A new energy density functional.

• Anisotropic decay rate of quasi-particles.

(4) Conclusion