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