1. Correlation Effect in the Normal State of a Dipolar Fermi Gas
Lan Yin
School of Physics, Peking University
Collaborator: Bo Liu

2. Outline (1) Introduction (2) Correlation energy
(3) Lifetime of quasi-particles
(4) Conclusion

3. Creating 87Rb40K polar molecules (JILA)
(1) Introduction
Creating 87Rb40K polar molecules (JILA)
Electric dipole:
0.052(2) Debye (Triplet ground state)
0.566(17) Debye (Singlet)
Density~1012 cm-3
Temperature~2TF
Stimulated Raman adiabatic passage

4. Dipole-Dipole interaction
( Long-range and anisotropic )
Consequences:
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…)

5. (2) Critical density of mechanical collapse
(T. Miyakawa, T. sogo, H. Pu)
(J.-N. Zhang, S. Yi)
(3) P-wave superfluid and other novel states…

6. (2) Correlation Energy Motivation:
Hartree-Fock ground state energy
(S. Ronen, J. Bohn)
Motivation:
In low density limit, the first-order Fock energy is zero. Therefore Fock and correlation energies are of the same order and importance.

7. Unperturbed ground state
Perturbation theory
Hamiltonian
Unperturbed ground state
First-order perturbation

8. Second-order perturbation
Collision process

9. Mechanical collapse with high density
Chemical potential
Critical density
( in H-F approximation; by zero sound)

10. Proposed energy-density-functional in a trap
(Including kinetic, trap, Hartree-Fock, and correlation energies)
Critical molecule number under exp. conditions
Singlet
Triplet

11. (3) Lifetime of quasi-particles
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
(b)
(a)

12. Decay rate of quasi-particles

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

14. (4) Conclusion Correlation and Fock energies of the same order.
Critical density of mechanical collapse.
A new energy density functional.
Anisotropic decay rate of quasi-particles.