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 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

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…)

(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…

(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.

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

Second-order perturbation Collision process

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

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

(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)

Decay rate of quasi-particles

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

(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.