1. The Equilibrium Properties of the Polarized Dipolar Fermi Gases 报告人：张静宁 导师：易俗

2. Outline: Polarized Dipolar Fermi Gases Motivation and model Methods  Hartree-Fock & local density approximation  Minimization of the free energy functional  Self-consistent field equations Results (normal phase)  Zero-temperature  Finite-temperature Summary

3. Model Physical System  Fermionic Polar Molecules ( 40 K 87 Rb )  Spin polarized  Electric dipole moment polarized  Normal Phase Second-quantized Hamiltonian

4. Dipole-dipole Interaction Polarized dipoles (long-range & anisotropic) Tunability Fourier Transform

5. Containers Box: homogenous case Harmonic potential: trapped case y z x Oblate trap: >1 Prolate trap: <1

6. Theoretical tools for Fermi gases

7. Energy functional: Preparation Energy functional Single-particle reduced density matrix Two-particle reduced density matrix

8. Wigner distribution function zero-temperature finite temperature

9. Free energy functional Total energy: Fourier transform Free energy functional (zero-temperature): Minimization: The Simulated Annealing Method

10. Self-consistent field equations: Finite temperature Independent quasi-particles (HFA) Fermi-Dirac statistics Effective potential Normalization condition

11. Result: Zero-temperature (1) Ellipsoidal ansatz T. Miyakawa et al., PRA 77, 061603 (2008); T. Sogo et al., NJP 11, 055017 (2009).

12. Result: Zero-temperature (2) Density distribution Stability boundary Collapse  Global collapse  Local collapse

13. Result: Zero-temperature (3) Phase-space deformation  Always stretched alone the attractive direction Interaction energy (dir. + exc.)

14. Result: Finite-temperature & Homogenous Dimensionless dipole-dipole interaction strength  Phase-space distribution Phase-space deformation Thermodynamic properties  Energy  Chemical potential  Entropy  Specific heat  Pressure

15. Result: Finite-temperature & Trapped Dimensionless dipole-dipole interaction strength  Stability boundary Phase-space deformation 

16. Summary The anisotropy of dipolar interaction induces deformation in both real and momentum space. Variational approach works well at zero-temperature when interaction is not too strong, but fails to predict the stability boundary because of the local collapse. The phase-space distribution is always stretched alone the attractive direction of the dipole-dipole interaction, while the deform is gradually eliminated as the temperature rising.

17. Thank you for your attention!