The Equilibrium Properties of the Polarized Dipolar Fermi Gases

1. The Equilibrium Properties ofthe 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 (40K87Rb) • Spin polarized • Electric dipole moment polarized • Normal Phase • Second-quantized Hamiltonian

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

5. z x y Containers • Box: homogenous case • Harmonic potential: trapped case 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. zero-temperature finite temperature Wigner distribution function

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) T. Miyakawa et al., PRA 77, 061603 (2008); T. Sogo et al., NJP 11, 055017 (2009). • Ellipsoidal ansatz

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

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

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

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

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!