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

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The Equilibrium Properties of the Polarized Dipolar Fermi Gases

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The Equilibrium Properties ofthe Polarized Dipolar Fermi Gases

报告人：张静宁

导师：易俗

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

Model

Physical System

Fermionic Polar Molecules (40K87Rb)

Spin polarized

Electric dipole moment polarized

Normal Phase

Second-quantized Hamiltonian

Dipole-dipole Interaction

Polarized dipoles (long-range & anisotropic)

Tunability

Fourier Transform

z

x

y

Containers

Box: homogenous case

Harmonic potential: trapped case

Oblate trap: >1

Prolate trap: <1

Theoretical tools for Fermi gases

Energy functional: Preparation

Energy functional

Single-particle reduced density matrix

Two-particle reduced density matrix

zero-temperature

finite temperature

Wigner distribution function

Free energy functional

Total energy:

Fourier transform

Free energy functional (zero-temperature):

Minimization: The Simulated Annealing Method

Self-consistent field equations: Finite temperature

Independent quasi-particles (HFA)

Fermi-Dirac statistics

Effective potential

Normalization condition

Result: Zero-temperature (1)

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

Ellipsoidal ansatz

Density distribution

Stability boundary

Collapse

Global collapse

Local collapse

Result: Zero-temperature (2)

Phase-space deformation

Always stretched alone the attractive direction

Interaction energy (dir. + exc.)

Result: Zero-temperature (3)

Dimensionless dipole-dipole interaction strength

Phase-space distribution

Phase-space deformation

Thermodynamic properties

Energy

Chemical potential

Entropy

Specific heat

Pressure

Result: Finite-temperature & Homogenous

Dimensionless dipole-dipole interaction strength

Stability boundary

Phase-space deformation

Result: Finite-temperature & Trapped

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.