The equilibrium properties of the polarized dipolar fermi gases
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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

The Equilibrium Properties ofthe Polarized Dipolar Fermi Gases

报告人:张静宁

导师:易俗


Outline polarized dipolar fermi gases
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
Model

  • Physical System

    • Fermionic Polar Molecules (40K87Rb)

    • Spin polarized

    • Electric dipole moment polarized

    • Normal Phase

  • Second-quantized Hamiltonian


Dipole dipole interaction
Dipole-dipole Interaction

  • Polarized dipoles (long-range & anisotropic)

  • Tunability

  • Fourier Transform


Containers

z

x

y

Containers

  • Box: homogenous case

  • Harmonic potential: trapped case

Oblate trap: >1

Prolate trap: <1



Energy functional preparation
Energy functional: Preparation

  • Energy functional

  • Single-particle reduced density matrix

  • Two-particle reduced density matrix


Wigner distribution function

zero-temperature

finite temperature

Wigner distribution function


Free energy functional
Free energy functional

  • Total energy:

  • Fourier transform

  • Free energy functional (zero-temperature):

  • Minimization: The Simulated Annealing Method


Self consistent field equations finite temperature
Self-consistent field equations: Finite temperature

  • Independent quasi-particles (HFA)

  • Fermi-Dirac statistics

  • Effective potential

  • Normalization condition


Result zero temperature 1
Result: Zero-temperature (1)

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

  • Ellipsoidal ansatz


Result zero temperature 2

Density distribution

Stability boundary

Collapse

Global collapse

Local collapse

Result: Zero-temperature (2)


Result zero temperature 3

Phase-space deformation

Always stretched alone the attractive direction

Interaction energy (dir. + exc.)

Result: Zero-temperature (3)


Result finite temperature homogenous

Dimensionless dipole-dipole interaction strength

Phase-space distribution

Phase-space deformation

Thermodynamic properties

Energy

Chemical potential

Entropy

Specific heat

Pressure

Result: Finite-temperature & Homogenous


Result finite temperature trapped

Dimensionless dipole-dipole interaction strength

Stability boundary

Phase-space deformation

Result: Finite-temperature & Trapped


Summary
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.