Post on 25-Feb-2016
description
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 InteractionPolarized dipoles (long-range & anisotropic)
Tunability
Fourier Transform
Containers
Box: homogenous case
Harmonic potential: trapped case
y
z
x
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
Wigner distribution function
zero-temperature finite temperature
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)
Ellipsoidal ansatzT. Miyakawa et al., PRA 77, 061603 (2008); T. Sogo et al., NJP 11, 055017 (2009).
Result: Zero-temperature (2)
Density distribution
Stability boundary
Collapse Global collapse Local collapse
Result: Zero-temperature (3)
Phase-space deformation Always stretched alone the
attractive direction
Interaction energy (dir. + exc.)
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 & Trapped Dimensionless dipole-dipole
interaction strength
Stability boundary
Phase-space deformation
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.
Thank you for your attention!