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.

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