The Equilibrium Properties of the Polarized Dipolar Fermi Gases

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The Equilibrium Properties of the Polarized Dipolar Fermi Gases

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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

- 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

- Physical System
- Fermionic Polar Molecules (40K87Rb)
- Spin polarized
- Electric dipole moment polarized
- Normal Phase

- Second-quantized Hamiltonian

- Polarized dipoles (long-range & anisotropic)
- Tunability
- Fourier Transform

z

x

y

- Box: homogenous case
- Harmonic potential: trapped case

Oblate trap: >1

Prolate trap: <1

- Energy functional
- Single-particle reduced density matrix
- Two-particle reduced density matrix

zero-temperature

finite temperature

- Total energy:
- Fourier transform
- Free energy functional (zero-temperature):
- Minimization: The Simulated Annealing Method

- Independent quasi-particles (HFA)
- Fermi-Dirac statistics
- Effective potential
- Normalization condition

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

Phase-space deformation

Always stretched alone the attractive direction

Interaction energy (dir. + exc.)

Dimensionless dipole-dipole interaction strength

Phase-space distribution

Phase-space deformation

Thermodynamic properties

Energy

Chemical potential

Entropy

Specific heat

Pressure

Dimensionless dipole-dipole interaction strength

Stability boundary

Phase-space deformation

- 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!