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The Equilibrium Properties of the Polarized Dipolar Fermi GasesPowerPoint Presentation

The Equilibrium Properties of the Polarized Dipolar Fermi Gases

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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

x

y

Containers- Box: homogenous case
- Harmonic potential: trapped case

Oblate trap: >1

Prolate trap: <1

Energy functional: Preparation

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

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

Stability boundary

Collapse

Global collapse

Local collapse

Result: Zero-temperature (2)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 & HomogenousDimensionless dipole-dipole interaction strength

Stability boundary

Phase-space deformation

Result: Finite-temperature & TrappedSummary

- 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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