The Equilibrium Properties of the Polarized Dipolar Fermi Gases

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The Equilibrium Properties ofthe 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

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Model

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

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Dipole-dipole Interaction

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

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Containers

• Box homogenous case
• Harmonic potential trapped case

Oblate trap ? gt1
Prolate trap ? lt1
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Theoretical tools for Fermi gases
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Energy functional Preparation

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

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Wigner distribution function

• zero-temperature

• finite temperature

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Free energy functional

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

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Self-consistent field equations
Finite temperature

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

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Result Zero-temperature (1)
T. Miyakawa et al., PRA 77, 061603 (2008) T.
Sogo et al., NJP 11, 055017 (2009).

• Ellipsoidal ansatz

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Result Zero-temperature (2)

• Density distribution
• Stability boundary

• Collapse
• Global collapse
• Local collapse

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Result Zero-temperature (3)

• Phase-space deformation
• Always stretched alone the attractive direction

• Interaction energy (dir. exc.)

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Result Finite-temperature Homogenous

• Dimensionless dipole-dipole interaction strength
• Phase-space distribution

• Phase-space deformation
• Thermodynamic properties
• Energy
• Chemical potential
• Entropy
• Specific heat
• Pressure

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Result Finite-temperature Trapped

• Dimensionless dipole-dipole interaction strength
• Stability boundary

• Phase-space deformation

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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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Thank you for your attention!