Dipolar Fermi Gases

1
Dipolar Fermi Gases
Han Pu Rice University

• In collaboration with
• Cheng Zhao, Lei Jiang, Xunxu Liu
• Takahiko Miyakawa (Aichi Univ. of Education)
• Su Yi (ITP, Chinese Academy of Sci.)

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Dipolar interaction between two atoms
(Polarized dipole)

• Long ranged (1/R3)
• Anisotropic

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Polar molecule as dipolar fermions
40K 87Rb
Large electric dipole moment 0.57 Debye
(singlet) Dipolar interaction 100 times larger
than in 52Cr
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Model
N spin polarized (along z-axis) fermions
Interacting with each other via the dipolar
interaction
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Semiclassical variational approach
PRA 77, 061603(R) (2008) New J. Phys. 11, 055017
(2009)
Choose the proper f that minimizes the total
energy
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Total energy
Goal minimize the total energy Strategy treat
the Wigner function variationally
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Homogeneous case Wigner function
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Homogeneous case energies
Kinetic energy favors an isotropic Fermi surface
(a 1) Fock energy tends to stretch the Fermi
surface along z-axis (a 0) Competition b/w the
two results in a prolate Fermi surface (0lt a lt1).

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Homogeneous case stability
unstable
stable
Sufficiently large dipolar strength leads to
collapse.
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Inhomogeneous case Wigner function
Similar treatment by Goral et al. in PRA 63,
033606 (2001), but with a1.
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Inhomogeneous case energies
Interaction energy is not bounded from below
(dipolar interaction is partially
attractive). The system is not absolutely stable
against collapse (? ? 8).
A local minimum may exist the system may sustain
a metastable state.
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Density profiles
Real space
Momentum space
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Hartree-Fock-Bogoliubov Thoery dipolar superfluid
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Self-consistent solution
0
Renormalization of gap equation Baranov et al.,
PRA 66, 013606 (2002)
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Normal state
Cdd1.096
HFB
Var.
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Superfluid state
Momentum distribution
Order parameter
kz
k?
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Angular distribution of order parameter
Order parameter
kz
k?
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Polar molecules as a high Tc superfluid
Baranov et al., PRA 2002)
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Possible quantum phases?
Biaxial nemetic phase
Fregoso et al., NJP (2009)
Charge density wave
Preliminary results from Miyakawa
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Conclusion

• Dipolar interaction deforms the density
  distribution of quantum Fermi gas in both real
  and momentum space.
• Dipolar interaction induces superfluid pairing
  and other potential quantum phases.