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arXiv:0710.5223 · Physical Review A

Phase-space deformation of a trapped dipolar Fermi gas

Takahiko Miyakawa, Takaaki Sogo, Han Pu

Published Jun 9, 2008• 106 citations
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Abstract

We consider a system of quantum degenerate spin-polarized fermions in a harmonic trap at zero temperature, interacting via dipole-dipole forces. We introduce a variational Wigner function to describe the deformation and compression of the Fermi gas in phase space and use it to examine the stability of the system. We emphasize the important roles played by the Fock exchange term of the dipolar interaction, which results in a nonspherical Fermi surface.

DOI
10.1103/physreva.77.061603

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We consider a system of quantum degenerate spin-polarized fermions in a harmonic trap at zero temperature, interacting via dipole-dipole forces. We introduce a variational Wigner function to describe the deformation and compression of the Fermi gas in phase space and use it to examine the stability of the system. We emphasize the important roles played by the Fock exchange term of the dipolar interaction, which results in a nonspherical Fermi surface.
We study the equilibrium properties of dipolar Bose and Fermi gases at finite temperatures. We recently developed a variational ansatz for the phase-space distribution function of a dipolar Fermi gas at finite temperatures. We extend the variational formalism to a Bose gas and discuss the effect of dipolar interactions with different statistics on the thermal equilibrium, with particular emphasis on the deformation in momentum space. We examine the stability of the system by varying the temperature, trap aspect ratio and the dipole moment. In addition, we discuss how deformation in both real and momentum space can be observed in the high-temperature regime, which is relevant for the current experiments at JILA [Ni et al. Science 322, 231 (2008)] and at University of Tokyo [Aikawa et al. New. J. Phys. 11, 055035 (2009)].
Under the framework of the semiclassical theory, we investigate the equilibrium-state properties of a spin polarized dipolar Fermi gas through full numerical calculation. We show that the Fermi surfaces in both real and momentum spaces are stretched along the attractive direction of dipolar interaction. We further verify that the deformed Fermi surfaces can be well approximated by ellipsoids. In addition, the deformation parameters slightly depend on the local real- and momentum-space densities. We also study the interaction strength dependence of the energy and real- and momentum-space densities. By comparing them with variational results, we find that the ellipsoidal ansatz usually generates accurate results for weak dipolar interaction, while under strong dipolar interaction limit, notable discrepancy can be observed. Finally, we map out the stability boundary of the system.
We study the equilibrium properties of dipolar Fermi gases at finite temperatures. We introduce a variational ansatz for the phase-space distribution function that can describe the deformation in both real and momentum space. The effect of dipole-dipole interactions on thermal equilibrium is discussed, with particular emphasis on the deformation in momentum space. We examine the stability of the system by varying the temperature, trap aspect ratio, and dipole moment. In addition, we discuss how the deformation in both real and momentum space can be observed in the high-temperature regime, which is relevant to the current experiment at JILA (Institute for Laboratory Astrophysics) [K. K. Ni et al., Science 322, 231 (2008)].
We study the equilibrium properties of dipolar Bose and Fermi gases at finite temperatures. We have recently developed a variational ansatz for the phase-space distribution function of a dipolar Fermi gas at finite temperatures. We extend the variational formalism to a Bose gas and discuss the effect of dipolar interactions with different statistics on thermal equilibrium, with particular emphasis on deformation in momentum space. We examine the stability of the system by varying the temperature, trap aspect ratio, and dipole moment. In addition, we discuss how deformation in both real and momentum spaces can be observed in the high-temperature regime, which is relevant for the current experiments at JILA [Ni et al. : Science 322 (2008) 231] and at the University of Tokyo [Aikawa et al. : New J. Phys. 11 (2009) 055035].
We calculate the stability diagram for a trapped normal Fermi or Bose gas with dipole-dipole interactions. Our study characterizes the roles of trap geometry and temperature on the stability using Hartree-Fock theory. We find that exchange appreciably reduces stability and that, for bosons, the double instability feature in oblate trapping geometries predicted previously is still predicted by the Hartree-Fock theory. Our results are relevant to current experiments with polar molecules and will be useful in developing strategies to obtain a polar molecule Bose-Einstein condensate or degenerate Fermi gas.
Trapped degenerate dipolar Bose and Fermi gases of the cylindrical symmetry with the polarization vector along the symmetry axis are only stable for the strength of dipolar interaction below a critical value. In the case of bosons, the stability of such a dipolar Bose–Einstein condensate (BEC) is investigated for different strengths of contact and dipolar interactions using a variational approximation and a numerical solution of a mean-field model. In the disc shape, with the polarization vector perpendicular to the plane of the disc, the atoms experience an overall dipolar repulsion and this fact should contribute to the stability. However, a complete numerical solution of the dynamics leads to the collapse of a strongly disc-shaped dipolar BEC due to the long-range anisotropic dipolar interaction. In the case of fermions, the stability of a trapped single-component degenerate dipolar Fermi gas is studied including the Hartree–Fock exchange and Brueckner–Goldstone correlation energies in the local-density approximation valid for a large number of atoms. Estimates for the maximum allowed number of polar Bose and Fermi molecules in the BEC and degenerate Fermi gas are given.