Phase-space deformation of a trapped dipolar Fermi gas

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.

Figure 1

Deformation function $I\left(x\right)$.

Figure 2

Density distributions in real space [upper plots, in units of $({\overline{k}}_F^{\lambda =1}{)}^3∕6{\pi }^2$] and in momentum space [lower plots, in units of $(R_F^{\lambda =1}{)}^3∕6{\pi }^2$] for an oblate trap with ${\beta }_0=0.5$ (left plots) and a prolate trap with ${\beta }_0=2$ (right plots) for $c_{dd}{N}^{1∕6}=1.5$.

Figure 3

(Color online) (a) Aspect ratio in momentum space $\sqrt{⟨k_z^2{⟩}_0∕⟨k_x^2{⟩}_0}$ and (b) aspect ratio in real space $\sqrt{⟨z^2{⟩}_0∕⟨x^2{⟩}_0}$ normalized to that for a noninteracting system as functions of ${\beta }_0$ for $c_{dd}{N}^{1∕6}=0$ (solid line), $0.5$ (dashed line), $1$ (dotted line), and $1.5$ (dot-dashed line).

Figure 4

(Color online) Thomas-Fermi surface in real space of the ground state for the noninteracting case (dashed line) and for interacting case $c_{dd}{N}^{1∕6}=1.5$ (solid line).

Figure 5

Critical value of $c_{dd}{N}^{1∕6}$ as a function of ${\beta }_0$. The solid line represents the full variational calculation from our work, while the dashed line is obtained by forcing $\alpha =1$.