Stability of a trapped dipolar quantum gas

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.

Figure 1

Critical exchange parameter ${\xi }_{\eta }^{\mathrm{crit}}$ for a Fermi gas (red), a purely dipolar Bose gas (blue), and a Bose gas with ${\epsilon }_{\mathrm{dd}}=6$ (green).

Figure 2

Stability boundaries based on the density of a Fermi gas (red curves), a purely dipolar Bose gas (blue), and a dipolar gas with ${\epsilon }_{\mathrm{dd}}=6$ (green) using Hartree-Fock theory (solid) and Hartree theory (dashed). Thin lines are from Eq. (25) for $t>2$ (almost obscured by the full results) and Eq. (26) for $t<4$.

Figure 3

Stability boundaries of a (a) Fermi and (b) purely dipolar Bose gas with Hartree-Fock theory (solid) and Hartree theory (dashed) for $\lambda =0.1$ (blue), $\lambda =1$ (green), and $\lambda =10$ (red). Corresponding results for a (a) Bose and (b) Fermi gas are shown as faint curves. We use $T_F^0=\hslash \omega {\left(6N\right)}^{1/3}/k_B$ and $T_c^0=\hslash \omega {[N/\zeta \left(3\right)]}^{1/3}/k_B$. Also shown are Hartree-Fock results from Ref. [26] ($\times$). The inset to (b) enlarges the double instability region near $T_c^0$ marked by the box.

Figure 4

Absolute local momentum distortion at instability using Hartree-Fock theory of a Fermi gas ($\delta <0$, red), a Bose gas ($\delta >0$), purely dipolar (blue), and with ${\epsilon }_{\mathrm{dd}}=6$ (green). Also shown are the HLF limits as $T\to \infty$ (thin lines) and $T\to 0$ ($\times$) showing qualitative agreement with the Hartree-Fock results.