Magnetostriction and exchange effects in trapped dipolar Bose and Fermi gases

We examine the magnetostrictive position and momentum space distortions that occur in harmonically confined dipolar Bose and Fermi gases. Direct interactions give rise to position space magnetostriction and exchange interactions give rise to momentum space magnetostriction. While the position space magnetostriction is similar in Bose and Fermi systems, the momentum space magnetostriction is markedly different: The Bose gas momentum distribution distorts in the opposite sense to that of the Fermi gas. By relating exchange effects to short-range correlations between the particles we discuss the energetic origin of this difference. Our main calculations are based on Hartree-Fock theory, but we also provide analytic approximations for the magnetostriction effects at zero and finite temperature. Our predictions should be verifiable in current experiments with ultracold polar molecules.

Figure 1

Position space distortion for fermions using HF (solid curves) and Hartree (diamonds), and for bosons using HF (dashed curves) and Hartree (circles); also the predictions from (16) (crosses) and (19) (thin curves) with $\lambda =0.1$ [blue (dark gray)], 1 [green (light gray)], and 10 [red (gray)]. (a) Bosons and fermions at $T=1.5T_c^0\approx 0.78T_F^0$. (b) Fermions with $D_t=1$; (inset) fermions at $T=0$.

Figure 2

Momentum distortion for fermions (solid curves) and bosons (dashed curves) and the predictions from (15) (black cross) and (18) (thin black curves) with $\lambda =0.1$ [blue (dark gray)], 1 [green (light gray)], and 10 [red (gray)]. (a) Bosons and fermions at $T=1.5T_c^0\approx 0.78T_F^0$. (b) Fermions with $D_t=1$; (inset) fermions at $T=0$.

Figure 3

Second-order correlation function for $\lambda =10$, $D_t=4$, $N={10}^5$, and $T=1.1T_c^0\approx 0.57T_F^0$ for Fermi (solid curve) and Bose (dashed curve) for $\mathbf{r}=\rho \widehat{\rho }$ (blue, dark gray) and $\mathbf{r}=z\widehat{z}$ (red, light gray). Inset shows the density profiles for comparison.

Figure 4

(a) The function $J\left(u\right)$ (solid curve) showing $J(-1)=\frac{2}{3}$ (cross), $J\left(0\right)=0$ (plus), and $J\left(u\right)\to -\frac{1}{3}$ as $u\to \infty$ (dashed line). (b) The term appearing in (16) and (19) as a function of the aspect ratio showing $J^{\prime }\left(0\right)=-\frac{2}{15}$ at $\lambda =1$ (plus).