Two-dimensional dipolar scattering with a tilt

We study two-body dipolar scattering in two dimensions with a tilted polarization axis. This tilt reintroduces the anisotropic interaction in a controllable manner. As a function of this polarization angle, we present the scattering rates in both the threshold and semiclassical regimes. Additionally, we study the properties of the molecular bound states as a function of the polarization angle.

Figure 1

The Born approximation (BA) for fermions shown as a function of the polarization angle ($\alpha$). We have plotted the energy independent: $\sigma /{\sigma }_{\mathit{BA}}^{\mathrm{odd}}(\alpha =0)$ as a function of $\alpha$ for $Dk={10}^{-1}$ (red open circle), ${10}^{-2}$ (blue +), ${10}^{-3}$ (green dash), ${10}^{-4}$ (purple open diamond), and the BA is shown as a bold blue line.

Figure 2

The total and inelastic $\sigma /{\sigma }_{\mathit{SC}}$ as a function of polarization angle ($\alpha$) is plotted for four different values of $Dk$: 10 (black solid line), 35 (red dashed), 53 (blue circles), and 80 (green +). The inelastic data is when $m$ is changed in a collisions, and in this case, it makes up a significant fraction of the scattering.

Figure 3

The binding energies for the first and second $m=0$ bound states at $\alpha /\pi =$ 0.25, 0.275, 0.3, 0.35, 0.4, and 0.5.  The universal 2D binding energy at large $a/D$ is shown as a blue dashed line.

Figure 4

(a) The size of the molecules are shown as a function of $a/D$ for various angles for both the first (black) and second (red circles) resonance. The universal form of the size is shown as a dashed blue line. (b) The partial wave population is shown (first bound state only), for all six angles as a function of $a/D$. The extreme angles are shown as solid circles ($\alpha /\pi =0.25$) and dashed lines ($\alpha /\pi =0.5$) for partial waves $m=0$ (black), $\left|m\right|=2$ (red), and $\left|m\right|=4$ (blue).

Figure 5

$\rho |\psi \left(\vec{\rho }\right){|}^2$ for as follows: $\alpha /\pi =$ (a) 0.25, (b) 0.35, (c) 0.5 for $a/D$ (i) 0.1, (ii) 1, (iii) 10, and (iv) 100. The contours indicated are drawn ever 20$\%$ of maximum value, with the largest 80$\%$ contour being drawn as red. The solid gray circle in the middle is the hard sphere short-range interaction. The scale changes for every plot on the left (i) and (ii); in contrast the scale is the same for the plots on the right (iii) and (iv) when the system is in the large $a/D$ regime.