Suppression of Quantum Scattering in Strongly Confined Systems

We demonstrate that scattering of particles strongly interacting in three dimensions (3D) can be suppressed at low energies in a quasi-one-dimensional (1D) confinement. The underlying mechanism is the interference of the $s$- and $p$-wave scattering contributions with large $s$- and $p$-wave 3D scattering lengths being a necessary prerequisite. This low-dimensional quantum scattering effect might be useful in “interacting” quasi-1D ultracold atomic gases, guided atom interferometry, and impurity scattering in strongly confined quantum wire-based electronic devices.

Figure 1

(a) The 3D scattering lengths $a_s$ (black) and $a_p$ (red) and (b) the quasi-1D transmission coefficients $T$ for a few values of $a_{\perp }$ and fixed $\epsilon =0.002(k_0=0.0632)$. For a discussion, see text.

Figure 2

The influence of the center of mass coupling on the transmission $T$ for ${\omega }_2=0.02$ and $\epsilon =0.002$. Here ${\omega }_1=1.35{\omega }_2$, $a_{\perp }/r_0=6.52$ (solid curve) and ${\omega }_1={\omega }_2$, $a_{\perp }/r_0=7.07$ (dotted curve).

Figure 3

Scattering lengths and transmission for the square-well potential (depth $V_0$ and radius $r_0$) for ${\omega }_1={\omega }_2$ and $\epsilon =0.04$. (a) $a_s=a_s(V_0)$ (black) and $a_p=a_p(V_0)$ (red). (b) $T=T(V_0)$ for several values of $a_{\perp }$ [see Fig. 1b]. For comparison, $f_{0u}$ is omitted in the dashed curves and only the $s$-wave CIR behavior $T\approx 0$ due to large $a_s$ appears.