Atom-Atom Scattering under Cylindrical Harmonic Confinement: Numerical and Analytic Studies of the Confinement Induced Resonance

It was recently predicted [Phys. Rev. Lett. 81, 938 (1998)] that atom-atom scattering under transverse harmonic confinement is subject to a “confinement-induced resonance” where the effective one-dimensional coupling strength diverges at a particular ratio of the confinement and scattering lengths. As the initial prediction made use of the zero-range pseudopotential approximation, we now report numerical results for finite-range interaction potentials that corroborate this resonance. In addition, we now present a physical interpretation of this effect as a novel type of Feshbach resonance in which the transverse modes of the confining potential assume the roles of “open” and “closed” scattering channels.

Figure 1

The 1D coupling constant, $g_{1\mathrm{D}}$, in units of ${\hslash }^2/(\mu a_{\perp })$, as a function of $a/a_{\perp }$ for the 6–12 potential (stars) and the spherical well potential (triangles), as compared to the pseudopotential theory (solid line). The inset shows $g_{1\mathrm{D}}$ in units of ${\hslash }^2/(\mu |a|)$ versus $a_{\perp }/a$, to illustrate the behavior in the tight-confinement regime ($a_{\perp }/a\to 0$).

Figure 2

Numerical bound-state energies and schematic of the Feshbach resonance scheme. The solid lines correspond to the analytic pseudopotential results.