We solve the two-body problem of ultracold heteronuclear atoms in a quasi-two-dimensional (quasi-2D) geometry. The quasi-2D confinement is realized by a harmonic trap along the longitudinal ($z$) direction, with different trap frequencies for the two atoms, as in many current experiments on ultracold heteronuclear gases. As a consequence, the longitudinal center-of-mass (c.m.) motion is coupled to the relative motion, which significantly complicates the two-body problem. We solve this problem exactly and derive the 2D scattering length $a_{2\mathrm{D}}$, the 2D effective range parameter $R_{2\mathrm{D}}$, and the bound-state energies, as functions of the $s$-wave scattering length and effective range of the two atoms in free 3D space. We show that multiple 2D scattering resonances can be induced by the coupling between the longitudinal c.m. and relative motion. Around these resonances, $a_{2\mathrm{D}}$ varies rapidly with the 3D scattering parameters, while $R_{2\mathrm{D}}$ is strongly enhanced. Since the effective pairwise interaction in quasi-2D ultracold gases is determined by the two-body scattering amplitudes and bound-state energies, our results can be used for manipulating the effective 2D interatomic interaction in quasi-2D ultracold heteronuclear gases by tuning the confinement frequencies and the 3D scattering parameters.

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• Atomic & molecular collisions
• Ultracold collisions
• Atomic gases