Confinement induced resonances in anharmonic waveguides

TL;DR

This paper develops a theory for anharmonic confinement-induced resonances in waveguides, explaining experimental observations of resonance splitting and new resonances in quasi-1D and quasi-2D systems due to anharmonic effects.

Contribution

The paper introduces a comprehensive theory of ACIR, accounting for anharmonic effects and explaining experimental phenomena not captured by harmonic models.

Findings

Resonance splitting in anisotropic quasi-1D systems

New resonance for repulsive interactions in quasi-2D systems

Excellent agreement with experimental resonance positions

Abstract

We develop the theory of anharmonic confinement-induced resonances (ACIR). These are caused by anharmonic excitation of the transverse motion of the center of mass (COM) of two bound atoms in a waveguide. As the transverse confinement becomes anisotropic, we find that the COM resonant solutions split for a quasi-1D system, in agreement with recent experiments. This is not found in harmonic confinement theories. A new resonance appears for repulsive couplings ($a_{3D}>0$) for a quasi-2D system, which is also not seen with harmonic confinement. After inclusion of anharmonic energy corrections within perturbation theory, we find that these ACIR resonances agree extremely well with anomalous 1D and 2D confinement induced resonance positions observed in recent experiments. Multiple even and odd order transverse ACIR resonances are identified in experimental data, including up to N=4 transverse COM quantum numbers.