Dipolar confinement-induced molecular states in harmonic waveguides

The bound states of two identical dipoles in a harmonic waveguide are investigated. In the regime of weak dipole-dipole interactions, the local frame transformation (LFT) method is applied to determine the spectrum of dipolar confinement-induced bound states analytically. The accuracy of the LFT approach is discussed by comparing the analytical results with the numerical ones based on a solution of the close-coupling equations. It is found that close to the threshold energy in the waveguide, the LFT method needs to include more partial wave states to obtain accurate bound state energies. As the binding energy increases, the LFT method using a single partial wave state becomes more accurate. We also compare the bound states in waveguides and in free space. For the bosonic case, the s-wave dominated bound state looks like a free-space state when its energy is below a certain value. For the fermionic case, the p-wave dominated bound state energies in waveguides and in free-space coincide even close to zero energy.