Phonon-Mediated Attraction between Heavy Molecules in a Bosonic Bath

Starting from the molecular-phonon interaction Hamiltonian in angulon form, we analytically calculate the second-order scattering process mediated by the exchange of a single virtual phonon between two molecules and derive an effective Fröhlich-type intermolecular interaction. For several typical molecular states with low rotational angular momentum quantum numbers, we compute the relative interaction strength. The results reveal that attractive interactions appear in states with the maximum magnetic quantum number of rotational angular momentum, i.e., in-plane polarized molecular states. For the λ = 2 interaction channel, the attraction mediated by exchanging an in-plane d-wave symmetric phonon (magnetic quantum number μ = ±2) is several times stronger than that mediated by exchanging an in-plane s-wave symmetric (μ = 0) phonon.