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We study ultracold long-range collisions of heteronuclear alkali-metal dimerswith a reservoir gas of alkali-metal Rydberg atoms in a two-photon laserexcitation scheme. In a low density regime where molecules remain outside theRydberg orbits of the reservoir atoms, we show that the two-photonphotoassociation (PA) of the atom-molecule pair into a long-range bound trimerstate is efficient over a broad range of atomic Rydberg channels. As a casestudy, we obtain the PA lineshapes for the formation of trimers composed of KRbmolecules in the rovibrational ground state and excited Rb atoms in theasymptotic Rydberg levels $n^{2}S_j$ and $n^{2}D_j$, for $n=20-80$. We predictatom-molecule binding energies in the range $10-10^3$ kHz for the firstvibrational state below threshold. The average trimer formation rate is order$10^8\, {\rm s}^{-1}$ at 1.0 $\mu$K, and depends weakly on the principalquantum number $n$. Our results set the foundations for a broader understandingof exotic long range collisions of dilute molecules in ultracold atomic Rydbergreservoirs.

Laser-assisted binding of ultracold polar molecules with Rydberg atoms in the van der Waals regime