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We study a linear rotor in a bosonic bath within the angulon formalism. Ourfocus is on systems where isotropic or anisotropic impurity-boson interactionssupport a shallow bound state. To study the fate of the angulon in the vicinityof bound-state formation, we formulate a beyond-linear-coupling angulonHamiltonian. First, we use it to study attractive, spherically symmetricimpurity-boson interactions for which the linear rotor can be mapped onto astatic impurity. The well-known polaron formalism provides an adequatedescription in this limit. Second, we consider anisotropic potentials, and showthat the presence of a shallow bound state with pronounced anisotropiccharacter leads to a many-body instability that washes out the angulondynamics.

Linear rotor in an ideal Bose gas near the threshold for binding