  We demonstrate the failure of the adiabatic Born-Oppenheimer approximation to
describe the ground state of a quantum impurity within an ultracold Fermi gas
despite substantial mass differences between the bath and impurity species.
Increasing repulsion leads to the appearance of non-adiabatic couplings between
the fast bath and slow impurity degrees of freedom which reduce the parity
symmetry of the latter according to the pseudo Jahn-Teller effect. The presence
of this mechanism is associated to a conical intersection involving the
impurity position and the inverse of the interaction strength which acts as a
synthetic dimension. We elucidate the presence of these effects via a detailed
ground state analysis involving the comparison of ab initio fully-correlated
simulations with effective models. Our study suggests ultracold atomic
ensembles as potent emulators of complex molecular phenomena.
