  Classical dynamical systems close to a critical point are known to act as
efficient sensors due to a strongly nonlinear response. We explore such systems
in the quantum regime by modeling a quantum version of a driven van der Pol
oscillator. We find the classical response survives down to one excitation
quantum. At very weak drives, genuine quantum features arise, including
diverging and negative susceptibilities. Further, the linear response is
greatly enhanced by using a strong incoherent pump. These results are largely
generic and can be probed in current experimental platforms suited for quantum
sensing.
