  We propose a quantum metrology protocol for measuring frequencies and weak
forces based on a periodic modulating quantum Jahn-Teller system composed of a
single spin interacting with two bosonic modes. We show that in the first order
of the frequency drive the time-independent effective Hamiltonian describes
spin-dependent interaction between the two bosonic modes. In the limit of
high-frequency drive and low bosonic frequency the quantum Jahn-Teller system
exhibits critical behaviour which can be used for high-precision quantum
estimation. A major advantage of our scheme is the robustness of the system
against spin decoherence which allows to perform parameter estimations with
measurement time not limited by spin dephasing.
