The major goal of quantum metrology (QM) is to exploit the quantum resources to raise the measurement precision (MP) as high as possible. While the quantum resources such as squeezing have been widely explored, light-matter interaction systems set up a highly controllable platform applicable for QM in novel pursuit of high MP. However, critical QM by the conventional linear interaction is confronted with the limitation of a local parameter regime, restriction of a low-frequency-limit condition, and the detrimental problem of diverging preparation time of probe state (PTPS). This work shows that mixed interactions by linear and nonlinear light-matter couplings in the presence of bias field can provide various quantum resources, including squeezing, degeneracy lifting, displacement, and quantum phase transition. These resources manifest high sensitivity for QM as demonstrated by analytically obtained critical exponents or exponential behavior of quantum Fisher information. We find that these sensitivity resources can be combined to upgrade the upper bound of MP by many orders over the widely applied squeezing resource. As further advantages in contrast to the linear critical QM, such an upgraded metrology protocol can have a global parameter regime, break the frequency-limit restriction, and avoid the diverging PTPS. Our work paves a way to exploit and combine all the resources in momentum, position, and spin spaces to maximize the MP and expand the applicable conditions simultaneously.

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• Light-matter interaction
• Quantum metrology