Standard optomechanical sensors operating in the low-temperature regime often face fundamental precision limits imposed by vacuum fluctuations. Here we demonstrate that moving beyond conventional radiation-pressure interactions and exploiting quadratic coupling can surpass these limits, generating intrinsic squeezing and non-Gaussian features in the probe state. We study quantum thermometry and magnetometry in a coupled two-resonator system, focusing on estimating the temperature of a thermal bath and an external magnetic field. The resonators are assumed to be in thermal equilibrium with a common bath, while a weak magnetic field acts on one of the resonators. We perform measurements on a single resonator, which serves as the probe to estimate both parameters. We compute the quantum Fisher information of the probe for two different interaction models between the resonators. Our results show that the counterrotating terms in the quadratic interaction naturally induce squeezing at intermediate coupling and strong non-Gaussian correlations as the coupling increases further. These effects yield orders-of-magnitude enhancement in sensitivity in the low-temperature and weak-field regimes compared to standard radiation-pressure couplings. Finally, we investigate multiparameter estimation and find that, although the optimal measurements remain compatible, statistical correlations between parameters prevent the simultaneous estimation of temperature and magnetic field from attaining single-parameter precision.

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• Quantum metrology
• Quantum parameter estimation