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 the estimation of a thermal bath temperature 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 for estimating both parameters. We compute the quantum Fisher information of the probe for two different interaction models between the resonators. Our results show that the counter-rotating 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.
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 the estimation of a thermal bath temperature 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 for estimating both parameters. We compute the quantum Fisher information of the probe for two different interaction models between the resonators. Our results show that the counter-rotating 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.
We present a quantum thermometry method utilizing an optomechanical system composed of an optical field coupled to a mechanical resonator for measuring the unknown temperature of a thermal bath. To achieve this, we connect a thermal bath to the mechanical resonator and perform measurements on the optical field, serving as a probe thermometer. Using the open quantum systems approach, we numerically calculate the quantum Fisher information for the probe. We find that, in specific parameter regimes, the system exhibits clusters of densely packed energy eigenstates interspaced with substantial energy gaps. This clustering of energy levels results in quasi-degeneracy within these energy eigenstate groups and hence widens the operational range of temperature estimation. Moreover, thermal sensitivity, especially at low temperatures, can be further boosted by appropriately tuning the essential system parameters.
Abstract An experimentally feasible magnetometer based on a dual‐coupling optomechanical system is proposed, where the radiation‐pressure coupling transduces the magnetic signal to the optical phase, and the quadratic optomechanical interaction induces a periodic squeezing effect. The latter not only amplifies the signal to be measured, but also accelerates the signal transducing rate characterized by an experimentally observable phase accumulation efficiency. In the vicinity of opto‐mechanical decoupled time, the ultimate bound to the estimability of magnetic signal is proportional to , and then the optimized accuracy of estimation can be enhanced nearly three orders with a controllable squeezing parameter . Moreover, this proposal is robust against the mechanical thermal noise, and the sensitivity of a specific measurement can reach to the order of in the presence of dissipations and without ground state cooling of mechanical oscillator. The proposal fundamentally broadens the fields of quantum metrology and cavity optomechanics, with the potential application for on‐chip magnetic detection with high precision.
Multiparameter quantum estimation in open optomechanical systems is fundamentally constrained by dissipation, thermal fluctuations, and measurement incompatibility. In this work, we investigate a coupled cavity optomechanical platform in which two mechanical modes interact with driven optical cavities, two mode squeezed vacuum, intracavity degenerate parametric amplification, and coherent optical feedback. Using the continuous variable Gaussian state formalism, we derive the linearized quantum Langevin dynamics and steady state covariance matrix and evaluate the quantum Fisher information matrices associated with simultaneous estimation of the optomechanical coupling strength and cavity dissipation rate. We characterize the precision bounds using the symmetric and right logarithmic derivative formalisms and employ BMI=max{BS,BR} as a comparative figure of merit within the SLD/RLD framework. We find that parametric amplification can substantially reduce the most informative bound, BMI, thereby enhancing multiparameter estimation precision over a broad range of operating conditions. Coherent feedback can further reduce BMI and improve the estimation precision, particularly in the strong feedback regime. Moreover, the simultaneous presence of coherent feedback, parametric amplification, and squeezed light injection provides a combined mechanism for controlling quantum fluctuations and parameter dependent correlations, leading to enhanced and more robust multiparameter estimation. We further analyze the dynamical and steady state regimes to identify the parameter regions in which these quantum resources provide the largest metrological gain. Our results establish coupled cavity optomechanics as a flexible platform for quantum-noise engineering in multiparameter sensing.
Abstract We address the dephasing dynamics of the quantum Fisher information for the process of quantum thermometry with probes coupled to squeezed thermal baths via the nondemolition interaction. We also calculate the upper bound for the parameter estimation and investigate how the optimal estimation is affected by the initial conditions and decoherence, particularly the squeezing parameters. Moreover, the feasibility of the optimal measurement of the temperature is discussed in detail. Then, the results are generalized for entangled probes and the multi-qubit scenarios for probing the temperature are analysed. Our results show that the squeezing can decrease the number of channel uses for optimal thermometry. Comparing different schemes for multi-qubit estimation, we find that an increase in the number of the qubits, interacting with the channel, does not necessarily vary the precision of estimating the temperature. Besides, we discuss the enhancement of the quantum thermometry using the parallel strategy and starting from the W state.
Accurate temperature estimation in the quantum and cryogenic regimes remains a fundamental challenge. Here, we investigate nonequilibrium quantum thermometry using a single-qubit probe coupled to a bosonic bath through noncommuting interaction operators, which unify pure dephasing and dissipative dynamics within a spin-boson model. We show that the interference between these two coupling channels induces strong non-Markovian feedback between populations and coherences, leading to coherence trapping and enhanced thermal sensitivity. Remarkably, by tuning the coupling structure, the probe's temperature sensitivity exhibits a quadratic low-temperature scaling, even under weak coupling. Moreover, while coherence-based measurements are formally suboptimal, they become the most informative in the early nonequilibrium regime, where memory effects dominate. Our findings identify noncommutative system-bath couplings as a practical and tunable resource for achieving high-precision quantum thermometry in realistic open-system architectures.
We study the performance of quantum sensors composed of four qubits arranged in different geometries for magnetometry and thermometry. The qubits interact via the transverse-field Ising model with both ferromagnetic and antiferromagnetic couplings, maintained in thermal equilibrium with a heat bath under an external magnetic field. Using quantum Fisher information, we evaluate the metrological precision of these sensors. For ferromagnetic couplings, weakly connected graphs (e.g., the chain graph, P_4) perform optimally in estimating weak magnetic fields, whereas highly connected graphs (e.g., the complete graph, K_4) excel at strong fields. Conversely, K_4 achieves the highest sensitivity for temperature estimation in the weak-field regime. In the antiferromagnetic case, we uncover a fundamental trade-off dictated by spectral degeneracy: configurations with non-degenerate energy spectra - such as the pan-like graph (three qubits in a triangle with the fourth attached) - exhibit strong magnetic field sensitivity due to their pronounced response to perturbations. In contrast, symmetric structures like the square graph, featuring degenerate energy levels (particularly ground-state degeneracy), are better suited for precise thermometry. Notably, our four-qubit sensors achieve peak precision in the low-temperature, weak-field regime. Finally, we introduce a spectral sensitivity measure that quantifies energy spectrum deformations under small perturbations, providing a simple heuristic indicator of metrological sensitivity.