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 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.
Comments
20 pages, 12 figures. Accepted for publication in PRA; title modified, two new appendices added, and additional text and figures included
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 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 theoretically investigate the steady-state bipartite entanglements, mechanical ground-state cooling, and mechanical quadrature squeezing in a hybrid electro-optomechanical system where a moving membrane is linearly coupled to the microwave field mode of an LC circuit, while it simultaneously interacts both linearly and quadratically with the radiation pressure of a single-mode optical cavity. We show that by choosing a suitable sign and amplitude for the quadratic optomechanical coupling (QOC), one can achieve enhanced and thermally robust stationary bipartite entanglement between the subsystems, improved mechanical ground-state cooling, and Q-quadrature squeezing of the mechanical mode beyond the 3-dB limit of squeezing. In particular, we find that in the presence of QOC with negative sign and in the resolved sideband regime the bipartite optical-mechanical entanglement can be increased by about 2 orders of magnitude around the temperature of 1 mK, and it can be preserved against thermal noise up to the ambient temperature of 0.1 K. Furthermore, the QOC with positive sign can give rise to the enhancement of the mechanical ground-state cooling by about 1 order of magnitude in the optical and microwave red-detuned regime. We also find that for the positive sign of QOC and near the microwave resonance frequency the squeezing degree of the Q quadrature of the mechanical mode can be amplified up to 15 dB. Such a hybrid electro-optomechanical system can serve as a promising platform to engineer an improved entangled source for quantum sensing as well as quantum information processing.