We propose that a pulsed quantum optomechanical system can be applied to the problem of quantum parameter estimation, which targets yielding a higher precision of parameter estimation utilizing quantum resources than using classical methods. Concentrating mainly on the quantum Fisher information with respect to the mechanical frequency, we find that the corresponding precision of parameter estimation for the mechanical frequency can be enhanced by applying applicable optical resonant pulsed driving to the cavity of the optomechanical system. Further investigation shows that the mechanical squeezing resulting from the optical pulsed driving is the quantum resource used in optimal quantum estimation of the frequency.
We propose that a pulsed quantum optomechanical system can be applied to the problem of quantum parameter estimation, which targets yielding a higher precision of parameter estimation utilizing quantum resources than using classical methods. Concentrating mainly on the quantum Fisher information with respect to the mechanical frequency, we find that the corresponding precision of parameter estimation for the mechanical frequency can be enhanced by applying applicable optical resonant pulsed driving to the cavity of the optomechanical system. Further investigation shows that the mechanical squeezing resulting from the optical pulsed driving is the quantum resource used in optimal quantum estimation of the frequency.
We study the fundamental bounds on precision measurements of parameters contained in a time-dependent nonlinear optomechanical Hamiltonian, which includes the nonlinear light-matter coupling, a mechanical displacement term, and a single-mode mechanical squeezing term. By using a recently developed method to solve the dynamics of this system, we derive a general expression for the quantum Fisher information and demonstrate its applicability through three concrete examples: estimation of the strength of a nonlinear light-matter coupling, the strength of a time-modulated mechanical displacement, and a single-mode mechanical squeezing parameter, all of which are modulated at resonance. Our results can be used to compute the sensitivity of a nonlinear optomechanical system to a number of external and internal effects, such as forces acting on the system or modulations of the light-matter coupling.
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.
We study the dynamics of an optomechanical system consisting of a single-mode optical field coupled to a mechanical oscillator, where the nonlinear interaction includes both linear and quadratic terms in the oscillator's position. We present an analytical solution to this quantum-mechanical Hamiltonian problem by employing the formalism of two-phonon coherent states. Quantum estimation theory is applied to the resulting state of the optical field, with a focus on evaluating the quantum Fisher information with respect to the strength of the quadratic coupling. Our estimation scheme employs balanced homodyne photodetection and demonstrates that the corresponding classical Fisher information can reach the quantum Fisher information limit, with the phase of the local coherent oscillator playing a crucial role.
Accurate simultaneous estimation of temperature and effective detuning is crucial for understanding, controlling, and optimizing optomechanical systems. Temperature characterizes the thermal state and mechanical properties, while detuning governs the light-motion interaction, influencing stability and enabling diverse quantum applications. Precise estimates of these parameters are therefore essential to exploit the full potential of such systems in high-precision metrology and the exploration of macroscopic quantum phenomena. In this work we investigate the simultaneous estimation of the effective detuning Δ and the mirror temperature T in a Fabry-Pérot cavity system, with a particular focus on the performance of heterodyne detection. Using analytical expressions for the quantum Fisher information matrices (QFIM) derived from the symmetric logarithmic derivative (SLD) and the right logarithmic derivative (RLD), we demonstrate that the quantum Cramér-Rao bound associated with the RLD is consistently lower than that based on the SLD, highlighting superior estimation precision. This gap between the SLD- and RLD-based bounds becomes especially pronounced in certain physical regimes, emphasizing the relevance of choosing the appropriate formalism in noncommutative estimation scenarios. From a physical perspective, the improved estimation performance stems from the fact that temperature directly influences thermal fluctuations in the mechanical mode, while the effective detuning modulates the strength of the optomechanical interaction, shaping the information exchange between optical and mechanical subsystems. We showed that using higher optical power, greater cavity decay rate, increased photon and phonon numbers, and reduced coupling strength improves the precision of both parameter estimates. These physical mechanisms affect the available quantum resources in the system—such as squeezing, entanglement, and state purity—which in turn determine the ultimate sensitivity achievable. Furthermore, our analysis shows that heterodyne detection can, under certain conditions, approach the ultimate precision set by the QFIM. Thus, a measurement strategy based on heterodyne detection could enable the efficient estimation of temperature, achieving performance close to that of ideal quantum-limited strategies.
We show that strongly amplified dynamical responses in cavity optomechanical systems can be harnessed for enhanced quantum sensing. By tuning the optomechanical interaction to a regime of enhanced susceptibility, weak perturbations produce disproportionately large changes in the system response, leading to substantially improved estimation precision. Using Gaussian estimation theory, we demonstrate that the quantum Fisher information exhibits a divergent scaling as the perturbation strength decreases, implying a corresponding suppression of the estimation error. We further show that heterodyne detection of the output cavity field yields the classical Fisher information with the same asymptotic scaling as the quantum Fisher information, demonstrating that the enhanced sensitivity is accessible with a standard measurement protocol. These results identify amplified optomechanical dynamics as a controllable resource for quantum enhanced sensing and metrology.
In this article we present an experimental proposal for quantum enhanced estimation of optomechanical parameters. The precision of the estimation is improved by using the technique of weak value amplification, which can enlarge the radiation pressure effect of a single-photon on a nano/micro mechanical oscillator. This task is accomplished by using two interferometric setups. Single-photon pulses are sent through one interferometer, producing a maximally path entangled state which drives the cavity optomechanical system. The photons are then postselected in one of the detectors in the output. A second interferometer, whose operation is triggered by every successful postselection, performs an optical measurement of the phase shift generated by the optomechanical system on a classical beam, which encodes the information of the optomechanical parameters. In the presence of fully time-correlated noise, we show that the Fisher information is improved as compared to a standard measurement that employs no postselection.