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Scientific Reports

High-precision multiparameter estimation of mechanical force by quantum optomechanics

László Ruppert, Andrey A. Rakhubovsky, Radim Filip

Published Sep 26, 2022• 4 citations
Publisher

Abstract

A nanomechanical oscillator can be used as a sensitive probe of a small linearized mechanical force. We propose a simple quantum optomechanical scheme using a coherent light mode in the cavity and weak short-pulsed light-matter interactions. Our main result is that if we transfer some displacement to the mechanical mode in an initialization phase, then a much weaker optomechanical interaction is enough to obtain a high-precision multiparameter estimation of the unknown force. This approach includes not only estimating the displacement caused by the force but also simultaneously observing the phase shift and squeezing of the mechanical mode. We show that the proposed scheme is robust against typical experimental imperfections and demonstrate the feasibility of our scheme using orders of magnitude weaker optomechanical interactions than in previous related works. Thus, we present a simple, robust estimation scheme requiring only very weak light-matter interactions, which could open the way to new nanomechanical sensors.

DOI
10.1038/s41598-022-20150-6

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A nanomechanical oscillator can be used as a sensitive probe of a small linearized mechanical force. We propose a simple quantum optomechanical scheme using a coherent light mode in the cavity and weak short-pulsed light-matter interactions. Our main result is that if we transfer some displacement to the mechanical mode in an initialization phase, then a much weaker optomechanical interaction is enough to obtain a high-precision multiparameter estimation of the unknown force. This approach includes not only estimating the displacement caused by the force but also simultaneously observing the phase shift and squeezing of the mechanical mode. We show that the proposed scheme is robust against typical experimental imperfections and demonstrate the feasibility of our scheme using orders of magnitude weaker optomechanical interactions than in previous related works. Thus, we present a simple, robust estimation scheme requiring only very weak light-matter interactions, which could open the way to new nanomechanical sensors.
Nano- and micromechanical oscillators act as great sensors of a wide variety of signals, but their sensitivity and bandwidth can be limited by quantum backaction imposed by optomechanical displacement measurement. We experimentally demonstrate a new paradigm for optomechanical measurement and control based on strong interactions with short light pulses. Using unique nanophotonic optomechanical cavities, we show that single pulsed measurements can achieve sub-quantum-limit resolution. Moreover, we demonstrate a new protocol to deterministically produce squeezed mechanical states, which can reduce single-quadrature fluctuations to arbitrarily small magnitudes. We discuss the application of the resulting squeezing and entanglement for mechanical quantum sensing.
We propose a sensing scheme for detecting weak forces that achieves Heisenberg-limited sensitivity without relying on entanglement or other non-classical resources. Our scheme utilizes coherent averaging across a chain of N optomechanical cavities, unidirectionally coupled via a laser beam. As the beam passes through the cavities, it accumulates phase shifts induced by a common external force acting on the mechanical elements. Remarkably, this fully classical approach achieves the sensitivity scaling typically associated with quantum-enhanced protocols, providing a robust and experimentally feasible route to precision sensing. Potential applications range from high-sensitivity gravitational field measurements at the Large Hadron Collider to probing dark matter interactions and detecting gravitational waves. This work opens a new pathway for leveraging coherent light-matter interactions for force sensing.
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}\mathcal{B}_{\rm MI}=\max\{\mathcal{B}_S,\mathcal{B}_R\}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\mathcal{B}_{\rm MI}BMI​, thereby enhancing multiparameter estimation precision over a broad range of operating conditions. Coherent feedback can further reduce BMI\mathcal{B}_{\rm MI}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 This study presents an effective scheme for estimating the weak Coulomb force through a hybrid optomechanical system. In this scheme, information regarding the weak Coulomb force can be transferred to the cavity field through the coupling between the cavity field and the mechanical oscillator, and it can be fully extracted from the cavity field when the cavity field and the mechanical oscillator are disentangled. We employed the quantum Fisher information and the error propagation formula to analyze the effects of the coupling strength, the cavity average photon number and the Coulomb force on the estimation precision. We observed that the estimation precision can be improved by increasing the coupling strength. In addition, when choosing the proper value of average photon number and the proper range of the Coulomb force, we can approach the theoretical-attainable precision determined by quantum Fisher information. Particularly, the magnitude of the estimated weak Coulomb force in this scheme is up to 10 −10 N or even smaller, which is better than the results obtained from previously conducted studies. Moreover, the decoherence of the mechanical oscillator and that of the cavity field are considered by solving the master equation. We show that the leakage of photons from the cavity greatly influences the measurement precision.
Cavity optomechanics originated from the research of interferometric detection of gravitational waves, and later became a fast-growing area of techniques and approaches ranging from the fields of atomic, molecular, and optical physics to nano-science and condensed matter physics as well. Recently, it focused on the exploration of operating mechanical oscillators deep in the quantum regime, with an interest ranging from quantum-classical interface tests to high-precision quantum metrology. In this paper, recent theoretical work of our group in the field of quantum measurement with cavity optomechanical systems is reviewed. We explore the quantum measurement theory and its applications with several unconventional cavity optomechanical schemes working in the quantum regime. This review covers the basics of quantum noises in the cavity optomechanical setups and the resulting standard quantum limit of precision displacement and force measurement. Three novel quantum measurement proposals based on the hybrid optomechanical system are introduced. First, we describe a quantum back-action insulated weak force sensor. It is realized by forming a quantum-mechanics-free subsystem with two optomechanical oscillators of reversed effective mass. Then we introduce a role-reversed atomic optomechanical system which enables the preparation and the quantum tomography of a variety of non-classical states of atoms. In this system, the cavity field acts as a mechanical oscillator driven by the radiation pressure force from an ultracold atomic field. In the end, we recommend a multimode optomechanical transducer that can detect intensities significantly below the single-photon level via adiabatic transfer of the microwave signal to the optical frequency domain. These proposals demonstrate the possible applications of optomechanical devices in understanding of quantum-classical crossover and in achieving quantum measurement limit.
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.