Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1910.04485 · Physical Review A

Optimal estimation with quantum optomechanical systems in the nonlinear regime

Fabienne Schneiter, Sofia Qvarfort, Alessio Serafini, André Xuereb, Daniel Braun, Dennis Rätzel, David Edward Bruschi

Published Mar 20, 2020• 37 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physreva.101.033834

Related papers

Optimal estimation of time-dependent gravitational fields with quantum optomechanical systems

Sofia Qvarfort, Plato, ADK, Bruschi, DE +4 more

We study the fundamental sensitivity that can be achieved with an ideal optomechanical system in the nonlinear regime for measurements of time-dependent gravitational fields. Using recently developed methods to solve the dynamics of a nonlinear optomechanical system with a time-dependent Hamiltonian, we compute the quantum Fisher information for linear displacements of the mechanical element due to gravity. We demonstrate that the sensitivity can not only be further enhanced by injecting squeezed states of the cavity field, but also by modulating the light--matter coupling of the optomechanical system. We specifically apply our results to the measurement of gravitational fields from small oscillating masses, where we show that, in principle, the gravitational field of an oscillating nano-gram mass can be detected based on experimental parameters that will likely be accessible in the near-term future. Finally, we identify the experimental parameter regime necessary for gravitational wave detection with a quantum optomechanical sensor.

•Apr 1, 2021•23 citations

Quantum metrology with optomechanical systems in the nonlinear regime

Sofia Qvarfort

This thesis focuses on the mathematical description and application of nonlinear cavity optomechanical systems. The first part is concerned with solving the dynamics of the standard nonlinear optomechanical Hamiltonian with an additional time-dependent mechanical displacement and single-mode squeezing term. The solution is based on identifying a Lie algebra that generates the time-evolution of the system, which reduces the problem to considering a finite set of coupled ordinary differential equations of real functions. The second part applies the solutions of the extended optomechanical Hamiltonian to the study of non-Gaussianity. We compute the non-Gaussian character of an optomechanical state as a function of the parameters in the Hamiltonian, and investigate the interplay between the non-Gaussianity, the strength of the nonlinear coupling and the strength of the single-mode mechanical squeezing term. We find that the strength and form of the nonlinear coupling strongly impacts the non-Gaussianity, and that its relationship with the squeezing term is highly complex. The third part concerns the use of nonlinear optomechanical systems as quantum sensors. We derive a general expression of the quantum Fisher information given the extended optomechanical Hamiltonian and demonstrate its applicability through three concrete examples: estimating the strength of a nonlinear light--matter coupling, the strength of a time-modulated mechanical displacement, and the strength of a single-mode mechanical squeezing parameter, all of which are modulated at resonance. In the last Chapter of the thesis, we consider the estimation of a constant gravitational acceleration with an optomechanical system. Our results suggest that optomechanical systems could, in principle, be used as powerful quantum sensors.

arXiv:2003.11656•Mar 25, 2020•0 citations

Optimal estimation of time-dependent gravitational fields with quantum optomechanical systems

Sofia Qvarfort, A. D. K. Plato, David Edward Bruschi +4 more

We study the fundamental sensitivity that can be achieved with an ideal optomechanical system in the nonlinear regime for measurements of time-dependent gravitational fields. The optomechanical system consists of a cavity mode and a mechanical oscillator coupled to it via (non-linear) radiation pressure coupling. Using recently developed methods to solve the dynamics of a nonlinear optomechanical system with a time-dependent Hamiltonian, we compute the quantum Fisher information for linear displacements of the mechanical element due to gravity. We demonstrate that the sensitivity can be further enhanced by injecting squeezed states of the cavity field or by modulating the light–matter coupling of the optomechanical system. We specifically apply our results to the measurement of gravitational fields from small oscillating masses, where we show that, in principle, the gravitational field of an oscillating nanogram mass can be detected based on experimental parameters that will likely be accessible in the near-term future. Finally, we identify the experimental parameter regime necessary for gravitational wave detection with a quantum optomechanical sensor.

Optical and Quantum Sensing and Precision Metrology II•Mar 9, 2022•0 citations

Comparing the sensing power of the nonlinearand the linear optomechanical Hamiltonian

Nils Sebastian Martin Wilhelm Schneider

Quantum sensing is a field of study concerned with understanding the fundamental limits of sensitivity imposed by quantum mechanics as well as using quantum effects to improve sensitivity beyond classical limits. Optomechanical systems; that is, systems where light or another probe field interacts with a mechanical degree of freedom, are promising platforms for quantum sensing. Currently, almost all optomechanical experiments operate in the so-called linearised regime, using a strong drive of the probe field to achieve sufficient radiation pressure. However, it has been suggested that the nonlinear regime could improve sensing, in particular by offering a better scaling of the sensitivity with the occupation number of the probe field, N_a. One of the main bottlenecks in developing better optomechanics platforms is to engineer a sufficiently large light-matter coupling g. Measuring g is therefore key when characterising new optomechanical setups. In this thesis, we investigate whether g can be measured more precisely in the nonlinear or the linearised regime. To this end, we solved the dynamics of both the nonlinear optomechanical Hamiltonian and of a linearised Hamiltonian that has been further simplified through the rotating-wave approximation (beam-splitter Hamiltonian). We then computed the Quantum Fisher Information (QFI) for both Hamiltonians as well as for two different classes of initial states - (non-Gaussian) Fock-state superpositions (FSSPs) and (Gaussian) coherent states. We found that in general, the scaling of the QFI with N_a is better for the nonlinear Hamiltonian than for the linearised Hamiltonian. As for the initial states, the scaling with N_a is better for FSSP states than for coherent states. However, when comparing the QFI between the two Hamiltonians, the outcome of the comparison also depends heavily on the power of the probe field drive and the strength of g, as well as on the detuning between the optical and the mechanical frequency. Thus, which regime - nonlinear or linearised - is more suitable for measuring the coupling depends on what parameter regimes are experimentally accessible. Thus, the advantage conferred by the nonlinear Hamiltonian - and to a lesser extend also that conferred by non-Gaussian initial states - might not be experimentally accessible at the moment. It is also worth noting that while this work could in principle inform experiments, the predictive power of this work is limited by the fact that open system dynamics where not taken into account; as well as by the fact that the drive of the probe field was neglected in the nonlinear regime.

•Jan 1, 2026•0 citations

Squeezed light and coherent feedback enhanced multiparameter quantum estimation in a double-cavity optomechanics: steady and dynamical states

Hamza Harraf, Mohamed Amazioug, Amjad Sohail +2 more

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 $\mathcal{B}_{\rm MI}=\max\{\mathcal{B}_S,\mathcal{B}_R\}$ as a comparative figure of merit within the SLD/RLD framework. We find that parametric amplification can substantially reduce the most informative bound, $\mathcal{B}_{\rm MI}$, thereby enhancing multiparameter estimation precision over a broad range of operating conditions. Coherent feedback can further reduce $\mathcal{B}_{\rm MI}$ 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.

quant-pharXiv:2609.05402•Sep 7, 2026•0 citations

Optomechanical systems with linear and quadratic position couplings: Dynamics and optimal estimation

Yaqing Xy Wang, Claudio Sanavio, József Zsolt Bernád

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.

arXiv:2507.00187•Physical Review A•Jan 16, 2026•1 citation
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.
We study the fundamental sensitivity that can be achieved with an ideal optomechanical system in the nonlinear regime for measurements of time-dependent gravitational fields. Using recently developed methods to solve the dynamics of a nonlinear optomechanical system with a time-dependent Hamiltonian, we compute the quantum Fisher information for linear displacements of the mechanical element due to gravity. We demonstrate that the sensitivity can not only be further enhanced by injecting squeezed states of the cavity field, but also by modulating the light--matter coupling of the optomechanical system. We specifically apply our results to the measurement of gravitational fields from small oscillating masses, where we show that, in principle, the gravitational field of an oscillating nano-gram mass can be detected based on experimental parameters that will likely be accessible in the near-term future. Finally, we identify the experimental parameter regime necessary for gravitational wave detection with a quantum optomechanical sensor.
This thesis focuses on the mathematical description and application of nonlinear cavity optomechanical systems. The first part is concerned with solving the dynamics of the standard nonlinear optomechanical Hamiltonian with an additional time-dependent mechanical displacement and single-mode squeezing term. The solution is based on identifying a Lie algebra that generates the time-evolution of the system, which reduces the problem to considering a finite set of coupled ordinary differential equations of real functions. The second part applies the solutions of the extended optomechanical Hamiltonian to the study of non-Gaussianity. We compute the non-Gaussian character of an optomechanical state as a function of the parameters in the Hamiltonian, and investigate the interplay between the non-Gaussianity, the strength of the nonlinear coupling and the strength of the single-mode mechanical squeezing term. We find that the strength and form of the nonlinear coupling strongly impacts the non-Gaussianity, and that its relationship with the squeezing term is highly complex. The third part concerns the use of nonlinear optomechanical systems as quantum sensors. We derive a general expression of the quantum Fisher information given the extended optomechanical Hamiltonian and demonstrate its applicability through three concrete examples: estimating the strength of a nonlinear light--matter coupling, the strength of a time-modulated mechanical displacement, and the strength of a single-mode mechanical squeezing parameter, all of which are modulated at resonance. In the last Chapter of the thesis, we consider the estimation of a constant gravitational acceleration with an optomechanical system. Our results suggest that optomechanical systems could, in principle, be used as powerful quantum sensors.
We study the fundamental sensitivity that can be achieved with an ideal optomechanical system in the nonlinear regime for measurements of time-dependent gravitational fields. The optomechanical system consists of a cavity mode and a mechanical oscillator coupled to it via (non-linear) radiation pressure coupling. Using recently developed methods to solve the dynamics of a nonlinear optomechanical system with a time-dependent Hamiltonian, we compute the quantum Fisher information for linear displacements of the mechanical element due to gravity. We demonstrate that the sensitivity can be further enhanced by injecting squeezed states of the cavity field or by modulating the light–matter coupling of the optomechanical system. We specifically apply our results to the measurement of gravitational fields from small oscillating masses, where we show that, in principle, the gravitational field of an oscillating nanogram mass can be detected based on experimental parameters that will likely be accessible in the near-term future. Finally, we identify the experimental parameter regime necessary for gravitational wave detection with a quantum optomechanical sensor.
Quantum sensing is a field of study concerned with understanding the fundamental limits of sensitivity imposed by quantum mechanics as well as using quantum effects to improve sensitivity beyond classical limits. Optomechanical systems; that is, systems where light or another probe field interacts with a mechanical degree of freedom, are promising platforms for quantum sensing. Currently, almost all optomechanical experiments operate in the so-called linearised regime, using a strong drive of the probe field to achieve sufficient radiation pressure. However, it has been suggested that the nonlinear regime could improve sensing, in particular by offering a better scaling of the sensitivity with the occupation number of the probe field, N_a. One of the main bottlenecks in developing better optomechanics platforms is to engineer a sufficiently large light-matter coupling g. Measuring g is therefore key when characterising new optomechanical setups. In this thesis, we investigate whether g can be measured more precisely in the nonlinear or the linearised regime. To this end, we solved the dynamics of both the nonlinear optomechanical Hamiltonian and of a linearised Hamiltonian that has been further simplified through the rotating-wave approximation (beam-splitter Hamiltonian). We then computed the Quantum Fisher Information (QFI) for both Hamiltonians as well as for two different classes of initial states - (non-Gaussian) Fock-state superpositions (FSSPs) and (Gaussian) coherent states. We found that in general, the scaling of the QFI with N_a is better for the nonlinear Hamiltonian than for the linearised Hamiltonian. As for the initial states, the scaling with N_a is better for FSSP states than for coherent states. However, when comparing the QFI between the two Hamiltonians, the outcome of the comparison also depends heavily on the power of the probe field drive and the strength of g, as well as on the detuning between the optical and the mechanical frequency. Thus, which regime - nonlinear or linearised - is more suitable for measuring the coupling depends on what parameter regimes are experimentally accessible. Thus, the advantage conferred by the nonlinear Hamiltonian - and to a lesser extend also that conferred by non-Gaussian initial states - might not be experimentally accessible at the moment. It is also worth noting that while this work could in principle inform experiments, the predictive power of this work is limited by the fact that open system dynamics where not taken into account; as well as by the fact that the drive of the probe field was neglected in the nonlinear regime.
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.
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.