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Fisher Information, Weak Values and Correlated Noise in Interferometry

Sergio Carrasco, Miguel Orszag

Published Feb 25, 2019• 0 citations
OpenAlex

Abstract

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.

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quant-pharXiv:2606.09716•Jun 9, 2026•0 citations
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.
In this article we present an experimental proposal for the estimation of an optomechanical parameter in the presence of noise. The estimation is based on the technique of weak-value amplification which can enlarge the radiation pressure effect of a single photon on a mechanical oscillator. In our setup we show that the weak-value amplification technique is preferable for the estimation over a method that relies on a strong measurement with postselection because the first method does not require a good prior knowledge of the parameter we wish to estimate, while both strategies reach the same level of precision from a Fisher information perspective. In the presence of strongly correlated noise, the weak-value amplification method is preferable, from a Fisher information perspective, than a standard measurement strategy that does not employ postselection and that is affected by the same type of noise.
An experimental proposal is presented in which dark port postselection together with weak measurements are used to enlarge the radiation pressure effect of a single photon on a mechanical oscillator placed in the middle of a Fabry-P\'erot cavity and initialized in the ground state. By preparing and postselecting the photon (the system) in two quasiorthogonal states, the weak value of the radiation force operator can lie outside the eigenvalue spectrum, producing a large shift on the wave function of the mechanical oscillator (the measuring device) in the position representation. Consequently, the effect of a single photon on the average position of the oscillator can be amplified as compared to the effect caused by a photon without postselection, i.e., only preselected. The strong measurement scenario is also analyzed. In this case, a higher amplification effect is achieved and the mean position of the oscillator can reach the level of the zero-point fluctuations, but the postselection probabilities are smaller. Finally, the situation in which the oscillator starts in a thermal equilibrium state is studied. In this case, the amplification of the average position remains the same, i.e., proportional to the weak value, but the signal-to-noise ratio is reduced by a factor that depends on the average number of thermal phonons.
An interferometric experiment is proposed in order to measure the radiation force exerted by a single photon on a nano mechanical oscillator placed in the middle of a Fabry-P\'erot cavity. The force is measured by observing the shift given to the probability density function of the position of the oscillator, using weak measurements and post-selection of photons. We show that this shift is proportional to the weak value of the operator that accounts for the difference of photons between both sides of the cavity. For single-photon states, this operator has eigenvalues 1 or -1, depending on the side of the cavity in which is the photon, but the weak value can exceed by far this range. Thus, by preparing and post-selecting the photon in two nearly orthogonal states the weak value is increased and the radiation effect of a single photon turns out to be much larger than the pressure exerted by a photon without post-selection. This opens the possibility to study weak values of number operators in optomechanics and the radiation effect in pre- and post-selected ensembles.
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 Most studies for postselected weak measurement in optomechanical system focus on using a single photon as a measured system. However, we find that using weak coherent light instead of a single photon can also amplify the mirror’s position displacement of one photon. In the weak value amplification (WVA) regime, the weak value of one photon can lie outside the eigenvalue spectrum, proportional to the difference of the mirror’s position displacement between the successful and failed postselection and its successful postselection probability is dependent of the mean photon number of the coherent light and improved by adjusting it accordingly. Outside the WVA regime, the amplification limit can reach the level of the vacuum fluctuations, and when the mean photon number and the optomechanical coupling parameter are selected appropriately, its successful postselection probability becomes higher, which is beneficial to observe the maximum amplification value under the current experimental conditions. This result breaks the constraint that it is difficult to detect outside the WVA regime. This opens up a new regime for the study of a single photon nonlinearity in optomechanical system.
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.