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Journal of Physics B Atomic Molecular and Optical Physics

The weak Coulomb force estimation via an optomechanical system

Li-Mei Xie, Zhucheng Zhang, Qin Wu, Zhi‐Ming Zhang, Ya‐Fei Yu

Published Mar 3, 2020• 0 citations
Publisher

Abstract

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.

DOI
10.1088/1361-6455/ab7c3d

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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.
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.
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.
We propose a scheme to implement a supersensitive estimation of the coupling strength in a hybrid optomechanical system which consists of a cavity-Bose-Einstein condensate system coupled to an impurity. This method can dramatically improve the estimation precision even when the involved photon number is small. The quantum Fisher information indicates that the Heisenberg scale sensitivity of the coupling rate could be obtained when the photon loss rate is smaller than the corresponding critical value in the input of either coherent state or squeezed state. The critical photon decay rate for the coherent state is larger than that of the squeezed state, and the coherent state input case is more robust against the photon loss than the squeezed state case. We also present the measurement scheme which can saturate the quantum Cramér-Rao bound.
Multiparameter quantum estimation has emerged as a central task in quantum metrology. In this work, we investigate multiparameter quantum estimation in a hybrid exciton--optomechanical (EOM) system. The system consists of a semiconductor quantum well embedded inside a driven optomechanical microcavity, where the excitonic, optical, and mechanical modes interact coherently through exciton--photon and radiation-pressure couplings. Using the Gaussian-state formalism, we derive the covariance matrix of the steady-state quantum fluctuations and employ both the symmetric logarithmic derivative (SLD) and right logarithmic derivative (RLD) approaches to evaluate the quantum Fisher information matrix associated with the simultaneous estimation of the exciton--photon coupling strength ggg and the excitonic decay rate kxk_xkx​. We analyze the corresponding quantum Cramér--Rao bounds and determine the most informative precision limit governing the attainable estimation accuracy. The influence of several experimentally relevant parameters, including temperature, driving power, optomechanical coupling strength, and dissipation rates, is investigated in detail. Our results show that strong hybrid interactions and low-temperature regimes significantly enhance the estimation precision, whereas thermal fluctuations and dissipation processes deteriorate the metrological performance. Furthermore, we compare the ultimate quantum limits with experimentally feasible Gaussian measurement strategies based on homodyne and heterodyne detection. We show that heterodyne detection provides better estimation performance than homodyne schemes and can approach the optimal quantum precision limit in suitable parameter regimes.
The formalism of quantum estimation theory, focusing on the quantum and classical Fisher information, is applied to the estimation of the coupling strength in an optomechanical system. In order to estimate the optomechanical coupling, we have considered a cavity optomechanical model with non-Markovian Brownian motion of the mirror and employed input-output formalism to obtain the cavity output field. Our estimation scenario is based on balanced homodyne photodetection of the cavity output field. We have explored the difference between the associated measurement-dependent classical Fisher information and the quantum Fisher information, thus addressing the question of whether it is possible to reach the lower bound of the mean-squared error of an unbiased estimator by means of balanced homodyne detection. We have found that the phase of the local oscillator in the homodyne detection is crucial; certain quadrature measurements allow very accurate estimation.