Optimal estimation of gravitation with Kerr nonlinearity in an optomechanical system
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Optimal estimation of gravitation with Kerr nonlinearity in an optomechanical system Xiao Xiao1
· Hongbin Liang1
· Xiaoguang Wang1
Received: 16 April 2020 / Accepted: 29 October 2020 © Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract We present a high precision scheme of a gravitational accelerometer which consists of an optomechanical system embedding a Kerr nonlinear medium. The quantum Cramér–Rao bound and the quantum Fisher information (QFI) are well-known tools to depict the ultimate precision limit in quantum parameter estimation. In our scheme, the analytical expression of time-dependent QFI is obtained with the absence of noise, which shows that the precision has been improved due to the existence of Kerr nonlinearity. At the light-matter decoupling time, the theoretical bound for the relative sensitivity is Δg/g ≈ 6.36 × 10−13 . Keywords Optomechanical system · Precision measurements · Gravitation · Quantum Fisher information
1 Introduction Quantum metrology is becoming more and more practical due to the development of quantum information theory and quantum technology nowadays. According to the quantum Cramér–Rao theorem, the quantum Fisher information (QFI) plays a key role in the quantum parameter estimation [1–7], which provides the ultimate bound of the precision. The attractiveness of quantum metrology is that it promises a better precision limit which can beat the shot-noise limit and approach the Heisenberg limit. The scaling 1/N for the deviation is known as the Heisenberg limit [8], which can be saturated by some highly nonclassical states, such as NOON states [9,10]. Besides, another resource to provide a high sensitivity is the nonlinearity, which has been thoroughly studied in different physical systems [11–18], and proved to be very useful.
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Xiao Xiao [email protected] Zhejiang Institute of Modern Physics, Department of Physics, Zhejiang University, Hangzhou 310027, China 0123456789().: V,-vol
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Cavity optomechanics, which couples mechanical and optical degrees of freedom through radiation pressure, has been a widespread theoretical and experimental research topic in recent years [19]. For the particular light-matter interaction, optomechanical systems provide an excellent framework to investigate the quantum of massive objects. Optomechanical systems have been widely used in a range of different areas from microscopic systems to mesoscopic devices, including phonon cooling [20,21], optomechanically induced transparency [22,23], mechanical squeezing [24,25], photon or phonon blockade [26,27], quantum illumination [28], and optical nonreciprocity for quantum information technology [29–31]. Optomechanical systems have also provided a new area for investigation of the fundamental questions on the quantum behavior of macroscopic systems [32,33], the quantum-to-classical transition [34], the test of fundamental physics [35], quantum coherence and entanglement [36], and quantum computation [37,38]. With the rapid ad
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