Time uncertainty and fundamental sensitivity limits in quantum sensing: application to optomechanical gravimetry
Qatar Center for Quantum Computing, Collage of Science and Engineering, Hamad Bin Khalifa University（卡塔尔量子计算中心，科学与工程学院，哈利法大学）；Canadian Quantum Research Center（加拿大量子研究中心）；Dipartimento di Fisica e Astronomia, Universitá di Firenze（佛罗伦萨大学物理与天文学系）；CNR-Istituto Nazionale di Ottica and INFN（国家研究委员会光学研究所和INFN）；Irving K. Barber School of Arts and Sciences, University of British Columbia Okanagan（英属哥伦比亚大学奥卡纳根分校欧文K巴伯艺术与理学院）；Department of Mathematical Sciences, Durham University（达勒姆大学数学科学系）；Computational Mathematics Group, Faculty of Sciences, Hasselt University（哈瑟尔特大学理学院计算数学组）
Salman Sajad Wani, Saif Al-Kuwari, Arshid Shabir, Paolo Vezio, Francesco Marino, Mir Faizal
High-sensitivity accelerometers and gravimeters, achieving the ultimate limits of measurement sensitivity are key tools for advancing both fundamental and applied physics. While numerous platforms have been proposed to achieve this goal, from atom interferometers to optomechanical systems, all of these studies neglect the effects of intrinsic quantum uncertainty in time estimation. Starting from the Hamiltonian of a generic linear quantum sensor, we derive the two-parameter quantum Fisher information matrix and establish the corresponding Cram'er-Rao bound, treating time as an uncertain (nuisance) parameter. Our analysis reveals a fundamental coupling between time and signal estimation that inherently degrades measurement sensitivity, with the standard single-parameter quantum limit recovered only at specific interrogation times or under special decoupling conditions. We then apply these results to an optomechanical gravimeter and explicitly derive an optimal decoupling condition under which the effects of time uncertainty are averaged out in a continuous measurement scheme. Our approach is general and can be readily extended to a broad class of quantum sensors.
We propose a new method for measurements of gravitational acceleration using a quantum optomechanical system. As a proof-of-concept, we investigate the fundamental sensitivity for a cavity optomechanical system for gravitational accelerometry with a light-matter interaction of the canonical `trilinear' radiation pressure form. The phase of the optical output of the cavity encodes the gravitational acceleration $g$ and is the only component which needs to be measured to perform the gravimetry. We analytically show that homodyne detection is the optimal readout in our scheme, based on the cyclic…
Following the first demonstration of a levitated nanosphere cooled to the quantum ground state in 2020 [1], macroscopic quantum sensors are seemingly on the horizon. The nanosphere's large mass as compared to other quantum systems enhances the susceptibility of the nanoparticle to gravitational and inertial forces. In this viewpoint we describe the features of experiments with optically levitated nanoparticles [2] and their proposed utility for acceleration sensing. Unique to the levitated nanoparticle platform is the ability to implement not only quantum noise limited transduction, predicted …
Towards gravimetry enhancement with squeezed states
Universidade Federal do Piauí（皮奥伊联邦大学）；Universidade Federal da Grande Dourados（大杜拉多斯联邦大学）；Universidade Federal do ABC（ABC联邦大学）；Southern University of Science and Technology（南方科技大学）
Quantum gravimetry with intrinsic quantum time uncertainty
Qatar Center for Quantum Computing, College of Science and Engineering, Hamad Bin Khalifa University（卡塔尔量子计算中心，科学与工程学院，哈马德·本·哈利法大学）；Department of Mathematical and Computational Sciences, University of Toronto（数学与计算科学系，多伦多大学）；Canadian Quantum Research Center（加拿大量子研究中心）
We consider an optomechanical system that is composed of a mechanical and an optical mode interacting through a linear and quadratic optomechanical dispersive couplings. The system is operated in an unresolved side band limit with a high quality factor mechanical resonator. Such a system then acts as parametrically driven oscillator, giving access to an intensity assisted tunability of the spring constant. This enables the operation of optomechanical system in its 'soft mode' wherein the mechanical spring softens and responds with a lower resonance frequency. We show that this soft mode can be…
Optomechanically controlled response amplification for enhanced quantum sensing
Joint Laboratory of Optics of Palacký University and Institute of Physics ASCR, Faculty of Science, Palacký University（帕拉茨基大学与捷克科学院物理研究所联合光学实验室，帕拉茨基大学理学院）
Quantum control techniques applied at macroscopic scales provide us with opportunities in fundamental physics and practical applications. Among them, measurement-based feedback allows efficient control of optomechanical systems and quantum-enhanced sensing. In this paper, we propose a near-resonant narrow-band force sensor with extremely low optically added noise in an optomechanical system subject to a feedback-controlled in-loop light. The membrane's intrinsic motion consisting of zero-point motion and thermal motion is affected by the added noise of measurement due to the backaction noise a…
Institute of Science and Technology Austria (ISTA)（奥地利科学技术研究所）；Institute for Theoretical Physics, Eberhard Karls Universität Tübingen（蒂宾根大学理论物理研究所）；Naturwissenschaftlich-Technische Fakultät, Universität Siegen（锡根大学自然科学技术学院）；Department of Physics and Astronomy, University College London（伦敦大学学院物理与天文系）；ZARM, University of Bremen（不来梅大学ZARM中心）
We investigate quantum-squeezing-enhanced weak-force sensing via a nonlinear optomechanical resonator containing a movable mechanical mirror and an optical parametric amplifier (OPA). Herein, we determined that tuning the OPA parameters can considerably suppress quantum noise and substantially enhance force sensitivity, enabling the device to extensively surpass the standard quantum limit. This indicates that under realistic experimental conditions, we can achieve ultrahigh-precision quantum force sensing by harnessing nonlinear optomechanical devices.
We simulate an optomechanical system via a cavity QED scenario with a movable atom and investigate its application in the tiny mass sensing. We find that the steady-state solution of the system exhibits a multiple stability behavior, which is similar to that in the optomechanical system. We explain this phenomenon by the opto-mechanical interaction term in the effective Hamiltonian. Due to the dressed states formed by the effective coupling between the vibration degree of the atom and the optical mode in the cavity, we observe a narrow transparent window in the output field. We utilize this vi…
We propose an optomechanical nano-gravimeter based on exceptional points. The system is a coupled cavity optomechanical system, in which the gain and loss are applied by driving the cavities with a blue detuned and red detuned electromagnetic field, respectively. When the gain and loss reach a balance, the system will show the degeneracy of exceptional points, and any perturbation will cause an eigenfrequencies split, which is proportional to the square root of the perturbation strength. Compared with the traditional optomechanical sensors, the sensitivity is greatly enhanced. This work paves …
Nanoscale photonic crystal cavity optomechanical devices enable detection of nanomechanical phenomena with a sensitivity sufficient to observe quantum effects. Here we present the design of a one-dimensional air-mode photonic crystal cavity patterned in a silicon nitride nanobeam, and show that it forms the basis for cavity optomechanical split-beam and paddle nanocavity devices useful for force detection and nonlinear quantum sensing. The air-mode of this device is advantageous for optomechanical coupling, while also having ultrahigh optical quality factor $Q_o\sim 10^6$ despite its proximity…
Enhanced squeezing for quantum gravimetry in a Bose-Einstein condensate with focussing
ARC Centre of Excellence for Engineered Quantum Systems, School of Mathematics and Physics, University of Queensland（澳大利亚国立大学量子科学与技术系）；Department of Quantum Science and Technology, Research School of Physics, Australian National University（澳大利亚国立大学物理研究学院量子科学与技术系）
In this review, we study how a hybrid optomechanical system (OMS), in which a quantum micro- or nano-mechanical oscillator (MO) is coupled to the electromagnetic (EM) radiation pressure, consisting of an ensemble of ultracold atoms or an atomic Bose-Einstein condensate (BEC), can be used as an ultra precision quantum sensor for measuring very weak signals. As is well-known in any precise quantum measurement the competition between the shot noise (SN) and the backaction noise of measurement executes a limitation on the measurement precision which is the so-called standard quantum limit (SQL). I…
Exploring quantum technology to precisely measure physical quantities is a meaningful task for practical scientific researches. Here, we propose a novel quantum sensing model based on dressed states driving (DSD) in stimulated Raman adiabatic passage. The model is universal for sensing different physical quantities, such as magnetic field, mass, rotation and etc. For different sensors, the used systems can range from macroscopic scale, e.g. optomechanical systems, to microscopic nanoscale, e.g. nitrogen-vacancy color centres in diamond. By investigating the dynamics of color detuning of DSD pa…
We discuss the design of quantum hybrid inertial sensor that combines an optomechanical inertial sensor with the retro-reflector of a cold atom interferometer. This sensor fusion approach provides absolute and high accuracy measurements with cold atom interferometers, while utilizing the optomechanical inertial sensor at frequencies above the repetition rate of the atom interferometer. This improves the overall measurement bandwidth as well as the robustness and field deployment capabilities of these systems. We evaluate which parameters yield an optimal acceleration sensitivity, from which we…
We use an all-optical pump-probe method to develop a mass sensing mechanism in a molecular plasmonic system at room temperature. The system consists of a double-clamped graphene nanoribbon that parametrically interacts with two types of isotropic and anisotropic spherical plasmonic cavities in the presence of a strong pump field and a weak probe pulse. Based on the mode-selective quantization scheme and analogy with the canonical model of the cavity optomechanics, we formulate the Hamiltonian of the system in terms of the electromagnetic Greens tensor. In this manner, we derive an explicit for…
Probing the boundary between classical and quantum mechanics has been one of the central themes in modern physics. Recently, experiments to precisely measure the force acting on milligram scale oscillators with optical cavities are attracting interest as promising tools to test quantum mechanics, decoherence mechanisms, and gravitational physics. In this paper, we review the present status of experiments using milligram scale optomechanical systems. We compare the feasibility of reaching the quantum regime with a pendulum, torsion pendulum, and optically levitated mirror. Considerations for de…
Noise-Limited Sensitivity in Cavity Optomechanical Molecular Sensing Enabled by Quantum Zero-Point Displacement Coupling and Strong Photon-Phonon Interaction for Chiral Detection
An inertial sensor design is proposed in this paper to achieve high sensitivity and large dynamic range in the sub-Hz frequency regime. High acceleration sensitivity is obtained by combining optical cavity readout systems with monolithically fabricated mechanical resonators. A high-sensitivity heterodyne interferometer simultaneously monitors the test mass with an extensive dynamic range for low-stiffness resonators. The bandwidth is tuned by optical feedback cooling to the test mass via radiation pressure interaction using an intensity-modulated laser. The transfer gain of the feedback system…
Precise measurements of the displacement of, and force acting on, a mechanical oscillator can be performed by coupling the oscillator to an optical cavity. Brownian thermal forces represent a fundamental limit to measurement sensitivity which impedes the ability to use precise force measurements as a tool of fundamental enquiry, particularly in the context of macroscopic quantum measurements and table-top gravitational experiments. A torsion pendulum with a low mechanical resonant frequency can be limited by very small thermal forces - from its suspensions - at frequencies above resonance. Her…
Entanglement had played a crucial role in developing frontier technologies as a critical resource, for instance, in quantum teleportation and quantum sensing schemes. Notably, thanks to the ability to cool down the vibrational modes of mechanical oscillators to its quantum regime, entanglement between mechanical modes and the production of nonclassical mechanical states have emerged as central resources for quantum technological applications. Thus, proposing deterministic schemes to achieve those tasks is of paramount importance. While the dominant scheme for bipartite mechanical entanglement …
Self-Sustained Oscillations of a Nonlinear Optomechanical System in the Low-Excitation Regime
Institute for Quantum Materials and Technology, Karlsruhe Institute of Technology（卡尔斯鲁厄理工学院量子材料与技术研究所）；Walther-Meißner-Institut, Bayerische Akademie der Wissenschaften（巴伐利亚科学院瓦尔特·迈斯纳研究所）；Physics Department, TUM School of Natural Sciences, Technical University of Munich（慕尼黑工业大学自然科学学院物理系）；Munich Center for Quantum Science and Technology (MCQST)（慕尼黑量子科学与技术中心）；Institute for Theory of Condensed Matter, Karlsruhe Institute of Technology（卡尔斯鲁厄理工学院凝聚态理论研究所）；Institut de Science et d’Ingénierie Supramoléculaires (ISIS, UMR7006), University of Strasbourg and CNRS（斯特拉斯堡大学与法国国家科学研究中心超分子科学与工程研究所）
Optomechanical sensors involving multiple optical carriers can experience mechanically mediated interactions causing multi-mode correlations across the optical fields. One instance is laser-interferometric gravitational wave detectors which introduce multiple carrier frequencies for classical sensing and control purposes. An outstanding question is whether such multi-carrier optomechanical sensors outperform their single-carrier counterpart in terms of quantum-limited sensitivity. We show that the best precision is achieved by a single-carrier instance of the sensor. For the current LIGO detec…
