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CN114859076A - Acceleration measurement method and device based on optical suspension multi-microsphere array - Google Patents

Acceleration measurement method and device based on optical suspension multi-microsphere array Download PDF

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CN114859076A
CN114859076A CN202210788629.1A CN202210788629A CN114859076A CN 114859076 A CN114859076 A CN 114859076A CN 202210788629 A CN202210788629 A CN 202210788629A CN 114859076 A CN114859076 A CN 114859076A
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acceleration
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spectral density
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CN114859076B (en
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李闯
董莹
胡慧珠
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Zhejiang Lab
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    • G01—MEASURING; TESTING
    • G01P—MEASURING LINEAR OR ANGULAR SPEED, ACCELERATION, DECELERATION, OR SHOCK; INDICATING PRESENCE, ABSENCE, OR DIRECTION, OF MOVEMENT
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Abstract

本发明公开一种基于光悬浮多微球阵列的加速度测量方法及装置，采用全息光镊将N个纳米微粒悬浮在光学腔中，N≥2，通过激光驱动光学腔，使光学腔内产生稳定的驻波光场；通过调节全息光镊，使得每个纳米微粒与光学腔中光场的耦合强度相等，形成稳定的光悬浮多微球阵列探测系统；通过测量光学腔的透射光，获取透射光的功率谱密度；利用加速度功率谱密度与透射光功率谱密度的关系，计算加速度功率谱密度，从而获取加速度信息。本发明提出的加速度测量方法利用机械振子的集体质心运动进行加速度测量可以等效地增大机械振子质量的原理，提升加速度测量灵敏度。本发明的方法的加速度测量灵敏度随机械振子数量的增加不断提高。

Figure 202210788629

The invention discloses an acceleration measurement method and device based on an optically suspended multi-microsphere array. Holographic optical tweezers are used to suspend N nano-particles in an optical cavity, N≥2, and the optical cavity is driven by a laser, so that a stable generation in the optical cavity is generated. By adjusting the holographic optical tweezers, the coupling intensity of each nanoparticle and the optical field in the optical cavity is equal to form a stable optically suspended multi-microsphere array detection system; by measuring the transmitted light of the optical cavity, the transmitted light is obtained The power spectral density is calculated by using the relationship between the acceleration power spectral density and the transmitted light power spectral density to obtain the acceleration information. The acceleration measurement method proposed by the present invention utilizes the principle that the collective mass center motion of the mechanical vibrator can be used to measure the acceleration, which can equivalently increase the mass of the mechanical vibrator and improve the sensitivity of the acceleration measurement. The acceleration measurement sensitivity of the method of the present invention is continuously improved with the increase of the number of mechanical vibrators.

Figure 202210788629

Description

基于光悬浮多微球阵列的加速度测量方法及装置Acceleration measurement method and device based on optically suspended multi-microsphere array

技术领域technical field

本发明涉及加速度测量领域，尤其涉及一种基于光悬浮多微球阵列的加速度测量方法及装置。The invention relates to the field of acceleration measurement, in particular to an acceleration measurement method and device based on an optically suspended multi-microsphere array.

背景技术Background technique

光镊作为一种操控微纳尺度物体的有效工具，广泛地应用在生物学、材料科学、物理学、信息学等诸多领域，其发明者阿瑟·阿什金也因此被授予2018年诺贝尔物理学奖。近些年，利用真空光镊悬浮微纳尺度物体构成悬浮光力系统成为物理学的研究热点。悬浮光力系统具有超高精度测量和操控微纳尺度物体（机械振子）运动的能力，因而被广泛地应用在基础科学和工程技术中。光悬浮机械振子的方式避免了机械支承带来的损耗与噪声，高真空环境又能极大地减小周围气体分子热噪声的影响，让悬浮光力系统具有了超高的探测灵敏度，使悬浮光力系统成为精密测量和传感领域的热门研究方向。不仅如此，悬浮光力系统中的机械振子几乎处在与外界环境完全隔离的状态，形成了一个近孤立的系统，是进行基础物理研究的理想体系。因此，悬浮光力系统成为了精密测量和前沿基础物理研究的有力工具。悬浮光力系统本身体积小巧、俘获光阱灵活可控、可工作在室温状态且可片上集成，这些特点使悬浮光力系统在商业探测器和传感器领域展现出广阔的应用前景。Optical tweezers, as an effective tool for manipulating micro- and nano-scale objects, are widely used in biology, materials science, physics, informatics and many other fields. Its inventor, Arthur Ashkin, was awarded the 2018 Nobel Prize for this. Physics Prize. In recent years, the use of vacuum optical tweezers to suspend micro-nano-scale objects to form a suspended opto-mechanical system has become a research hotspot in physics. The suspended optomechanical system has the ability to measure and manipulate the motion of micro-nano-scale objects (mechanical oscillators) with ultra-high precision, so it is widely used in basic science and engineering technology. The optical suspension mechanical vibrator avoids the loss and noise caused by the mechanical support, and the high vacuum environment can greatly reduce the influence of the thermal noise of the surrounding gas molecules, so that the suspension optical system has ultra-high detection sensitivity, making the suspension light Force systems have become a hot research direction in the field of precision measurement and sensing. Not only that, the mechanical oscillator in the suspended optomechanical system is almost completely isolated from the external environment, forming a nearly isolated system, which is an ideal system for basic physics research. Therefore, the suspended optomechanical system has become a powerful tool for precise measurement and cutting-edge basic physics research. The levitating optomechanical system itself is small in size, flexible and controllable in the trapping optical trap, can work at room temperature and can be integrated on-chip. These characteristics make the levitating optomechanical system show broad application prospects in the field of commercial detectors and sensors.

近些年，随着光镊技术和微纳加工技术的不断进步，悬浮光力学系统中机械振子的品质因子越来越高，捕获寿命也越来越长，这使悬浮光力系统在精密测量和传感领域迅速发展。基于悬浮光力学的探测装置已实现对力、加速度等多种力学量的高精度探测。但是，悬浮光力系统的进一步发展仍面临诸多挑战。In recent years, with the continuous progress of optical tweezers technology and micro-nano processing technology, the quality factor of the mechanical oscillator in the suspended optomechanical system is getting higher and higher, and the capture life is getting longer and longer, which makes the suspended optomechanical system in the precision measurement. And the field of sensing is developing rapidly. The detection device based on levitation optomechanics has achieved high-precision detection of various mechanical quantities such as force and acceleration. However, the further development of suspended optomechanical systems still faces many challenges.

传统单振子悬浮光力探测装置利用光镊将单个微纳尺度的微粒（机械振子）悬浮在真空中，机械振子在光镊产生的光阱中进行微小简谐运动。待测外力作用在机械振子上改变机械振子运动状态，相应的变化反映在机械振子的散射光中，从而通过测量散射光实现力学量探测。在加速度测量方面，传统单振子悬浮光力加速度测量方案的灵敏度为The traditional single-vibrator suspension optical force detection device uses optical tweezers to suspend a single micro-nano-scale particle (mechanical oscillator) in a vacuum, and the mechanical oscillator performs tiny simple harmonic motion in the optical trap generated by the optical tweezers. The external force to be measured acts on the mechanical oscillator to change the motion state of the mechanical oscillator, and the corresponding change is reflected in the scattered light of the mechanical oscillator, so that the mechanical quantity detection can be realized by measuring the scattered light. In terms of acceleration measurement, the sensitivity of the traditional single-vibrator suspension optical acceleration measurement scheme is

Figure 160122DEST_PATH_IMAGE001
Figure 160122DEST_PATH_IMAGE001

其中，

Figure 546104DEST_PATH_IMAGE002
为玻尔兹曼常数，
Figure 919317DEST_PATH_IMAGE003
为环境温度，
Figure 517788DEST_PATH_IMAGE004
为机械振子阻尼率。从上式中可以看出，加速度测量灵敏度与机械振子质量成反比，增大机械振子质量可以提高加速度测量灵敏度。但是，技术上利用光镊悬浮大质量机械振子却十分困难。其主要原因在于机械振子所受重力随其质量增加而增大，导致光镊需要提供很大的光场梯度力来平衡机械振子所受重力。增加激光器输出功率可以增大光镊产生的光场力，但同时会增强光镊对机械振子的加热效应，导致其内温上升，降低灵敏度，甚至过大的光功率还会融化机械振子。in,
Figure 546104DEST_PATH_IMAGE002
is the Boltzmann constant,
Figure 919317DEST_PATH_IMAGE003
is the ambient temperature,
Figure 517788DEST_PATH_IMAGE004
is the damping rate of the mechanical vibrator. It can be seen from the above formula that the acceleration measurement sensitivity is inversely proportional to the mass of the mechanical vibrator, and increasing the mass of the mechanical vibrator can improve the acceleration measurement sensitivity. However, it is technically difficult to use optical tweezers to suspend large-mass mechanical oscillators. The main reason is that the gravitational force on the mechanical oscillator increases with the increase of its mass, so that the optical tweezers need to provide a large optical field gradient force to balance the gravitational force on the mechanical oscillator. Increasing the output power of the laser can increase the optical field force generated by the optical tweezers, but at the same time, it will enhance the heating effect of the optical tweezers on the mechanical vibrator, resulting in an increase in its internal temperature and a decrease in sensitivity, and even excessive optical power will melt the mechanical vibrator.

发明内容SUMMARY OF THE INVENTION

针对现有基于单振子悬浮光力系统加速度测量技术的不足，本发明提供一种基于光悬浮多微球阵列的加速度测量方法及装置。利用全息光镊将多个微纳尺度微球（微粒）悬浮在一个光学腔中形成光悬浮多微球阵列系统，每个纳米微球作为一个机械振子，纳米微球的集体质心运动通过光力相互作用耦合到腔内光场中，从而通过测量腔透射光场获取纳米微球的加速度信息。Aiming at the deficiencies of the existing acceleration measurement technology based on a single-vibrator suspension optical system, the present invention provides an acceleration measurement method and device based on an optical suspension multi-microsphere array. Using holographic optical tweezers, multiple micro- and nano-scale microspheres (microparticles) are suspended in an optical cavity to form an optically suspended multi-microsphere array system. The interaction is coupled into the optical field in the cavity, so that the acceleration information of the nano-microspheres can be obtained by measuring the transmitted optical field of the cavity.

本发明的目的通过如下技术方案实现：The object of the present invention is achieved through the following technical solutions:

一种基于光悬浮多微球阵列的加速度测量方法，使用全息光镊将N个纳米微粒悬浮在光学腔中，N≥2，通过激光驱动光学腔，使光学腔内产生稳定的驻波光场；通过调节全息光镊，使得每个纳米微粒与光学腔中光场的耦合强度相等，形成稳定的光悬浮多微球阵列探测系统；An acceleration measurement method based on an optically suspended multi-microsphere array, using holographic optical tweezers to suspend N nanoparticles in an optical cavity, N≥2, and driving the optical cavity by a laser to generate a stable standing wave optical field in the optical cavity; By adjusting the holographic optical tweezers, the coupling intensity of each nanoparticle and the optical field in the optical cavity is equal, forming a stable optically suspended multi-microsphere array detection system;

通过测量光学腔的透射光，获取透射光功率谱密度；利用加速度功率谱密度与透射光功率谱密度的关系，计算加速度功率谱密度，从而获取加速度信息。The transmitted light power spectral density is obtained by measuring the transmitted light of the optical cavity; the acceleration power spectral density is calculated by using the relationship between the acceleration power spectral density and the transmitted light power spectral density to obtain the acceleration information.

进一步地，所述加速度功率谱密度与透射光功率谱密度的关系如下：Further, the relationship between the acceleration power spectral density and the transmitted light power spectral density is as follows:

Figure 676368DEST_PATH_IMAGE005
Figure 676368DEST_PATH_IMAGE005

Figure 967672DEST_PATH_IMAGE006
Figure 967672DEST_PATH_IMAGE006

其中，

Figure 500285DEST_PATH_IMAGE007
为待测加速度的功率谱密度，包含待测加速度信息，对其在频域积分可获取加速度幅值；
Figure 292660DEST_PATH_IMAGE008
为光学腔透射光的功率谱密度，可通过探测装置获取；
Figure 164801DEST_PATH_IMAGE009
、
Figure 499443DEST_PATH_IMAGE010
、
Figure 722614DEST_PATH_IMAGE011
分别为环境布朗随机力功率谱密度、腔光场振幅输入噪声功率谱密度、腔光场相位输入噪声功率谱密度；
Figure 725205DEST_PATH_IMAGE012
为机械振子转移函数；
Figure 842066DEST_PATH_IMAGE013
为光场转移函数；
Figure 740752DEST_PATH_IMAGE014
为联合转移函数；
Figure 61006DEST_PATH_IMAGE015
为约化普朗克常数；
Figure 804971DEST_PATH_IMAGE016
为纳米微粒质量；
Figure 41917DEST_PATH_IMAGE017
为纳米微粒个数；
Figure 845925DEST_PATH_IMAGE018
为纳米微粒的共振频率；
Figure 840426DEST_PATH_IMAGE019
为腔光场失谐量；
Figure 263448DEST_PATH_IMAGE020
为纳米微粒阻尼率；
Figure 230267DEST_PATH_IMAGE021
为光学腔光场衰减率；
Figure 329810DEST_PATH_IMAGE022
为纳米微粒和腔光场的耦合强度。in,
Figure 500285DEST_PATH_IMAGE007
is the power spectral density of the acceleration to be measured, including the acceleration information to be measured, and the acceleration amplitude can be obtained by integrating it in the frequency domain;
Figure 292660DEST_PATH_IMAGE008
is the power spectral density of the transmitted light of the optical cavity, which can be obtained by the detection device;
Figure 164801DEST_PATH_IMAGE009
,
Figure 499443DEST_PATH_IMAGE010
,
Figure 722614DEST_PATH_IMAGE011
are the environmental Brownian random force power spectral density, the cavity light field amplitude input noise power spectral density, and the cavity light field phase input noise power spectral density;
Figure 725205DEST_PATH_IMAGE012
is the mechanical oscillator transfer function;
Figure 842066DEST_PATH_IMAGE013
is the light field transfer function;
Figure 740752DEST_PATH_IMAGE014
is the joint transfer function;
Figure 61006DEST_PATH_IMAGE015
is the reduced Planck constant;
Figure 804971DEST_PATH_IMAGE016
is the nanoparticle mass;
Figure 41917DEST_PATH_IMAGE017
is the number of nanoparticles;
Figure 845925DEST_PATH_IMAGE018
is the resonance frequency of the nanoparticles;
Figure 840426DEST_PATH_IMAGE019
is the detuning amount of the cavity light field;
Figure 263448DEST_PATH_IMAGE020
is the nanoparticle damping rate;
Figure 230267DEST_PATH_IMAGE021
is the optical field attenuation rate of the optical cavity;
Figure 329810DEST_PATH_IMAGE022
is the coupling strength of the nanoparticle and the cavity light field.

进一步地，将N个纳米微粒在沿光学腔的腔轴方向上等间距排列，且间距满足

Figure 749290DEST_PATH_IMAGE023
，其中
Figure 897375DEST_PATH_IMAGE024
为光学腔中驻波场波长，n为正整数。Further, the N nanoparticles are arranged at equal intervals along the cavity axis of the optical cavity, and the spacing satisfies
Figure 749290DEST_PATH_IMAGE023
,in
Figure 897375DEST_PATH_IMAGE024
is the wavelength of the standing wave field in the optical cavity, and n is a positive integer.

进一步地，采用零差探测或外差探测的方式测量光学腔的透射光。Further, the transmitted light of the optical cavity is measured by means of homodyne detection or heterodyne detection.

进一步地，采用波长为1064 nm的激光驱动光学腔。Further, a laser with a wavelength of 1064 nm is used to drive the optical cavity.

一种实现基于光悬浮多微球阵列的加速度测量方法的装置，该装置包括激光器、光学腔、全息光镊、光场探测装置；其中光学腔中悬浮有N个纳米微粒；其中，所述激光器的光轴和光学腔的光轴重合；A device for realizing an acceleration measurement method based on an optically suspended multi-microsphere array, the device comprising a laser, an optical cavity, a holographic optical tweezers, and an optical field detection device; wherein N nanoparticles are suspended in the optical cavity; wherein, the laser The optical axis of the optical axis coincides with the optical axis of the optical cavity;

所述激光器从所述光学腔的一侧入射，在所述光学腔中激发形成稳定驻波光场；所述全息光镊用于将N个纳米微粒悬浮在光学腔中，并调节它们在光学腔中的平衡位置；所述光场探测装置用于探测光学腔另一侧的透射光，获取透射光功率谱密度；利用加速度功率谱密度与透射光功率谱密度的关系，计算加速度功率谱密度，从而获取加速度信息。The laser is incident from one side of the optical cavity, and is excited in the optical cavity to form a stable standing wave light field; the holographic optical tweezers are used to suspend N nanoparticles in the optical cavity and adjust them in the optical cavity. The optical field detection device is used to detect the transmitted light on the other side of the optical cavity to obtain the transmitted light power spectral density; the relationship between the acceleration power spectral density and the transmitted light power spectral density is used to calculate the acceleration power spectral density, Thereby obtaining acceleration information.

进一步地，所述光场探测装置是零差探测装置或外差探测装置。Further, the light field detection device is a homodyne detection device or a heterodyne detection device.

本发明的有益效果如下：The beneficial effects of the present invention are as follows:

本发明提出的加速度测量方法利用机械振子集体质心运动进行加速度测量，通过机械振子集体质心运动可以等效地增大机械振子质量的原理提升加速度测量灵敏度。本发明的方法的加速度测量灵敏度随机械振子数量的增加不断提高。在热噪声极限条件下（环境热噪声为主要噪声来源），本发明方法的灵敏度是传统单振子悬浮光力加速度测量方法灵敏度的1/N，即加速度灵敏度提升了N倍，突破机械振子质量对加速度灵敏度的限制。The acceleration measurement method proposed in the present invention uses the collective mass center motion of the mechanical vibrator to measure the acceleration, and improves the acceleration measurement sensitivity through the principle that the mass of the mechanical vibrator can be equivalently increased by the collective mass center motion of the mechanical vibrator. The acceleration measurement sensitivity of the method of the present invention is continuously improved with the increase of the number of mechanical vibrators. Under the condition of thermal noise limit (environmental thermal noise is the main noise source), the sensitivity of the method of the present invention is 1/N of the sensitivity of the traditional single-vibrator suspension optical acceleration measurement method, that is, the acceleration sensitivity is improved by N times, breaking through the mechanical vibrator mass pair. Acceleration sensitivity limit.

附图说明Description of drawings

图1为根据一示例性实施例示出的本发明的装置示意图。FIG. 1 is a schematic diagram of a device of the present invention according to an exemplary embodiment.

图2为根据一示例性实施例示出的本发明加速度测量方法的原理图。FIG. 2 is a schematic diagram illustrating an acceleration measurement method of the present invention according to an exemplary embodiment.

图3为根据一示例性实施例示出的本发明的方法流程图。FIG. 3 is a flow chart of the method of the present invention according to an exemplary embodiment.

图4为不同机械振子数量下加速度测量灵敏度的变化曲线；其中，(a)为加速度灵敏度随频率的变化曲线，(b)为共振条件下加速度测量灵敏度随机械振子数量的变化曲线。Figure 4 shows the change curve of acceleration measurement sensitivity under different numbers of mechanical vibrators; among them, (a) is the change curve of acceleration sensitivity with frequency, and (b) is the change curve of acceleration measurement sensitivity with the number of mechanical vibrators under resonance conditions.

图5为利用光悬浮三微球阵列系统测量不同频率加速度的数值模拟结果。Figure 5 shows the numerical simulation results of measuring acceleration at different frequencies using the optically suspended three-microsphere array system.

图6为在相同条件下，使用传统单振子加速度测量方案和本发明基于光悬浮三微球阵列的加速度测量方法测量相同强度加速度的数值模拟结果。6 is a numerical simulation result of measuring the acceleration of the same intensity by using the traditional single vibrator acceleration measurement scheme and the acceleration measurement method based on the optical suspension three microsphere array of the present invention under the same conditions.

图1中，激光器1、光学腔2、全息光镊3、光场探测装置4、第一纳米微粒5、第二纳米微粒6……第N纳米微粒N+4。In FIG. 1 , a laser 1 , an optical cavity 2 , a holographic optical tweezers 3 , an optical field detection device 4 , a first nanoparticle 5 , a second nanoparticle 6 . . . the Nth nanoparticle N+4 .

具体实施方式Detailed ways

下面根据附图和优选实施例详细描述本发明，本发明的目的和效果将变得更加明白，应当理解，此处所描述的具体实施例仅仅用以解释本发明，并不用于限定本发明。The present invention will be described in detail below according to the accompanying drawings and preferred embodiments, and the purpose and effects of the present invention will become clearer.

如图1所示，作为其中一种实施方式，本发明的基于光悬浮多微球阵列的加速度测量装置，包括激光器1、光学腔2、全息光镊3、光场探测装置4、第一纳米微粒5、第二纳米微粒6……第N纳米微粒N+4。As shown in FIG. 1, as one of the embodiments, the acceleration measurement device based on the optically suspended multi-microsphere array of the present invention includes a laser 1, an optical cavity 2, a holographic optical tweezers 3, an optical field detection device 4, a first nanometer Particle 5, second nanoparticle 6... Nth nanoparticle N+4.

激光器1的光轴和光学腔2的光轴重合，从左侧驱动光学腔2用于形成驻波光场。全息光镊3将第一纳米微粒5、第二纳米微粒6……第N纳米微粒N+4悬浮在光学腔2中。利用全息光镊3调整每个纳米微粒在光学腔2中的平衡位置，使所有纳米微粒与腔光场的耦合强度相等。光场探测装置4可以使用零差探测装置或者外差探测装置，其主要用于测量腔另一侧的透射光，从而通过透射光获取纳米微粒的加速度信息。The optical axis of the laser 1 coincides with the optical axis of the optical cavity 2, and the optical cavity 2 is driven from the left to form a standing wave optical field. The holographic optical tweezers 3 suspend the first nanoparticle 5 , the second nanoparticle 6 . . . the Nth nanoparticle N+4 in the optical cavity 2 . The holographic optical tweezers 3 are used to adjust the equilibrium position of each nanoparticle in the optical cavity 2, so that the coupling strength of all nanoparticles and the cavity optical field is equal. The light field detection device 4 can use a homodyne detection device or a heterodyne detection device, which is mainly used to measure the transmitted light on the other side of the cavity, so as to obtain the acceleration information of the nanoparticles through the transmitted light.

本发明的加速度测量原理见图2，具体如下：全息光镊将N个纳米微粒悬浮在激光驱动的光学腔中，使它们与同一个腔光场耦合。每个纳米微粒为一个机械振子，机械振子与腔光场间的光力相互作用将所有机械振子的集体质心运动加速度信息耦合到腔光场中，从而通过测量腔光场就可以获取机械振子集体质心运动的加速度信息。The acceleration measurement principle of the present invention is shown in Figure 2, and the details are as follows: The holographic optical tweezers suspend N nanoparticles in an optical cavity driven by a laser, so that they are coupled with the same cavity optical field. Each nanoparticle is a mechanical oscillator, and the optical force interaction between the mechanical oscillator and the cavity optical field couples the collective centroid motion acceleration information of all mechanical oscillators into the cavity optical field, so that the collective mechanical oscillator can be obtained by measuring the cavity optical field. Acceleration information for centroid motion.

如图3所示，本发明的基于光悬浮多微球阵列的加速度测量方法，具体包括：As shown in FIG. 3 , the acceleration measurement method based on the optically suspended multi-microsphere array of the present invention specifically includes:

使用全息光镊3将N个纳米微粒悬浮在光学腔2中，通过激光驱动光学腔2，使光学腔2内产生稳定的驻波光场；通过调节全息光镊3，使得每个纳米微粒与光学腔2中光场的耦合强度相等，形成稳定的光悬浮多微球阵列探测系统；Use the holographic optical tweezers 3 to suspend N nanoparticles in the optical cavity 2, and drive the optical cavity 2 by laser to generate a stable standing wave optical field in the optical cavity 2; The coupling intensity of the optical field in cavity 2 is equal, forming a stable optical suspension multi-microsphere array detection system;

通过测量光学腔2的透射光，获取透射光的功率谱密度；利用加速度功率谱密度与透射光功率谱密度的关系，计算加速度功率谱密度，从而获取加速度信息。By measuring the transmitted light of the optical cavity 2, the power spectral density of the transmitted light is obtained; using the relationship between the acceleration power spectral density and the transmitted light power spectral density, the acceleration power spectral density is calculated to obtain the acceleration information.

本发明提高加速度测量灵敏度的原理可以简单概述如下：利用光悬浮多纳米微球的集体质心运动代替单个机械振子运动进行加速度测量，等效地提高了机械振子的质量，从而可以提高加速度测量灵敏度。The principle of the present invention for improving the sensitivity of acceleration measurement can be briefly summarized as follows: the collective centroid motion of the optically suspended multi-nanometer microspheres is used to replace the motion of a single mechanical vibrator for acceleration measurement, which equivalently improves the quality of the mechanical vibrator, thereby improving the sensitivity of acceleration measurement.

下面在理论上具体分析说明基于光悬浮多微球阵列的加速度测量方法的测量原理以及灵敏度提升原理和效果。The following is a detailed analysis and description of the measurement principle of the acceleration measurement method based on the optically suspended multi-microsphere array and the principle and effect of the sensitivity improvement in theory.

一. 基于光悬浮多微球阵列的加速度测量原理1. Principle of acceleration measurement based on optically suspended multi-microsphere array

不失一般性，考虑 N个质量为m的纳米微球（机械振子）被全息光镊悬浮在一个光学腔中，形成光悬浮N微球阵列系统。由于所有机械振子被悬浮在同一个光学腔中，均处在相同真空条件下，因此，它们具有相同的阻尼率

Figure 594066DEST_PATH_IMAGE025
，并且它们受到周围环境的布朗随机力也是相互独立的。在悬浮光力系统中，机械振子的共振频率与俘获它的光阱强度有关，因而通过调整全息光镊改变俘获光阱的强度分布可以使所有机械振子具有相同共振频率
Figure 5456DEST_PATH_IMAGE026
。因此，整个光悬浮N微球阵列系统的哈密顿量可写为Without loss of generality, consider N nano-microspheres (mechanical oscillators) with mass m suspended in an optical cavity by holographic optical tweezers to form an optically suspended N-microsphere array system. Since all mechanical oscillators are suspended in the same optical cavity under the same vacuum conditions, they have the same damping rate
Figure 594066DEST_PATH_IMAGE025
, and they are also independent of each other by the Brownian random force of the surrounding environment. In the suspended optomechanical system, the resonant frequency of the mechanical oscillator is related to the intensity of the optical trap that traps it, so by adjusting the holographic optical tweezers to change the intensity distribution of the trapped optical trap, all mechanical oscillators can have the same resonance frequency
Figure 5456DEST_PATH_IMAGE026
. Therefore, the Hamiltonian of the entire optically suspended N-microsphere array system can be written as

Figure 36866DEST_PATH_IMAGE027
Figure 36866DEST_PATH_IMAGE027

其中，

Figure 660745DEST_PATH_IMAGE028
为约化普朗克常数；
Figure 474593DEST_PATH_IMAGE029
为机械振子标号；
Figure 56884DEST_PATH_IMAGE030
为腔光场的湮灭算符；
Figure 247694DEST_PATH_IMAGE031
为机械振子的无量纲动量算符；
Figure 65477DEST_PATH_IMAGE032
为机械振子的无量纲位移算符，
Figure 595816DEST_PATH_IMAGE033
为腔光场失谐量。
Figure 958795DEST_PATH_IMAGE034
为机械振子与腔光场的耦合强度，它与机械振子的平衡位置
Figure 840164DEST_PATH_IMAGE035
、腔光场波长
Figure 461638DEST_PATH_IMAGE036
有关，可简单表示为in,
Figure 660745DEST_PATH_IMAGE028
is the reduced Planck constant;
Figure 474593DEST_PATH_IMAGE029
is the label of the mechanical vibrator;
Figure 56884DEST_PATH_IMAGE030
is the annihilation operator of the cavity light field;
Figure 247694DEST_PATH_IMAGE031
is the dimensionless momentum operator of the mechanical oscillator;
Figure 65477DEST_PATH_IMAGE032
is the dimensionless displacement operator of the mechanical oscillator,
Figure 595816DEST_PATH_IMAGE033
is the detuning amount of the cavity light field.
Figure 958795DEST_PATH_IMAGE034
is the coupling strength of the mechanical oscillator and the cavity light field, and its equilibrium position with the mechanical oscillator
Figure 840164DEST_PATH_IMAGE035
, the wavelength of the cavity light field
Figure 461638DEST_PATH_IMAGE036
related, can be simply expressed as

Figure 112062DEST_PATH_IMAGE037
Figure 112062DEST_PATH_IMAGE037

其中，C为一个与腔光场波长、介电常数等有关的参数。因此，通过全息光镊调整每一个机械振子的位置，可以使所有机械振子与腔光场具有相等的耦合强度

Figure 567314DEST_PATH_IMAGE038
。这里提供一种可供选择的纳米微粒位置排布方案：使所有机械振子在沿腔轴方向等间距排列，且间距满足
Figure 811345DEST_PATH_IMAGE039
，其中
Figure 580718DEST_PATH_IMAGE040
为正整数。其他的纳米微粒排布方式，只要能使得所有机械振子与腔光场具有相等的耦合强度均可。Among them, C is a parameter related to the wavelength of the cavity light field, the dielectric constant, and the like. Therefore, by adjusting the position of each mechanical oscillator through holographic optical tweezers, all mechanical oscillators can have equal coupling strength with the cavity light field
Figure 567314DEST_PATH_IMAGE038
. Here is an alternative solution for the placement of nanoparticles: all mechanical oscillators are arranged at equal intervals along the cavity axis, and the spacing satisfies
Figure 811345DEST_PATH_IMAGE039
,in
Figure 580718DEST_PATH_IMAGE040
is a positive integer. Other arrangements of nanoparticles can be used as long as all mechanical oscillators have equal coupling strength with the cavity light field.

机械振子与外部作用力（加速度）的相互作用哈密顿量为The Hamiltonian of the interaction between the mechanical oscillator and the external force (acceleration) is

Figure 475861DEST_PATH_IMAGE041
Figure 475861DEST_PATH_IMAGE041

其中，

Figure 305277DEST_PATH_IMAGE042
为机械振子的位移算符，它与机械振子的无量纲位移算符的关系为
Figure 957975DEST_PATH_IMAGE043
。
Figure 671984DEST_PATH_IMAGE044
为机械振子受到的外部作用力，由上述机械振子的位移算符与机械振子的无量纲位移算符间的关系，可以将相互作用哈密顿量改写为in,
Figure 305277DEST_PATH_IMAGE042
is the displacement operator of the mechanical oscillator, and its relationship with the dimensionless displacement operator of the mechanical oscillator is:
Figure 957975DEST_PATH_IMAGE043
.
Figure 671984DEST_PATH_IMAGE044
is the external force on the mechanical oscillator, from the relationship between the displacement operator of the mechanical oscillator and the dimensionless displacement operator of the mechanical oscillator, the interaction Hamiltonian can be rewritten as

Figure 31422DEST_PATH_IMAGE045
Figure 31422DEST_PATH_IMAGE045

其中，

Figure 156372DEST_PATH_IMAGE046
为机械振子受到的无量纲外部作用力，进一步由牛顿第二定律
Figure 234050DEST_PATH_IMAGE047
，可以得到无量纲外部作用力与待测加速度的关系为
Figure 673121DEST_PATH_IMAGE048
。不失一般性，假定所有机械振子具有相等的加速度
Figure 25081DEST_PATH_IMAGE049
，由此可得
Figure 461878DEST_PATH_IMAGE050
。in,
Figure 156372DEST_PATH_IMAGE046
is the dimensionless external force on the mechanical oscillator, further defined by Newton's second law
Figure 234050DEST_PATH_IMAGE047
, the relationship between the dimensionless external force and the acceleration to be measured can be obtained as
Figure 673121DEST_PATH_IMAGE048
. Without loss of generality, it is assumed that all mechanical oscillators have equal acceleration
Figure 25081DEST_PATH_IMAGE049
,Therefore
Figure 461878DEST_PATH_IMAGE050
.

考虑到上述参数条件以及假设，整个光悬浮N微球阵列系统的哈密顿量可重新写为Considering the above parameter conditions and assumptions, the Hamiltonian of the entire optically suspended N-microsphere array system can be rewritten as

Figure 151486DEST_PATH_IMAGE051
Figure 151486DEST_PATH_IMAGE051

由上述哈密顿量可以得到系统运动满足的量子郎之万方程，From the above Hamiltonian, the quantum Langevin equation satisfied by the motion of the system can be obtained,

Figure 66352DEST_PATH_IMAGE052
Figure 66352DEST_PATH_IMAGE052

其中，

Figure 275748DEST_PATH_IMAGE053
为腔光场的衰减率（线宽）；
Figure 680184DEST_PATH_IMAGE054
为腔光场的噪声输入算符，
Figure 732454DEST_PATH_IMAGE055
为布朗随机力的噪声输入算符。这里引入腔光场的振幅算符
Figure 575645DEST_PATH_IMAGE056
和相位算符
Figure 29760DEST_PATH_IMAGE057
，它们可以在实验上通过零差探测或者外差探测的方法获取。同时，引入相应的噪声输入算符
Figure 418147DEST_PATH_IMAGE058
和
Figure 957713DEST_PATH_IMAGE059
，以及机械振子集体质心运动算符
Figure 276699DEST_PATH_IMAGE060
。将上述算符代入量子郎之万方程，可以得到in,
Figure 275748DEST_PATH_IMAGE053
is the attenuation rate (line width) of the cavity light field;
Figure 680184DEST_PATH_IMAGE054
is the noise input operator of the cavity light field,
Figure 732454DEST_PATH_IMAGE055
Enter the operator for the noise of the Brownian random force. Here the amplitude operator of the cavity light field is introduced
Figure 575645DEST_PATH_IMAGE056
and the phase operator
Figure 29760DEST_PATH_IMAGE057
, which can be obtained experimentally by homodyne detection or heterodyne detection. At the same time, the corresponding noise input operator is introduced
Figure 418147DEST_PATH_IMAGE058
and
Figure 957713DEST_PATH_IMAGE059
, and the collective center of mass motion operator of the mechanical oscillator
Figure 276699DEST_PATH_IMAGE060
. Substituting the above operator into the quantum Langevin equation, we can get

Figure 709954DEST_PATH_IMAGE061
Figure 709954DEST_PATH_IMAGE061

Figure 659456DEST_PATH_IMAGE062
Figure 659456DEST_PATH_IMAGE062

Figure 296104DEST_PATH_IMAGE063
Figure 296104DEST_PATH_IMAGE063

其中,

Figure 356464DEST_PATH_IMAGE064
和
Figure 644226DEST_PATH_IMAGE065
分别表示机械振子受到的外部作用力之和以及环境布朗随机力噪声算符之和。in,
Figure 356464DEST_PATH_IMAGE064
and
Figure 644226DEST_PATH_IMAGE065
Respectively represent the sum of the external force on the mechanical oscillator and the sum of the environmental Brownian random force noise operator.

通过傅里叶变换

Figure 764629DEST_PATH_IMAGE066
将上述量子郎之万方程变换到频域空间，并利用腔内外光场间的输入输出关系
Figure 75525DEST_PATH_IMAGE067
，可以得到腔外透射光场的功率谱密度与外部作用力功率谱密度间的关系为by Fourier transform
Figure 764629DEST_PATH_IMAGE066
Transform the above quantum Langevin equation into the frequency domain space, and use the input-output relationship between the light fields inside and outside the cavity
Figure 75525DEST_PATH_IMAGE067
, the relationship between the power spectral density of the transmitted light field outside the cavity and the power spectral density of the external force can be obtained as

Figure 835449DEST_PATH_IMAGE068
Figure 835449DEST_PATH_IMAGE068

其中，

Figure 853084DEST_PATH_IMAGE069
，
Figure 269022DEST_PATH_IMAGE070
，
Figure 4897DEST_PATH_IMAGE071
，
Figure 469376DEST_PATH_IMAGE072
分别表示外部作用力、环境布朗随机力、腔光场振幅输入噪声以及腔光场相位输入噪声的功率谱密度，机械转移函数、光场转移函数、联合转移函数的具体表达式如下：in,
Figure 853084DEST_PATH_IMAGE069
,
Figure 269022DEST_PATH_IMAGE070
,
Figure 4897DEST_PATH_IMAGE071
,
Figure 469376DEST_PATH_IMAGE072
Represent the power spectral density of external force, environmental Brownian random force, cavity optical field amplitude input noise and cavity optical field phase input noise, respectively. The specific expressions of mechanical transfer function, optical field transfer function, and joint transfer function are as follows:

Figure 216883DEST_PATH_IMAGE073
Figure 216883DEST_PATH_IMAGE073

利用外部作用力与加速度的关系

Figure 944668DEST_PATH_IMAGE074
，可以得到加速度功率谱密度的表达式为Use the relationship between external force and acceleration
Figure 944668DEST_PATH_IMAGE074
, the expression of the acceleration power spectral density can be obtained as

Figure 26893DEST_PATH_IMAGE075
Figure 26893DEST_PATH_IMAGE075

因此，通过腔的透射光可以推断出微球的加速度信息。Therefore, the transmitted light through the cavity can infer the acceleration information of the microspheres.

二. 加速度灵敏度的提升原理2. The principle of improving acceleration sensitivity

根据测量灵敏度的定义：灵敏度是信噪比SNR=1时的信号功率谱密度，可以得到外部作用力的测量灵敏度为According to the definition of measurement sensitivity: the sensitivity is the signal power spectral density when the signal-to-noise ratio SNR=1, and the measurement sensitivity of the external force can be obtained as

Figure 232747DEST_PATH_IMAGE076
Figure 232747DEST_PATH_IMAGE076

由外部作用力与加速度的关系

Figure 21711DEST_PATH_IMAGE077
，可以得到加速度的测量灵敏度为The relationship between external force and acceleration
Figure 21711DEST_PATH_IMAGE077
, the measurement sensitivity of acceleration can be obtained as

Figure 795763DEST_PATH_IMAGE078
Figure 795763DEST_PATH_IMAGE078

由于各个机械振子所遭受的布朗随机力互不关联，因而总布朗随机力的功率谱密度可化简为

Figure 240651DEST_PATH_IMAGE079
，其中
Figure 109250DEST_PATH_IMAGE080
为环境中的平均声子数。同时，由于腔光场的频率非常大
Figure 221563DEST_PATH_IMAGE081
，因而环境中的平均光子数近似为零，由此可以得到
Figure 900937DEST_PATH_IMAGE082
。将上述功率谱密度代入加速度灵敏度的表达式中，可得Since the Brownian random force suffered by each mechanical oscillator is not related to each other, the power spectral density of the total Brownian random force can be simplified as
Figure 240651DEST_PATH_IMAGE079
,in
Figure 109250DEST_PATH_IMAGE080
is the average number of phonons in the environment. At the same time, since the frequency of the cavity light field is very large
Figure 221563DEST_PATH_IMAGE081
, so the average number of photons in the environment is approximately zero, which leads to
Figure 900937DEST_PATH_IMAGE082
. Substituting the above power spectral density into the expression of acceleration sensitivity, we can get

Figure 98700DEST_PATH_IMAGE083
Figure 98700DEST_PATH_IMAGE083

从上式可以看出，加速度测量灵敏度随机械振子数量N的增加而减小（提高）。It can be seen from the above formula that the acceleration measurement sensitivity decreases (increases) with the increase of the number N of mechanical vibrators.

在热噪声极限条件下（环境热噪声为主要噪声来源），加速度测量灵敏度可以进一步化简为Under the thermal noise limit (environmental thermal noise is the main noise source), the acceleration measurement sensitivity can be further simplified as

Figure 443094DEST_PATH_IMAGE084
Figure 443094DEST_PATH_IMAGE084

上式表明，基于光悬浮N微球阵列系统的加速度测量方案的灵敏度是传统单振子光力加速度探测方案灵敏度的

Figure 534546DEST_PATH_IMAGE085
，即加速度测量灵敏度提高了
Figure 509456DEST_PATH_IMAGE086
倍。The above formula shows that the sensitivity of the acceleration measurement scheme based on the optically suspended N-microsphere array system is the sensitivity of the traditional single-vibrator optical acceleration detection scheme.
Figure 534546DEST_PATH_IMAGE085
, that is, the acceleration measurement sensitivity is improved
Figure 509456DEST_PATH_IMAGE086
times.

三. 本发明的加速度测量方法及装置的灵敏度提升验证3. Sensitivity improvement verification of the acceleration measurement method and device of the present invention

根据目前实验上可实现的系统参数给出了不同机械振子数量下加速度测量灵敏度的变化曲线。如图4所示，其中(a)为加速度测量灵敏度随频率的变化曲线，(b)为共振条件下加速度测量灵敏度随机械振子数量的变化曲线。相关系统参数如下：机械振子共振频率

Figure 801372DEST_PATH_IMAGE087
，半径
Figure 152719DEST_PATH_IMAGE088
，质量
Figure 98678DEST_PATH_IMAGE089
，腔光场失谐量
Figure 306806DEST_PATH_IMAGE090
，机械振子与腔光场耦合强度
Figure 213582DEST_PATH_IMAGE091
，腔光场衰减率
Figure 712827DEST_PATH_IMAGE092
，机械振子阻尼率
Figure 654239DEST_PATH_IMAGE093
，环境温度
Figure 95584DEST_PATH_IMAGE094
，重力加速度
Figure 489657DEST_PATH_IMAGE095
。从图4中可以看出，采用本发明的方法及装置测得的加速度测量灵敏度随机械振子数量的增加而减小。According to the system parameters that can be realized in the current experiment, the curve of acceleration measurement sensitivity under different numbers of mechanical oscillators is given. As shown in Figure 4, (a) is the curve of the acceleration measurement sensitivity with frequency, and (b) is the curve of the acceleration measurement sensitivity with the number of mechanical vibrators under the resonance condition. The relevant system parameters are as follows: Mechanical oscillator resonance frequency
Figure 801372DEST_PATH_IMAGE087
,radius
Figure 152719DEST_PATH_IMAGE088
,quality
Figure 98678DEST_PATH_IMAGE089
, the detuning amount of the cavity light field
Figure 306806DEST_PATH_IMAGE090
, the coupling strength of the mechanical oscillator and the cavity optical field
Figure 213582DEST_PATH_IMAGE091
, the cavity light field attenuation rate
Figure 712827DEST_PATH_IMAGE092
, the damping rate of the mechanical oscillator
Figure 654239DEST_PATH_IMAGE093
, the ambient temperature
Figure 95584DEST_PATH_IMAGE094
, the acceleration of gravity
Figure 489657DEST_PATH_IMAGE095
. It can be seen from FIG. 4 that the acceleration measurement sensitivity measured by the method and device of the present invention decreases as the number of mechanical vibrators increases.

四. 对本发明测量方法的数值模拟验证4. Numerical simulation verification of the measuring method of the present invention

这里采用三个纳米微球进行加速度探测模拟，假定三个微球具有相同的加速度

Figure 979544DEST_PATH_IMAGE096
，其中
Figure 650828DEST_PATH_IMAGE097
和
Figure 404020DEST_PATH_IMAGE098
分别为加速度的振幅和频率。利用外部作用力与加速度间的关系可以得到相互作用哈密顿量中的作用力为
Figure 144443DEST_PATH_IMAGE099
，即当哈密顿量中无量纲作用力强度
Figure 375704DEST_PATH_IMAGE100
时，其对应的实际加速度振幅为
Figure 901494DEST_PATH_IMAGE101
。使用量子主方程数值模拟整个探测系统的动力学演化。Here, three nano-microspheres are used for acceleration detection simulation, assuming that the three microspheres have the same acceleration
Figure 979544DEST_PATH_IMAGE096
,in
Figure 650828DEST_PATH_IMAGE097
and
Figure 404020DEST_PATH_IMAGE098
are the amplitude and frequency of the acceleration, respectively. Using the relationship between external force and acceleration, the force in the interaction Hamiltonian can be obtained as
Figure 144443DEST_PATH_IMAGE099
, that is, when the strength of the dimensionless force in the Hamiltonian
Figure 375704DEST_PATH_IMAGE100
When , the corresponding actual acceleration amplitude is
Figure 901494DEST_PATH_IMAGE101
. The dynamic evolution of the entire detection system is numerically simulated using the quantum master equation.

图5给出了(a)

Figure 825588DEST_PATH_IMAGE102
和(b)
Figure 990990DEST_PATH_IMAGE103
两种不同频率加速度情况下的腔外透射光功率谱密度，其中相关系统参数选取如下：机械振子阻尼率
Figure 150576DEST_PATH_IMAGE104
；腔光场失谐量
Figure 389928DEST_PATH_IMAGE105
；腔光场线宽
Figure 357359DEST_PATH_IMAGE106
；机械振子与腔光场耦合强度
Figure 213320DEST_PATH_IMAGE107
，作用力强度
Figure 583121DEST_PATH_IMAGE108
。从图5中可以看出，在两种不同频率加速度的情况下，本发明的加速度探测方法都能从腔透射光中获取到加速度信息，实现加速度测量。Figure 5 gives (a)
Figure 825588DEST_PATH_IMAGE102
and (b)
Figure 990990DEST_PATH_IMAGE103
The power spectral density of the transmitted light outside the cavity under the acceleration of two different frequencies, where the relevant system parameters are selected as follows: the damping rate of the mechanical oscillator
Figure 150576DEST_PATH_IMAGE104
; Cavity light field detuning amount
Figure 389928DEST_PATH_IMAGE105
; cavity light field linewidth
Figure 357359DEST_PATH_IMAGE106
; the coupling strength of the mechanical oscillator and the cavity optical field
Figure 213320DEST_PATH_IMAGE107
, the force strength
Figure 583121DEST_PATH_IMAGE108
. It can be seen from FIG. 5 that the acceleration detection method of the present invention can obtain acceleration information from the cavity transmitted light in the case of accelerations of two different frequencies to realize acceleration measurement.

为了和传统的单振子加速度测量方法进行对比，图6给出了在相同系统参数条件下，使用传统单振子加速度测量方案N=1和本发明基于光悬浮三微球阵列的加速度测量方法N=3在测量相同强度加速度时，腔透射光功率谱密度的数值结果，其中，作用强度

Figure 332771DEST_PATH_IMAGE109
，加速度频率
Figure 333088DEST_PATH_IMAGE110
，机械振子阻尼率
Figure 286132DEST_PATH_IMAGE111
；腔光场失谐量
Figure 928466DEST_PATH_IMAGE112
；腔光场线宽
Figure 204726DEST_PATH_IMAGE113
；机械振子与腔光场耦合强度
Figure 766158DEST_PATH_IMAGE114
。从图6中可以看出，在传统单振子加速度探测方案无法获取加速度信息的情况下，本发明基于光悬浮多微球阵列加速度测量方法仍能获取到加速度信息。该实施例中，利用加速度功率谱密度与透射光功率谱密度的关系，得到加速度功率谱密度后，在频域积分功率谱密度得到加速度的幅值为
Figure 65552DEST_PATH_IMAGE115
，与输入加速度幅值一致。In order to compare with the traditional single-vibrator acceleration measurement method, Fig. 6 shows that under the same system parameters, using the traditional single-vibrator acceleration measurement scheme N=1 and the present invention's acceleration measurement method based on the optically suspended three-microsphere array N= 3 Numerical results of the cavity transmission light power spectral density when measuring the acceleration of the same intensity, where the action intensity
Figure 332771DEST_PATH_IMAGE109
, the acceleration frequency
Figure 333088DEST_PATH_IMAGE110
, the damping rate of the mechanical oscillator
Figure 286132DEST_PATH_IMAGE111
; Cavity light field detuning amount
Figure 928466DEST_PATH_IMAGE112
; cavity light field linewidth
Figure 204726DEST_PATH_IMAGE113
; the coupling strength of the mechanical oscillator and the cavity optical field
Figure 766158DEST_PATH_IMAGE114
. It can be seen from FIG. 6 that, in the case where the traditional single vibrator acceleration detection scheme cannot obtain the acceleration information, the present invention can still obtain the acceleration information based on the optical suspension multi-microsphere array acceleration measurement method. In this embodiment, using the relationship between the power spectral density of the acceleration and the power spectral density of the transmitted light, after obtaining the power spectral density of the acceleration, the amplitude of the acceleration obtained by integrating the power spectral density in the frequency domain is
Figure 65552DEST_PATH_IMAGE115
, which is consistent with the input acceleration amplitude.

本领域普通技术人员可以理解，以上所述仅为发明的优选实例而已，并不用于限制发明，尽管参照前述实例对发明进行了详细的说明，对于本领域的技术人员来说，其依然可以对前述各实例记载的技术方案进行修改，或者对其中部分技术特征进行等同替换。凡在发明的精神和原则之内，所做的修改、等同替换等均应包含在发明的保护范围之内。Those of ordinary skill in the art can understand that the above are only preferred examples of the invention and are not intended to limit the invention. Although the invention has been described in detail with reference to the foregoing examples, those skilled in the art can still Modifications are made to the technical solutions described in the foregoing examples, or equivalent replacements are made to some of the technical features. All modifications and equivalent replacements made within the spirit and principle of the invention shall be included within the protection scope of the invention.

Claims (7)

1. An acceleration measuring method based on an optical suspension multi-microsphere array is characterized in that,
suspending N nano particles in an optical cavity by using holographic optical tweezers, wherein N is more than or equal to 2, and driving the optical cavity by laser to generate a stable standing wave optical field in the optical cavity; by adjusting the holographic optical tweezers, the coupling strength of each nanoparticle and the optical field in the optical cavity is equal, so that a stable optical suspension multi-microsphere array detection system is formed;
acquiring the power spectral density of transmitted light by measuring the transmitted light of the optical cavity; and calculating the acceleration power spectral density by using the relation between the acceleration power spectral density and the transmitted light power spectral density so as to acquire acceleration information.
2. The acceleration measurement method based on the optical suspension multi-microsphere array according to claim 1, wherein the relation between the acceleration power spectral density and the transmission light power spectral density is as follows:
Figure 862514DEST_PATH_IMAGE001
Figure 462122DEST_PATH_IMAGE002
wherein,
Figure 148450DEST_PATH_IMAGE003
the power spectral density of the acceleration to be detected comprises acceleration information to be detected, and the acceleration amplitude can be obtained by integrating the acceleration information in a frequency domain;
Figure 325353DEST_PATH_IMAGE004
the power spectral density of the transmitted light of the optical cavity can be acquired by a detection device;
Figure 309490DEST_PATH_IMAGE005
、
Figure 638971DEST_PATH_IMAGE006
、
Figure 417571DEST_PATH_IMAGE007
respectively representing the power spectral density of the environmental Brownian random force, the power spectral density of cavity light field amplitude input noise and the power spectral density of cavity light field phase input noise;
Figure 81771DEST_PATH_IMAGE008
is a mechanical vibrator transfer function;
Figure 338440DEST_PATH_IMAGE009
is a light field transfer function;
Figure 785077DEST_PATH_IMAGE010
is a joint transfer function;
Figure 734578DEST_PATH_IMAGE011
is a reduced Planck constant;
Figure 620495DEST_PATH_IMAGE012
is the mass of the nanoparticles;
Figure 946434DEST_PATH_IMAGE013
the number of the nano particles is;
Figure 984928DEST_PATH_IMAGE014
is the resonance frequency of the nanoparticles;
Figure 839752DEST_PATH_IMAGE015
is the cavity light field detuning quantity;
Figure 744123DEST_PATH_IMAGE016
is the nanoparticle damping rate;
Figure 342594DEST_PATH_IMAGE017
is the optical cavity optical field attenuation ratio;
Figure 235595DEST_PATH_IMAGE018
is the coupling strength of the nanoparticle and cavity optical fields.
3. The method for measuring acceleration based on optical suspension multi-microsphere array according to claim 1, characterized in that N nanoparticles are arranged at equal intervals along the cavity axis of the optical cavity (2) and the interval is satisfied
Figure 792478DEST_PATH_IMAGE019
Wherein
Figure 325091DEST_PATH_IMAGE020
Is the wavelength of the standing wave field in the optical cavity,nis a positive integer.
4. The acceleration measurement method based on the optical suspension multi-microsphere array according to claim 1, characterized in that the transmitted light of the optical cavity is measured by homodyne detection or heterodyne detection.
5. The method for measuring the acceleration based on the optical suspension multi-microsphere array according to claim 1, wherein a laser with the wavelength of 1064 nm is used for driving the optical cavity.
6. An acceleration measuring device based on an optical suspension multi-microsphere array is characterized by comprising a laser (1), an optical cavity (2), holographic optical tweezers (3) and an optical field detection device (4); wherein N nanoparticles are suspended in the optical cavity (2); wherein the optical axis of the laser (1) and the optical axis of the optical cavity (2) coincide;
the laser (1) is incident from one side of the optical cavity (2) and is excited in the optical cavity (2) to form a stable standing wave optical field; the holographic optical tweezers (3) are used for suspending N nano particles in the optical cavity (2) and adjusting the balance positions of the N nano particles in the optical cavity (2); the light field detection device (4) is used for detecting the transmission light on the other side of the optical cavity (2) and acquiring the power spectral density of the transmission light; and calculating the acceleration power spectral density by using the relation between the acceleration power spectral density and the transmitted light power spectral density so as to acquire acceleration information.
7. The acceleration measurement device based on many microballons of light suspension array of claim 6, characterized in that, the light field detection device (4) is homodyne detection device or heterodyne detection device.
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Citations (27)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US5620857A (en) * 1995-06-07 1997-04-15 United States Of America, As Represented By The Secretary Of Commerce Optical trap for detection and quantitation of subzeptomolar quantities of analytes
RU2106627C1 (en) * 1996-07-22 1998-03-10 Андрей Федорович Александров Device for monitoring parameters of suspended particles
US20040239937A1 (en) * 2003-03-17 2004-12-02 Massachusetts Institute Of Technology Method and apparatus for inertial sensing via measurement of trapped orbit dynamics
US20050078343A1 (en) * 2003-05-16 2005-04-14 Grier David G. Optical fractionation methods and apparatus
CN101103416A (en) * 2005-01-21 2008-01-09 纽约大学 Modulated Optical Tweezers
CN101788571A (en) * 2010-01-28 2010-07-28 哈尔滨工业大学 Nanomanipulation method for compounding laser near-field optical tweezers and AFM probe
US20110059864A1 (en) * 2009-09-07 2011-03-10 Caerus Molecular Diagnostics Incorporated Sequence Determination By Use Of Opposing Forces
CN103941040A (en) * 2014-04-23 2014-07-23 浙江大学 Device and method for detecting acceleration on basis of back scattered light of nano particle detection
CN104503077A (en) * 2014-12-24 2015-04-08 中国科学院上海高等研究院 Opto-electronic hybrid system realizing quantum coherence
CN105759074A (en) * 2016-03-07 2016-07-13 浙江大学 Optical suspension-type microballoon rising and supporting method and device
JP2016218282A (en) * 2015-05-21 2016-12-22 国立研究開発法人産業技術総合研究所 Fine particle array creation and orientation control method
CN106935307A (en) * 2017-02-18 2017-07-07 浙江大学 Precise control microballoon based on pulse laser carries out the method and device of light suspension
CN108254632A (en) * 2017-12-22 2018-07-06 同济大学 Based on SiO2The method that microballoon movable information analyzes its surface charge density
CN108426633A (en) * 2018-05-25 2018-08-21 浙江大学 A kind of vibration measuring method and vibration detecting device based on ligh trap
CN109269980A (en) * 2018-10-16 2019-01-25 中国科学院光电技术研究所 High-resolution optical detection method based on single optical tweezers medium microspheres
CN111983708A (en) * 2020-08-07 2020-11-24 浙江大学 Optical trap-based gravity measurement device and method
US20210039102A1 (en) * 2018-02-01 2021-02-11 Arizona Board Of Regents On Behalf Of The University Of Arizona Methods and systems for designing and producing nano-structured optical devices
CN112612133A (en) * 2021-01-05 2021-04-06 华侨大学 Array optical tweezers based on grating moire fringes
CN113484538A (en) * 2021-07-05 2021-10-08 南京大学 Acceleration measurement method based on anti-magnetic suspension mechanical system
CN113514179A (en) * 2021-08-11 2021-10-19 之江实验室 Force field gradient measuring device and method based on double-vibrator suspension optomechanics system
CN113848382A (en) * 2021-09-07 2021-12-28 浙江大学 Frequency characteristic test method and optical tweezers system based on electric field force excitation
US20220026331A1 (en) * 2020-07-22 2022-01-27 Purdue Research Foundation Axially-Offset Differential Interference Contrast Correlation Spectroscopy
CN114049980A (en) * 2021-09-18 2022-02-15 浙江大学 Novel microsphere supporting system and method in vacuum optical tweezers
CN114077067A (en) * 2021-11-29 2022-02-22 曲阜师范大学 A device for generating a vector light field whose polarization varies along an arbitrary circular path on the Poincaré sphere
CN114280327A (en) * 2021-12-14 2022-04-05 广州大学 Highly sensitive acceleration measurement method and sensor based on fiber optic tweezers
CN114414905A (en) * 2022-04-01 2022-04-29 之江实验室 A method and device for measuring electric field based on suspended particles
CN114414043A (en) * 2021-12-23 2022-04-29 之江实验室 A device and method for measuring optical field intensity distribution based on optical tweezers and electric field force

Patent Citations (27)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US5620857A (en) * 1995-06-07 1997-04-15 United States Of America, As Represented By The Secretary Of Commerce Optical trap for detection and quantitation of subzeptomolar quantities of analytes
RU2106627C1 (en) * 1996-07-22 1998-03-10 Андрей Федорович Александров Device for monitoring parameters of suspended particles
US20040239937A1 (en) * 2003-03-17 2004-12-02 Massachusetts Institute Of Technology Method and apparatus for inertial sensing via measurement of trapped orbit dynamics
US20050078343A1 (en) * 2003-05-16 2005-04-14 Grier David G. Optical fractionation methods and apparatus
CN101103416A (en) * 2005-01-21 2008-01-09 纽约大学 Modulated Optical Tweezers
US20110059864A1 (en) * 2009-09-07 2011-03-10 Caerus Molecular Diagnostics Incorporated Sequence Determination By Use Of Opposing Forces
CN101788571A (en) * 2010-01-28 2010-07-28 哈尔滨工业大学 Nanomanipulation method for compounding laser near-field optical tweezers and AFM probe
CN103941040A (en) * 2014-04-23 2014-07-23 浙江大学 Device and method for detecting acceleration on basis of back scattered light of nano particle detection
CN104503077A (en) * 2014-12-24 2015-04-08 中国科学院上海高等研究院 Opto-electronic hybrid system realizing quantum coherence
JP2016218282A (en) * 2015-05-21 2016-12-22 国立研究開発法人産業技術総合研究所 Fine particle array creation and orientation control method
CN105759074A (en) * 2016-03-07 2016-07-13 浙江大学 Optical suspension-type microballoon rising and supporting method and device
CN106935307A (en) * 2017-02-18 2017-07-07 浙江大学 Precise control microballoon based on pulse laser carries out the method and device of light suspension
CN108254632A (en) * 2017-12-22 2018-07-06 同济大学 Based on SiO2The method that microballoon movable information analyzes its surface charge density
US20210039102A1 (en) * 2018-02-01 2021-02-11 Arizona Board Of Regents On Behalf Of The University Of Arizona Methods and systems for designing and producing nano-structured optical devices
CN108426633A (en) * 2018-05-25 2018-08-21 浙江大学 A kind of vibration measuring method and vibration detecting device based on ligh trap
CN109269980A (en) * 2018-10-16 2019-01-25 中国科学院光电技术研究所 High-resolution optical detection method based on single optical tweezers medium microspheres
US20220026331A1 (en) * 2020-07-22 2022-01-27 Purdue Research Foundation Axially-Offset Differential Interference Contrast Correlation Spectroscopy
CN111983708A (en) * 2020-08-07 2020-11-24 浙江大学 Optical trap-based gravity measurement device and method
CN112612133A (en) * 2021-01-05 2021-04-06 华侨大学 Array optical tweezers based on grating moire fringes
CN113484538A (en) * 2021-07-05 2021-10-08 南京大学 Acceleration measurement method based on anti-magnetic suspension mechanical system
CN113514179A (en) * 2021-08-11 2021-10-19 之江实验室 Force field gradient measuring device and method based on double-vibrator suspension optomechanics system
CN113848382A (en) * 2021-09-07 2021-12-28 浙江大学 Frequency characteristic test method and optical tweezers system based on electric field force excitation
CN114049980A (en) * 2021-09-18 2022-02-15 浙江大学 Novel microsphere supporting system and method in vacuum optical tweezers
CN114077067A (en) * 2021-11-29 2022-02-22 曲阜师范大学 A device for generating a vector light field whose polarization varies along an arbitrary circular path on the Poincaré sphere
CN114280327A (en) * 2021-12-14 2022-04-05 广州大学 Highly sensitive acceleration measurement method and sensor based on fiber optic tweezers
CN114414043A (en) * 2021-12-23 2022-04-29 之江实验室 A device and method for measuring optical field intensity distribution based on optical tweezers and electric field force
CN114414905A (en) * 2022-04-01 2022-04-29 之江实验室 A method and device for measuring electric field based on suspended particles

Non-Patent Citations (7)

* Cited by examiner, † Cited by third party
Title
RAFAEL A. B. SUAREZ: "《Optical trapping with non-diffracting Airy beams array using a holographic optical tweezers》", 《OPTICS & LASER TECHNOLOGY》 *
TENGFANG KUANG: "《2020 IEEE International Symposium on Inertial Sensors and Systems (INERTIAL)》", 《CHARACTERISTIC OF INTRACAVITY OPTICAL TWEEZERS IN ACCELERATION DETECTION》 *
ZHENHAI FU: "《Force detection sensitivity spectrum calibration of levitated nanomechanical sensor using harmonic coulomb force》", 《OPTICS AND LASERS IN ENGINEERING》 *
ZHENHAI FU: "《Launch and capture of a single particle in a pulse-laser-assisted dual-beam fiber-optic trap》", 《OPTICS COMMUNICATIONS》 *
沈瑜: "《基于激光捕获的加速度测量原理及仿真》", 《红外与激光工程》 *
缪立军: "《光阱中微粒位置高精度检测技术》", 《红外与激光工程》 *
蒋建斌: "《基于卡尔曼滤波的真空光阱悬浮微球位移探测》", 《光子学报》 *

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