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 PDFInfo
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Abstract
The invention discloses an acceleration measuring method and device based on an optical suspension multi-microsphere array.N nano-particles are suspended in an optical cavity by adopting holographic optical tweezers, N is more than or equal to 2, and the optical cavity is driven 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, and a stable optical suspension multi-microsphere array detection system is formed; acquiring the power spectral density of the 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. The acceleration measurement method provided by the invention utilizes the principle that the mass of the mechanical vibrator can be equivalently increased by utilizing the collective mass center motion of the mechanical vibrator to carry out acceleration measurement, and the acceleration measurement sensitivity is improved. The acceleration measurement sensitivity of the method of the invention is continuously improved along with the increase of the number of the mechanical vibrators.
Description
Technical Field
The invention relates to the field of acceleration measurement, in particular to an acceleration measurement method and device based on an optical suspension multi-microsphere array.
Background
The optical tweezers serving as an effective tool for controlling the micro-nano-scale object are widely applied to the fields of biology, material science, physics, informatics and the like, and the inventor of the optical tweezers is awarded a 2018 Nobel prize in Physics. In recent years, a suspended optical force system formed by suspending a micro-nano-scale object by using vacuum optical tweezers becomes a hot point for researching physics. The suspension optical force system has the capability of measuring and controlling the motion of a micro-nano scale object (mechanical vibrator) with ultrahigh precision, so that the suspension optical force system is widely applied to basic science and engineering technology. The optical suspension mechanical oscillator avoids loss and noise caused by mechanical support, and the high vacuum environment can greatly reduce the influence of thermal noise of surrounding gas molecules, so that the suspension optical power system has ultrahigh detection sensitivity, and the suspension optical power system becomes a popular research direction in the fields of precision measurement and sensing. Moreover, the mechanical vibrator in the suspension optical force system is almost in a state of being completely isolated from the external environment, so that a nearly isolated system is formed, and the system is an ideal system for basic physical research. Therefore, the suspended optical force system becomes a powerful tool for precise measurement and leading-edge basic physical research. The suspension optical force system has the advantages of small volume, flexible and controllable trapping optical traps, capability of working at room temperature and capability of being integrated on a chip, and the characteristics enable the suspension optical force system to have wide application prospects in the fields of commercial detectors and sensors.
In recent years, with the continuous progress of the optical tweezers technology and the micro-nano processing technology, the quality factor of a mechanical vibrator in a suspension optomechanics system is higher and higher, and the capture life is longer and longer, so that the suspension optomechanics system is rapidly developed in the fields of precision measurement and sensing. The detection device based on suspension optomechanics has realized the high accuracy detection to multiple mechanical quantities such as force, acceleration. However, many challenges are still faced in the further development of suspended optical power systems.
In a traditional single-vibrator suspended optomechanical detection device, single micro-nano-scale particles (mechanical vibrators) are suspended in vacuum by using optical tweezers, and the mechanical vibrators perform micro simple harmonic motion in optical traps generated by the optical tweezers. The external force to be measured acts on the mechanical vibrator to change the motion state of the mechanical vibrator, and the corresponding change is reflected in scattered light of the mechanical vibrator, so that mechanical quantity detection is realized by measuring the scattered light. In the aspect of acceleration measurement, the sensitivity of the traditional single-vibrator suspension light force acceleration measurement scheme is
Wherein the content of the first and second substances,
is the boltzmann constant, and is,
is at the temperature of the surroundings and is,
the mechanical vibrator damping rate. From the above formula, it can be seen that the acceleration measurement sensitivity is inversely proportional to the mass of the mechanical vibrator, and the acceleration measurement sensitivity can be improved by increasing the mass of the mechanical vibrator. However, it is difficult to suspend a large-mass mechanical oscillator technically using optical tweezers. The main reason is that the gravity borne by the mechanical vibrator increases with the increase of the mass of the mechanical vibrator, so that the optical tweezers need to provide a large optical field gradient force to balance the gravity borne by the mechanical vibrator. The optical field force generated by the optical tweezers can be increased by increasing the output power of the laser, but the heating effect of the optical tweezers on the mechanical oscillator can be enhanced, so that the internal temperature of the mechanical oscillator is increased, the sensitivity is reduced, and even the mechanical oscillator can be melted by excessive optical power.
Disclosure of Invention
Aiming at the defects of the existing acceleration measurement technology based on a single-vibrator suspension optical force system, the invention provides an acceleration measurement method and device based on an optical suspension multi-microsphere array. A plurality of micro-nano-scale microspheres (particles) are suspended in an optical cavity by utilizing holographic optical tweezers to form an optical suspension multi-microsphere array system, each nano-microsphere serves as a mechanical oscillator, the collective mass center motion of the nano-microspheres is coupled to an optical field in the cavity through the optical force interaction, and therefore the acceleration information of the nano-microspheres is obtained through a measuring cavity transmission optical field.
The purpose of the invention is realized by the following technical scheme:
an acceleration measuring method based on an optical suspension multi-microsphere array is characterized in that N nanoparticles are suspended in an optical cavity by using holographic optical tweezers, N is more than or equal to 2, and the optical cavity is driven 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.
Further, the relationship between the acceleration power spectral density and the transmission light power spectral density is as follows:
wherein the content of the first and second substances,
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;
the power spectral density of the transmitted light of the optical cavity can be acquired by a detection device;
、
、
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;
is a mechanical vibrator transfer function;
is a light field transfer function;
is a joint transfer function;
is a reduced planck constant;
is the mass of the nanoparticles;
the number of the nano particles is;
is the resonance frequency of the nanoparticles;
is the cavity light field detuning quantity;
is the nanoparticle damping rate;
is the optical cavity optical field attenuation ratio;
is the coupling strength of the nanoparticle and cavity optical fields.
Further, N nano particles are arranged at equal intervals along the cavity axis direction of the optical cavity, and the interval satisfies
Wherein
Is the wavelength of the standing wave field in the optical cavity,nis a positive integer.
Further, the transmitted light of the optical cavity is measured by means of homodyne detection or heterodyne detection.
Further, the optical cavity is driven with a laser having a wavelength of 1064 nm.
A device for realizing an acceleration measurement method based on an optical suspension multi-microsphere array comprises a laser, an optical cavity, holographic optical tweezers and an optical field detection device; wherein N nanoparticles are suspended in the optical cavity; wherein the optical axis of the laser and the optical axis of the optical cavity coincide;
the laser is incident from one side of the optical cavity, and a stable standing wave optical field is formed in the optical cavity through excitation; the holographic optical tweezers are used for suspending N nano particles in the optical cavity and adjusting the balance positions of the N nano particles in the optical cavity; the light field detection device is used for detecting the transmission light on the other side of the optical cavity 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.
Further, the light field detection device is a homodyne detection device or a heterodyne detection device.
The invention has the following beneficial effects:
the acceleration measurement method provided by the invention utilizes the mass center motion of the mechanical vibrator set to measure the acceleration, and the acceleration measurement sensitivity can be improved by the principle that the mass of the mechanical vibrator can be equivalently increased through the mass center motion of the mechanical vibrator set. The acceleration measurement sensitivity of the method of the invention is continuously improved along with the increase of the number of the mechanical vibrators. Under the limit condition of thermal noise (environmental thermal noise is a main noise source), the sensitivity of the method is 1/N of that of the traditional single-vibrator suspension light force acceleration measuring method, namely, the acceleration sensitivity is improved by N times, and the limitation of the mass of a mechanical vibrator on the acceleration sensitivity is broken through.
Drawings
Fig. 1 is a schematic diagram of the apparatus of the present invention according to an exemplary embodiment.
FIG. 2 is a schematic diagram illustrating an acceleration measurement method of the present invention according to an exemplary embodiment.
Fig. 3 is a flow chart illustrating a method of the present invention according to an exemplary embodiment.
FIG. 4 is a graph showing the variation of the sensitivity of acceleration measurement for different mechanical oscillators; wherein, (a) is the change curve of the acceleration sensitivity along with the frequency, and (b) is the change curve of the acceleration measurement sensitivity along with the number of mechanical vibrators under the resonance condition.
FIG. 5 is a numerical simulation result of measuring acceleration at different frequencies using an optically suspended three microsphere array system.
FIG. 6 is a numerical simulation result of measuring acceleration with the same intensity under the same conditions by using a traditional single-vibrator acceleration measurement scheme and the acceleration measurement method based on the optical suspension three-microsphere array.
In fig. 1, a laser 1, an optical cavity 2, holographic optical tweezers 3, an optical field detection device 4, a first nanoparticle 5, a second nanoparticle 6 … …, and an nth nanoparticle N + 4.
Detailed Description
The present invention will be described in detail below with reference to the accompanying drawings and preferred embodiments, and the objects and effects of the present invention will become more apparent, it being understood that the specific embodiments described herein are merely illustrative of the present invention and are not intended to limit the present invention.
As shown in fig. 1, as one embodiment, the acceleration measuring device based on the optical suspension multi-microsphere array of the present invention includes a laser 1, an optical cavity 2, holographic optical tweezers 3, an optical field detection device 4, a first nanoparticle 5, a second nanoparticle 6 … …, an nth nanoparticle N + 4.
The optical axis of the laser 1 and the optical axis of the optical cavity 2 coincide and the optical cavity 2 is driven from the left for forming 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 for adjusting the balance 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 optical field detection device 4 may use a homodyne detection device or a heterodyne detection device, which is mainly used for measuring the transmitted light at the other side of the cavity, so as to acquire the acceleration information of the nanoparticles through the transmitted light.
The acceleration measurement principle of the invention is shown in figure 2, which is as follows: the holographic optical tweezers suspend N nanometer particles in an optical cavity driven by laser, so that the N nanometer particles are coupled with the optical field of the same cavity. Each nanometer particle is a mechanical vibrator, the acceleration information of the collective mass center motion of all the mechanical vibrators is coupled into the cavity light field through the optical force interaction between the mechanical vibrators and the cavity light field, and therefore the acceleration information of the collective mass center motion of the mechanical vibrators can be obtained through measuring the cavity light field.
As shown in fig. 3, the acceleration measurement method based on the optical suspension multi-microsphere array specifically includes:
n nano particles are suspended in the optical cavity 2 by using the holographic optical tweezers 3, and the optical cavity 2 is driven by laser to generate a stable standing wave optical field in the optical cavity 2; by adjusting the holographic optical tweezers 3, the coupling strength of each nanoparticle and the optical field in the optical cavity 2 is equal, and a stable optical suspension multi-microsphere array detection system is formed;
acquiring the power spectral density of the transmitted light by measuring the transmitted light of the optical cavity 2; 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.
The principle of the invention for improving the sensitivity of acceleration measurement can be briefly summarized as follows: the acceleration measurement is carried out by utilizing the collective mass center motion of the light suspension multiple nano microspheres to replace the motion of a single mechanical vibrator, so that the quality of the mechanical vibrator is equivalently improved, and the sensitivity of the acceleration measurement can be improved.
The following theoretically and specifically analyzes and explains the measurement principle of the acceleration measurement method based on the optical suspension multi-microsphere array and the sensitivity improvement principle and effect.
Acceleration measurement principle based on optical suspension multi-microsphere array
Without loss of generality, N nano microspheres (mechanical vibrators) with mass m are considered to be suspended in an optical cavity by holographic optical tweezers to form an optical suspension N microsphere arrayProvided is a system. Since all mechanical vibrators are suspended in the same optical cavity and are all under the same vacuum condition, they have the same damping rate
And they are also independent of each other from the surrounding brownian random forces. In the suspension optical force system, the resonance frequency of the mechanical vibrator is related to the intensity of the optical trap for capturing the mechanical vibrator, so that all the mechanical vibrators can have the same resonance frequency by adjusting the holographic optical tweezers to change the intensity distribution of the captured optical trap
. Thus, the Hamiltonian of the entire photosuspension N-microsphere array system can be written as
Wherein the content of the first and second substances,
is a reduced Planck constant;
is labeled as a mechanical vibrator;
an annihilation operator that is a cavity light field;
dimensionless momentum operators for mechanical vibrators;
is a dimensionless displacement operator of a mechanical vibrator,
is the cavity light field detuning quantity.
The coupling strength of the mechanical vibrator and the cavity optical field and the balance position of the mechanical vibrator and the mechanical vibrator
Cavity optical field wavelength
Related, can be simply expressed as
Wherein, the first and the second end of the pipe are connected with each other,Cis a parameter related to the cavity optical field wavelength, dielectric constant, etc. Therefore, the position of each mechanical oscillator is adjusted through the holographic optical tweezers, so that all the mechanical oscillators and the cavity optical field have equal coupling strength
. An alternative nanoparticle placement scheme is provided herein: all the mechanical vibrators are arranged at equal intervals along the cavity axis direction, and the interval satisfies
Wherein
Is a positive integer. Other nanoparticle arrangements are possible as long as all mechanical vibrators and the cavity optical field have equal coupling strength.
The Hamilton quantity of the interaction between the mechanical vibrator and the external force (acceleration) is
Wherein the content of the first and second substances,
is a position of a mechanical vibratorA shift operator having a relation with the dimensionless shift operator of the mechanical vibrator
。
The Hamiltonian of the interaction can be rewritten to be an external force applied to the mechanical vibrator by a relationship between the displacement operator of the mechanical vibrator and the dimensionless displacement operator of the mechanical vibrator
Wherein the content of the first and second substances,
the dimensionless external force applied to the mechanical vibrator is further determined by Newton's second law
The relation between the dimensionless external acting force and the acceleration to be measured can be obtained as
. Without loss of generality, it is assumed that all mechanical vibrators have equal acceleration
From this can be obtained
。
Considering the above parametric conditions and assumptions, the Hamilton values of the entire photo-suspended N-microsphere array system can be rewritten as
The Hamiltonian can obtain quantum Langmuim equation satisfied by system motion,
wherein the content of the first and second substances,
the attenuation ratio (line width) of the cavity light field;
an operator is input for the noise of the cavity light field,
an operator is input for the noise of the brownian random force. Amplitude operator introduced here into the cavity light field
Sum phase operator
They can be acquired experimentally by homodyne or heterodyne detection methods. At the same time, corresponding noise input operators are introduced
And
and a mechanical vibrator collective centroid motion operator
. The above-mentioned operator is substituted into Quanlangevin equation to obtain
Wherein the content of the first and second substances,
and
respectively representing the sum of external forces to which the mechanical vibrator is subjected and the sum of environmental brownian random force noise operators.
By Fourier transform
Transforming the quantum Langmuim equation to frequency domain space, and using the input-output relationship between the light fields inside and outside the cavity
The relation between the power spectral density of the transmission optical field outside the cavity and the power spectral density of the external acting force can be obtained as
Wherein the content of the first and second substances,
，
，
，
respectively representing external acting force, environmental Brownian random force, cavity light field amplitude input noise and cavity light field phase inputSpecific expressions of power spectral density, mechanical transfer function, optical field transfer function and combined transfer function of noise are as follows:
using the relationship between external force and acceleration
The expression of the power spectral density of the acceleration can be obtained as
Thus, acceleration information of the microsphere can be inferred by the transmitted light of the cavity.
Acceleration sensitivity improvement principle
According to the definition of the 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
From external force to acceleration
The measurement sensitivity of the acceleration can be obtained as
Since the Brownian random forces suffered by the various mechanical vibrators are not related, the power spectral density of the total Brownian random force can be simplified into
Wherein
Is the average number of phonons in the environment. At the same time, the frequency of the optical field is very large due to the cavity
And thus the average number of photons in the environment is approximately zero, from which it can be derived
. Substituting the power spectral density into an expression of acceleration sensitivity to obtain
As can be seen from the above equation, the acceleration measurement sensitivity decreases (increases) with an increase in the number N of mechanical vibrators.
Under thermal noise limit conditions (ambient thermal noise being the dominant noise source), acceleration measurement sensitivity can be further reduced to
The formula shows that the sensitivity of the acceleration measurement scheme based on the optical suspension N microsphere array system is that of the traditional single-vibrator light force acceleration detection scheme
I.e. the sensitivity of acceleration measurement is improved
And (4) doubling.
Third, the sensitivity of the acceleration measuring method and device of the invention is improved and verified
The variation curve of the acceleration measurement sensitivity under different mechanical vibrator quantities is given according to the system parameters which can be realized in the current experiment. As shown in FIG. 4, where (a) is acceleration measurement sensitiveThe variation curve of degree along with frequency, and (b) the variation curve of acceleration measurement sensitivity along with the number of mechanical vibrators under the resonance condition. The relevant system parameters are as follows: resonant frequency of mechanical vibrator
Radius of
Mass of
Amount of cavity field detuning
Mechanical oscillator and cavity optical field coupling strength
Cavity optical field attenuation ratio
Damping ratio of mechanical vibrator
Ambient temperature
Acceleration of gravity
. As can be seen from fig. 4, the acceleration measurement sensitivity measured by the method and apparatus of the present invention decreases as the number of mechanical vibrators increases.
Fourth, the numerical simulation verification of the measuring method of the invention
Here, three nanospheres were used for acceleration detection simulation, assuming that the three nanospheres have the same acceleration
Wherein
And
respectively the amplitude and frequency of the acceleration. The relationship between the external force and the acceleration is used to obtain the force in the Hamiltonian of the interaction
I.e. dimensionless force intensity in Hamiltonian
At a corresponding actual acceleration amplitude of
. And numerically simulating the dynamic evolution of the whole detection system by using a quantum principal equation.
FIG. 5 shows (a)
And (b)
The outside cavity transmission optical power spectral density under two different frequency acceleration conditions is characterized in that the relevant system parameters are selected as follows: damping rate of mechanical vibrator
(ii) a Cavity optical field detuning quantity
(ii) a Cavity light field linewidth
(ii) a Mechanical oscillator and cavity optical field coupling strength
Strength of acting force
. As can be seen from FIG. 5, under the condition of acceleration with two different frequencies, the acceleration detection method of the present invention can acquire acceleration information from the cavity transmitted light, so as to realize acceleration measurement.
For comparison with the conventional single-vibrator acceleration measurement method, fig. 6 shows the numerical results of cavity transmitted light power spectral density when the acceleration with the same intensity is measured by using the conventional single-vibrator acceleration measurement scheme N =1 and the acceleration measurement method based on the optical suspension three-microsphere array N =3 under the same system parameter conditions, wherein the action intensity is
Frequency of acceleration
Damping ratio of mechanical vibrator
(ii) a Cavity optical field detuning quantity
(ii) a Cavity light field linewidth
(ii) a Mechanical oscillator and cavity optical field coupling strength
. As can be seen from fig. 6, in the case that the acceleration information cannot be obtained by the conventional single-oscillator acceleration detection scheme, the acceleration information can still be obtained by the optical suspension multi-microsphere array-based acceleration measurement method of the present invention. In the embodiment, after the acceleration power spectral density is obtained by using the relation between the acceleration power spectral density and the transmission light power spectral density, the amplitude of the acceleration is obtained by integrating the power spectral density in the frequency domain
Consistent with the input acceleration amplitude.
It will be understood by those skilled in the art that the foregoing is only a preferred embodiment of the present invention, and is not intended to limit the invention, and although the invention has been described in detail with reference to the foregoing examples, it will be apparent to those skilled in the art that various changes in the form and details of the embodiments may be made and equivalents may be substituted for elements thereof. All modifications, equivalents and the like which come within the spirit and principle of the invention are intended to be included within the 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:
wherein the content of the first and second substances,
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;
the power spectral density of the transmitted light of the optical cavity can be acquired by a detection device;
、
、
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;
is a mechanical vibrator transfer function;
is a light field transfer function;
is a joint transfer function;
is a reduced Planck constant;
is the mass of the nanoparticles;
the number of the nano particles is;
is the resonance frequency of the nanoparticles;
is the cavity light field detuning quantity;
is the nanoparticle damping rate;
is the optical cavity optical field attenuation ratio;
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
Wherein
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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