Method for measuring transverse temperature of atomic group in atomic interferometer

Abstract

The present application belongs to the field of precision measurement, and particularly discloses a method for measuring the transverse temperature of an atomic group in an atomic interferometer. The present application first controls the size of the atomic group at the moment of acting on the Raman light pulse by adjusting the opening time, and then performs a Rabi oscillation experiment under different atomic group sizes. Then, the experimental data are fitted with a trigonometric function, and the key parameters reflecting the transverse temperature are extracted therefrom. Finally, the transverse temperature of the atomic group is obtained by inversion calculation. The method is based on the Gaussian distribution of the atomic group density and the Raman light intensity in the transverse space, and the coupling result of the two is the non-uniformity of atomic transition in the transverse space, thereby affecting the average transition probability of the whole atomic group, i.e. the linearity of the Rabi oscillation curve. Conversely, the linearity of the Rabi oscillation of the atomic group contains the transverse parameters of the atomic group, and the transverse parameters of the atomic group are extracted from the linearity of the Rabi oscillation. The present application can be completed only by relying on the atomic interferometer itself, and has low requirements for equipment, simple process and easy operation.

Description

Technical Field

[0001] This invention belongs to the field of precision measurement, specifically relating to the field of neutral atom interferometry precision measurement technology, and more specifically, relating to a method for measuring the transverse temperature of atomic groups in an atomic interferometer. Background Technology

[0002] Atomic interferometers are measuring instruments based on the interference properties of matter waves. Over the past thirty years, cold atom interferometry technology has developed rapidly and has become an important means of achieving high-precision measurements in the field of measurement. Cold atom interferometers, represented by gravimeters (gravity gradient meters) and gyroscopes, have been widely used in fundamental physics research such as equivalence principle testing and the measurement of the gravitational constant, as well as in inertial sensing fields such as gravity, gravity gradient, and rotation measurements. Cold atom interferometry technology has significant implications for basic scientific research, resource exploration, and national defense security.

[0003] An atomic interferometer mainly consists of three parts: a vacuum system, an optical system, and a circuit system. The vacuum system provides an ultra-high vacuum environment for atomic interferometry experiments; the optical system generates laser beams for manipulating atoms, such as trapping light and Raman spectroscopy; and the circuit system locks the laser frequency and power, and can be controlled at the microsecond level via LabVIEW, thus indirectly controlling the optical system to meet the laser requirements of different experimental stages. In a typical atomic interferometer, atoms are first cooled and trapped using magneto-optical trap technology. The trapped atomic clusters are then released or thrown upwards to allow free fall. Polarization gradient cooling technology is then used to further cool the atomic clusters to a temperature of a few microkJ. The resulting atomic clusters are called initial atomic clusters, and their spatial density and velocity follow a Gaussian distribution. As the atomic clusters fly freely, they continuously diffuse in space, widening the space. This diffusion phenomenon causes a series of systematic error effects, affecting the measurement accuracy of the atomic interferometer. The key to achieving a high-precision atomic interferometer lies in accurately evaluating numerous systematic errors. Among them, wavefront distortion effect is a systematic error caused by the coupling of the phase distortion of the Raman light wavefront and the lateral distribution of the atomic clusters (the propagation direction of the Raman light is longitudinal). The lateral distribution of the atomic clusters depends on the lateral parameters such as the lateral temperature, center position, and initial size of the atomic clusters. Accurate measurement of the lateral parameters of the atomic clusters is a key link in improving the accuracy of wavefront distortion effect evaluation [1]. (Reference: 1: Qin Luo et al., "Observing the effect of wave-front aberrations in an atom interferometer by modulating the diameter of Raman beams", Phys. Rev. A 93, 043610 (2016))

[0004] Currently, the main methods for measuring the temperature of atomic clusters include: (a) Time-of-flight (TOF) technology: After a cold atomic cluster has been freely flying for a period of time, it diffuses to a certain volume, allowing it to pass through the probe light. The TOF signal is obtained by fluorescence collection, and the spatial broadening of the atomic cluster in the direction of motion can be estimated using the width of the TOF signal, thereby estimating its temperature. This method is widely used in cold atom experiments for estimating the temperature of atomic clusters; (b) CCD imaging method: Using a CCD (charge-coupled device) to photograph atomic clusters at different diffusion times, the change in the spatial density distribution of the atomic cluster is obtained, thereby measuring the temperature of the atomic cluster; (c) Knife-edge method: By precisely controlling the irradiation range of the near-resonance removal light, atoms at the edge of the atomic cluster are selectively removed, and the relationship between the number of remaining atoms and the knife-edge position is measured. Combined with a Gaussian distribution model, the temperature is finally calculated; (d) Raman spectroscopy: By adding a transverse vacuum window, Raman light can be applied transversely to interact with the atomic cluster. By scanning the Raman light frequency, the transverse velocity distribution of the atomic cluster can be directly measured according to the Doppler effect, thereby obtaining the transverse temperature of the atomic cluster.

[0005] Among the above measurement methods, the time-of-flight method does not require additional measuring equipment and has a simple operation procedure, but its measurement accuracy is limited by the initial size of the atomic group and generally measures the longitudinal temperature rather than the transverse temperature; the CCD imaging method requires a high-resolution CCD camera system, which is expensive and requires a spare window in the vacuum container to install the CCD; the knife-edge method has a relatively complex experimental setup and strict requirements for equipment stability, requiring a precision displacement stage and aperture control system, which is prone to introducing displacement errors, and the experimental operation is relatively complex; the Raman spectroscopy method directly measures the transverse velocity distribution of the atomic group and can accurately measure the transverse temperature of the atomic group, but requires an additional transverse window. Summary of the Invention

[0006] In view of the shortcomings of the prior art, the purpose of this invention is to provide a method for measuring the transverse temperature of atomic groups in an atomic interferometer, which aims to solve the problems of complex procedures and the need for additional testing equipment and windows in existing methods for measuring the transverse temperature of atomic groups.

[0007] To achieve the above objectives, this invention proposes a method for measuring the transverse temperature of atomic groups in an atomic interferometer, comprising:

[0008] Step 1, Raman spectroscopy The radius and divergence angle are calibrated, and the Raman light is generated by the optical path system in the atomic interferometer;

[0009] The second step is to use the calibrated Raman light... The radius is used to predict the Raman beam switching time.

[0010] The third step is to modulate the Raman light on-time near the predicted value and perform Rabi oscillation measurement.

[0011] The fourth step is data processing. The Rabi oscillation curve is fitted to determine the Raman light on-time that best matches the theoretical curve. The transverse temperature of the atomic group is calculated by combining the atomic mass, the spot radius, and the Boltzmann constant.

[0012] Preferably, the Raman light intensity distribution is obtained by measuring the light intensity distribution on the Raman light cross section and fitting it with a Gaussian function. The radius; by measuring the intensity distribution of the Raman beam cross section at different propagation distances and fitting it with a Gaussian function, the Raman beam is obtained. The radius varies with the propagation distance, thus allowing the divergence angle of the Raman light to be calculated.

[0013] Preferably, before proceeding to the second step, the spatial position of the Raman light is scanned so that the distance between the Raman light center and the center of the atomic group does not exceed [the specified value]. .

[0014] Furthermore, to ensure that the Raman beam center coincides with the atomic cluster center as much as possible, the Raman beam position can be scanned and Rabi oscillation measurements can be performed in the experiment. The frequency of Rabi oscillation is the highest when the two centers coincide.

[0015] Preferably, the divergence angle of the beam expander is calibrated before proceeding to the second step. and ensure .

[0016] Preferably, before proceeding to the second step, it is ensured that the probe beam width is greater than three times the spatial broadening of the atomic cluster. ,and To broaden the initial space of the atomic group, To broaden the velocity of atomic groups, This represents the diffusion time experienced by the atomic group during the detection process.

[0017] Preferably, the second step includes:

[0018] S21. Rough estimate: Combined system and , As an intermediate variable, To broaden the position of atomic groups, Raman light radius, To broaden the initial space of the atomic group, To broaden the velocity of atomic groups, The Raman pulse activation time represents the diffusion time experienced by the atomic group when the Raman pulse is applied. This is achieved by changing... The size of the atomic group is controlled by its magnitude. ,Right now At that time, the corresponding Called According to the calibration Expected and Give The estimated value; when ,Right now At that time, the spatial broadening of the atomic group is equal to the spatial broadening of the Raman light intensity, corresponding to Called Similarly, give The estimated value; When the above specific values ​​are taken, the average transition probability of the atomic group is With the duration of the Raman light pulse The changing relationships have different theoretical analytical expressions.

[0019] S22. Precise estimation: respectively in and Near the estimated value Perform a scan, each time it changes A corresponding Rabi oscillation measurement experiment should be conducted, that is, the average transition probability of the atomic group should be measured. With the duration of the Raman light pulse The changing relationship, to obtain different Rabi oscillation curve Then for different Rabi oscillation curve obtained below Perform a theoretical line fit, and the curve with the highest fit corresponds to... That is, the measurement obtained and The precise estimate.

[0020] Preferably, step S22 specifically involves: according to Estimate the value, scan the vicinity A Rabi oscillation experiment was performed at each point to obtain the results. Perform data processing; for each Received Perform linear fitting; the first fitting function is of the form: ,right Perform trigonometric function fitting. The result after processing The period was calculated, and the best fit was obtained. As The measured value; then repeat the above process to obtain the measured value. At this point, the second fitting function is Similarly, trigonometric function fitting is used.

[0021] Preferably, the transverse temperature of the atomic group The calculation formula is as follows:

[0022]

[0023] in, atomic mass Raman light radius, Boltzmann's constant, and The time between the two Raman beam activations was measured.

[0024] Preferably, the third step further includes: calculating the initial position broadening of the atomic group. :

[0025]

[0026] in, Raman light radius, and The time between the two Raman beam activations was measured.

[0027] Preferably, when obtaining the transverse temperature of the atomic cluster, the diffusion velocity and spatial distribution of the atomic cluster are also obtained simultaneously, which can then be used for the evaluation and correction of wavefront distortion effects in the atomic interferometer.

[0028] In summary, the technical solutions conceived by this invention have the following beneficial effects compared with the prior art:

[0029] This invention first controls the size of atomic clusters at the moment of the Raman pulse by adjusting the Raman light on-time, and conducts Rabi oscillation experiments under different atomic cluster sizes. Then, trigonometric function fitting is performed on the experimental data to extract key parameters reflecting the transverse temperature. Finally, the transverse temperature of the atomic clusters is calculated through inversion. This method is based on the Gaussian distribution of atomic cluster density and Raman light intensity in transverse space. The coupling result of these two factors manifests as non-uniformity in atomic transitions in transverse space, thus affecting the overall transition probability of the atomic clusters, i.e., the shape of the Rabi oscillation curve. Conversely, the shape of the Rabi oscillation curve of the atomic clusters contains the transverse parameters of the atomic clusters. This invention provides a method for extracting the transverse parameters of the atomic clusters from the Rabi oscillation curve. Furthermore, this invention provides the range of key experimental parameters (distance from the center of the atomic cluster to the center of the Raman light and the width of the probe light) required to ensure measurement accuracy, thereby improving the reliability of the experimental results. This method relies on measuring the Rabi oscillations of the atomic clusters and can be completed using only the atomic interferometer itself, without the need for additional beams, image acquisition equipment, or extra vacuum windows. Therefore, this method has low equipment requirements and can be widely used in atomic interferometers. The experimental procedure is simple and easy to operate. Attached Figure Description

[0030] Figure 1 This is a flowchart of a method for measuring the transverse temperature of atomic groups in an atomic interferometer, provided in an embodiment of the present invention. Detailed Implementation

[0031] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.

[0032] In this invention, the term "and / or" describes the relationship between related objects, indicating that three relationships can exist. For example, A and / or B can represent: A existing alone, A and B existing simultaneously, or B existing alone. In this invention, the symbol " / " indicates that the related objects are in an "or" relationship; for example, A / B means A or B.

[0033] In this invention, the terms "first" and "second," etc., are used to distinguish different objects, not to describe a specific order of objects. For example, "first response message" and "second response message," etc., are used to distinguish different response messages, not to describe a specific order of response messages.

[0034] In this invention, the term "electrical connection" can refer to a direct circuit connection or a signal transmission via a communication protocol.

[0035] In embodiments of the present invention, the terms "exemplary" or "for example" are used to indicate that something is an example, illustration, or description. Any embodiment or design described as "exemplary" or "for example" in embodiments of the present invention should not be construed as being more preferred or advantageous than other embodiments or designs. Specifically, the use of the terms "exemplary" or "for example" is intended to present the relevant concepts in a specific manner.

[0036] In the description of the embodiments of the present invention, unless otherwise stated, "multiple" means two or more, for example, multiple processing units means two or more processing units, multiple elements means two or more elements, etc.

[0037] The embodiments of the present invention will now be described with reference to the accompanying drawings.

[0038] This invention controls the diffusion size of atomic clusters by precisely controlling the timing of Raman pulse activation. Based on a coupled model of atomic cluster spatial density and Raman light intensity distribution, under specific diffusion size conditions, a Rabi oscillation theory analytical expression for the average transition probability of atomic clusters as a function of pulse duration is established, thus providing a quantitative correlation between the transverse temperature of the atomic clusters and the timing of two Raman pulse activations. The "atomic interferometer" involved in this invention includes, but is not limited to, atomic interferometric gyroscopes, gravimeters, and gravity gradiometers.

[0039] like Figure 1 As shown, this invention proposes a method for measuring the transverse temperature of atomic groups in an atomic interferometer, comprising the following steps:

[0040] Step 1, Raman spectroscopy The radius and divergence angle are calibrated, and the Raman light is generated by the optical path system in the atomic interferometer.

[0041] The Raman light generated by the optical path system is guided into the beam expander through a single-mode polarization-maintaining fiber for beam expansion and collimation, thereby obtaining the collimated Gaussian beam used in the experiment. In order to diffuse the atomic cluster size to the predetermined size within the limited atomic flight time, the spot radius of the Raman light should not be too large. In addition, an excessively large divergence angle of the Raman light will lead to measurement errors.

[0042] In laser optics, The radius is a parameter used to describe the quality of a laser beam. It represents the intensity distribution of the laser beam on a certain plane, where the intensity decreases to its maximum value. The radius at which the light intensity decreases from its central maximum to 13.5%.

[0043] Preferably, the Raman light after beam expansion and collimation... The radius is controlled between 5 and 10 mm, and the divergence angle is less than 1 mrad.

[0044] Preferably, the Raman light intensity distribution can be obtained by measuring the intensity distribution of the transverse cross section and then fitting it with a Gaussian function. radius.

[0045] Preferably, the Raman light can be measured at two different propagation distances. The radius is used to calculate the divergence angle of the Raman light.

[0046] This invention is not limited to calibrating Raman light using the methods described above. Radius and divergence angle, with other replacement options supported.

[0047] Preferably, the Raman beam spatial position is scanned so that the Raman beam center and the atomic cluster center are as close as possible (spacing less than 1 mm) to minimize the error introduced by center misalignment. Furthermore, to ensure the Raman beam center and atomic cluster center coincide as much as possible, the Raman beam position can be scanned and Rabi oscillation measurements can be performed; the Rabi oscillation frequency is highest when the two centers coincide.

[0048] Preferably, the present invention requires that the probe beam width be extended to cover the diffusion range of the atomic cluster as much as possible, in order to avoid measurement errors caused by detection loss. Generally, the probe beam width is ensured to be greater than 3 times the spatial expansion of the atomic cluster. ,and To broaden the initial space of the atomic group, To broaden the velocity of atomic groups, This represents the diffusion time experienced by the atomic group during the detection process.

[0049] The second step is to use the calibrated Raman light... The radius is used to predict the Raman light on-time.

[0050] Based on the coupling model of atomic cluster spatial density and Raman light intensity distribution, under ideal conditions where the Raman light center and the atomic cluster center completely coincide and there is no detection loss, the duration of the atomic cluster and the pulse is... After Raman light interaction, its average transition probability intermediate variables ,in, This represents the Rabi frequency sensed by the atom at the center of the Raman beam. This indicates the spatial broadening of atomic groups under Raman light. Raman light Radius. When At that time, this is equivalent to This indicates that the atoms are concentrated at the center of the light spot. This is equivalent to the single-atom case. When At that time, this is equivalent to This indicates that the spatial broadening of the atomic group is equal to that of Raman spectroscopy. Radius, note it down Average transition probability .when At that time, this is equivalent to Write it down This indicates that the spatial broadening of the atomic group distribution is equal to the broadening of the Raman light distribution. The present invention utilizes the above findings to determine the Raman light activation time twice.

[0051] S21. Coarse estimation: Estimating pulse time and .

[0052]

[0053]

[0054] Combining the above two equations, when the intermediate quantity At that time, the result was That is The estimated value; when At that time, the result was That is The estimated value.

[0055] S22. Precise estimation: respectively in and Near the estimated value Perform a scan (step size set to 1ms), changing it each time. A corresponding Rabi oscillation measurement experiment should be conducted, that is, the average transition probability of the atomic group should be measured. With the duration of the Raman light pulse The changing relationship, to obtain different Rabi oscillation curve Then for different Rabi oscillation curve obtained below Perform a theoretical line fit, and the curve with the highest fit corresponds to... That is, the measurement obtained and The precise estimate.

[0056] When the atomic cluster expands hour, For the first function Perform cosine fitting ( When the fit is at its highest ,in, express The spatial expansion of atomic clusters at certain moments Indicates the radius of the light spot. The center Rabi frequency is determined by the period of the corresponding fitted curve. We can deduce this by working backwards.

[0057] When the broadening of the atomic cluster is equal to the Raman light distribution ( ,correspond ), for the second function Perform sine fitting ( When the goodness of fit is highest ,in, express The spatial expansion of atomic clusters at certain moments Indicates the radius of the light spot. The center Rabi frequency is determined by the period of the corresponding fitted curve. We can deduce this by working backwards.

[0058] More specifically, firstly, based on the experimental parameters, predictions are made. Then scan the vicinity in 1 ms increments. Every time it changes Perform a Rabi oscillation experiment, that is, measure the average transition probability of the atomic group. With the duration of the Raman light pulse Every change Corresponding to one Curve; then perform data processing. , It can be obtained through processing The period was calculated to obtain ( nearby The cycle remains basically unchanged, and is always ); for each Received Perform trigonometric function fitting, the best fit corresponding Recorded as Then repeat the above process to obtain Note this time .

[0059] Step 3: Lateral Temperature of Atomic Groups The calculation formula is as follows:

[0060]

[0061] in, atomic mass Raman light radius, Boltzmann's constant, and The time between the two Raman beam activations was measured.

[0062] Preferably, the third step further includes: calculating the initial position broadening of the atomic group. :

[0063]

[0064] in, Raman light radius, and The time between the two Raman beam activations was measured.

[0065] The method proposed in this invention obtains the transverse temperature and initial broadening of atomic clusters, thereby obtaining the diffusion velocity and spatial distribution of atomic clusters. This information can then be used to evaluate and correct wavefront distortion effects in atomic interferometers, which helps improve the measurement accuracy of the interferometers and has good portability and application value.

[0066] It should be understood that the above-described device is used to execute the methods in the above embodiments. The implementation principle and technical effect of the corresponding program modules in the device are similar to those described in the above methods. The working process of the device can be referred to the corresponding process in the above methods, and will not be repeated here.

[0067] Based on the methods in the above embodiments, this invention provides an electronic device that may include a processor, a communications interface, a memory, and a communication bus, wherein the processor, communications interface, and memory communicate with each other via the communication bus. The processor may invoke logical instructions stored in the memory to execute the methods in the above embodiments.

[0068] Furthermore, the logical instructions in the aforementioned memory can be implemented as software functional units and, when sold or used as independent products, can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present invention, in essence, or the part that contributes to the prior art, or a portion of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of the present invention.

[0069] Based on the methods in the above embodiments, this embodiment of the invention provides a computer-readable storage medium storing a computer program that, when run on a processor, causes the processor to execute the methods in the above embodiments.

[0070] Based on the methods in the above embodiments, this embodiment of the invention provides a computer program product that, when run on a processor, causes the processor to execute the methods in the above embodiments.

[0071] It is understood that the processor in the embodiments of the present invention can be a central processing unit (CPU), or other general-purpose processors, digital signal processors (DSPs), application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), or other programmable logic devices, transistor logic devices, hardware components, or any combination thereof. The general-purpose processor can be a microprocessor or any conventional processor.

[0072] The method steps in these embodiments of the invention can be implemented in hardware or by a processor executing software instructions. The software instructions can consist of corresponding software modules, which can be stored in random access memory (RAM), flash memory, read-only memory (ROM), programmable read-only memory (PROM), erasable programmable read-only memory (EPROM), electrically erasable programmable read-only memory (EEPROM), registers, hard disks, portable hard disks, CD-ROMs, or any other form of storage medium known in the art. An exemplary storage medium is coupled to the processor, enabling the processor to read information from and write information to the storage medium. Of course, the storage medium can also be a component of the processor. The processor and the storage medium can reside in an ASIC.

[0073] In the above embodiments, implementation can be achieved entirely or partially through software, hardware, firmware, or any combination thereof. When implemented using software, it can be implemented entirely or partially as a computer program product. The computer program product includes one or more computer instructions. When the computer program instructions are loaded and executed on a computer, all or part of the processes or functions described in the embodiments of the present invention are generated. The computer can be a general-purpose computer, a special-purpose computer, a computer network, or other programmable device. The computer instructions can be stored in a computer-readable storage medium or transmitted through the computer-readable storage medium. The computer instructions can be transmitted from one website, computer, server, or data center to another website, computer, server, or data center via wired (e.g., coaxial cable, fiber optic, digital subscriber line (DSL)) or wireless (e.g., infrared, wireless, microwave, etc.) means. The computer-readable storage medium can be any available medium that a computer can access or a data storage device such as a server or data center that integrates one or more available media. The available medium can be a magnetic medium (e.g., floppy disk, hard disk, magnetic tape), an optical medium (e.g., DVD), or a semiconductor medium (e.g., solid-state disk (SSD)).

[0074] It is understood that the various numerical designations used in the embodiments of the present invention are merely for the convenience of description and are not intended to limit the scope of the embodiments of the present invention.

[0075] Those skilled in the art will readily understand that the above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for measuring the transverse temperature of atomic groups in an atomic interferometer, characterized in that, include: Step 1, Raman spectroscopy The radius and divergence angle are calibrated, and the Raman light is generated by the optical path system in the atomic interferometer; The second step is to use the calibrated Raman light... The radius is used to predict the Raman beam switching time. The third step is to modulate the Raman light on-time near the predicted value and perform Rabi oscillation measurement. The fourth step is data processing. The Rabi oscillation curve is fitted to determine the Raman light on-time that best matches the theoretical curve. The transverse temperature of the atomic group is calculated by combining the atomic mass, the spot radius and the Boltzmann constant. The second step includes: S21. Rough estimate: Combined system and , As an intermediate variable, To broaden the position of atomic groups, Raman light radius, To broaden the initial space of the atomic group, To broaden the velocity of atomic groups, The Raman pulse activation time represents the diffusion time experienced by the atomic group when the Raman pulse is applied. This is achieved by changing... The size of the atomic group is controlled by its size; when ,Right now At that time, the corresponding Called According to the calibration Expected and Give The estimated value; when ,Right now At that time, the spatial broadening of the atomic group is equal to the spatial broadening of the Raman light intensity, corresponding to Called Similarly, give The estimated value; When the above specific values ​​are taken, the average transition probability of the atomic group is With the duration of the Raman light pulse The changing relationships have different theoretical analytical expressions; S22. Precise estimation: respectively in and Near the estimated value Perform a scan, each time it changes Correspondingly, a Rabi oscillation measurement experiment is performed, that is, the average transition probability of the atomic group is measured. With the duration of the Raman light pulse The changing relationship, to obtain different Rabi oscillation curves under different conditions; then for different The obtained Rabi oscillation curves are fitted with theoretical line shapes, and the curve with the highest degree of fit corresponds to... That is, the measurement obtained and The precise estimate; Step S22 specifically involves: according to Estimate the value, scan the vicinity A Rabi oscillation experiment was performed at each point to obtain the results. Perform data processing; for each Received Perform linear fitting; the first fitting function is of the form: ,right Perform trigonometric function fitting. The result after processing The period was calculated, and the best fit was obtained. As The measured value; then repeat the above process to obtain the measured value. At this point, the second fitting function is Similarly, trigonometric function fitting is used; Lateral temperature of atomic groups The calculation formula is as follows: in, atomic mass Boltzmann's constant, and The time between the two Raman beam activations was measured.

2. The measurement method as described in claim 1, characterized in that, By measuring the intensity distribution on the Raman beam cross section and fitting it with a Gaussian function, the Raman beam was obtained. The radius; by measuring the intensity distribution of the Raman beam cross section at different propagation distances and fitting it with a Gaussian function, the Raman beam is obtained. The radius varies with the propagation distance, thus allowing the divergence angle of the Raman light to be calculated.

3. The measurement method as described in claim 1, characterized in that, Before proceeding to the second step, the spatial position of the Raman light is scanned so that the distance between the center of the Raman light and the center of the atomic group does not exceed [the specified value]. .

4. The measurement method as described in claim 1, characterized in that, Before proceeding to the second step, ensure that the probe beam width is greater than three times the spatial broadening of the atomic cluster. ,and This represents the diffusion time experienced by the atomic group during the detection process.

5. The measurement method as described in claim 1, characterized in that, Before proceeding to the second step, calibrate the divergence angle of the beam expander. and ensure .

6. The measurement method as described in claim 1, characterized in that, The fourth step also includes: calculating the initial position broadening of the atomic cluster. .

7. The measurement method according to any one of claims 1 to 6, characterized in that, When the transverse temperature of the atomic cluster is obtained, the diffusion velocity and spatial distribution of the atomic cluster are also obtained, which can then be used for the evaluation and correction of wavefront distortion effects in atomic interferometers.

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