Millimeter-level CPT magnetometer optical path based on magnetic rotation effect and measurement method of millimeter-level CPT magnetometer optical path

Abstract

The invention belongs to the technical field of magnetic field measurement and quantum magnetic sensing, and particularly relates to a millimetric CPT magnetometer optical path based on a magnetic rotation effect and a measurement method thereof. The polarization adjusting optical assembly is used for converting original single linear polarization polychromatic light into two beams of linear polarization polychromatic laser which are perpendicular to each other, on one hand, the original single-direction linear polarization polychromatic light can be converted into the two beams of linear polarization polychromatic light which are perpendicular to each other, and on the other hand, the optical path difference of the two beams of linear polarization polychromatic light which are perpendicular to each other can be adjusted. According to the invention, the quantum control is carried out on the interaction process of light and atoms, a better CPT interference signal is obtained, and a differential detection magnetic rotation effect signal is adopted, so that common-mode noise such as optical power in laser is effectively inhibited, the signal-to-noise ratio of a CPT resonance signal is improved, and the measurement accuracy and sensitivity of a millimetric magnetic field are improved.

Description

Technical Field

[0001] This invention belongs to the field of magnetic field measurement and quantum magnetic sensing technology, specifically relating to an optical path and measurement method of a millimeter-level CPT magnetometer based on the magneto-optical effect. Background Technology

[0002] Precise measurement of magnetic fields is of great significance in both the national economy and national defense. With the increasingly widespread application of magnetic measurement in recent years, various sensors used for magnetic field measurement have developed rapidly. The sensitivity and accuracy of quantum effect-based magnetic sensors have been continuously improved. Applying highly sensitive and accurate quantum magnetic sensors to magnetic field measurement can enhance the technical specifications of metrology devices, thereby promoting the development of metrology technology.

[0003] Currently, in magnetic field metrology, within the geomagnetic field range of 20μT to 100μT, quantum effect optically pumped magnetometers and Overhauser magnetometers are mainly used as magnetic sensors. For strong magnetic field metrology, nuclear magnetic resonance (NMR) magnetometers are generally used, enabling measurements over a wide range of 50mT to 30T with a measurement uncertainty of up to 5ppm. For magnetic field measurements between 0.1mT and 50mT, fluxgate magnetometers or flow-through NMR magnetometers can be used. Fluxgate magnetometers are vector magnetic sensors, while flow-through NMR magnetometers are complex, bulky, and have limited application scenarios.

[0004] It is evident that the currently realized milliter-level CPT magnetometers use a single linearly polarized laser for magnetic field measurement, which has a relatively low signal-to-noise ratio, thus limiting both measurement accuracy and sensitivity. Summary of the Invention

[0005] In view of this, the present invention provides an optical path and measurement method for a millimeter-level CPT magnetometer based on the magneto-optical effect, which can effectively suppress common-mode noise such as optical power in lasers, improve the signal-to-noise ratio of CPT resonance signals, and enhance the measurement accuracy and sensitivity of millimeter-level magnetic fields.

[0006] To achieve the objectives of this invention, the following technical solutions are provided.

[0007] An optical path for a milliter-level CPT magnetometer based on the magneto-optical effect includes a light source section, a polarization adjustment section, and a signal detection section arranged sequentially. The light source section is used to generate linearly polarized multicolor laser; The polarization adjustment section is used to convert a single linearly polarized multicolor laser from the light source section into two linearly polarized multicolor lasers with mutually perpendicular polarization directions, and to adjust the optical path difference between the two laser beams. The signal detection section includes an atomic gas cell and a differential photodetector unit, which is used to make the two mutually perpendicular linearly polarized multicolor laser beams interact with the atoms in the atomic gas cell and differentially detect the transmitted light signal to obtain the CPT resonance signal.

[0008] The polarization adjustment section includes a first half-wave plate, a first polarizing beam splitter, a first quarter-wave plate, a second quarter-wave plate, a first reflecting mirror, and a second reflecting mirror arranged sequentially along the optical path. The first polarization beam splitter separates the incident linearly polarized multicolor laser into transmitted P-beams and reflected S-beams. The first quarter-wave plate and the first reflecting mirror constitute the first optical path, which is used to rotate the polarization direction of the S-light by 90 degrees and convert it into P-light and return it to the first polarization beam splitter. The second quarter-wave plate and the second reflector constitute a second optical path for receiving and processing the P-beam emitted from the first polarizing beam splitter. By adjusting the position of the first reflector, the optical path of the first optical path is changed, thereby adjusting the optical path difference between the two ultimately emitted linearly polarized multicolor laser beams that are perpendicular to each other.

[0009] Specifically, the position of the first reflector is adjusted so that the equivalent optical path difference between the first and second reflectors is one-quarter of a microwave wavelength, where the microwave wavelength is the wavelength of the microwave signal corresponding to the splitting of the hyperfine energy level of the atomic ground state in the atomic gas chamber.

[0010] The light source includes a laser, a microwave source, and a DC source; The microwave source is used to output a microwave signal with a frequency that matches the splitting frequency of the hyperfine level of the ground state of the target atom. The DC source is used to provide bias current to the laser; The microwave signal is coupled to the DC signal and together drive the laser to generate a linearly polarized multicolor laser containing two frequency components.

[0011] The atomic chamber is filled with rubidium-87 atomic vapor.

[0012] The signal detection section further includes a second half-wave plate and a second polarizing beam splitter prism; Two mutually perpendicular linearly polarized multicolor laser beams emitted from the polarization adjustment section pass through the second half-wave plate and then enter the atomic gas cell; The emitted light after passing through the atomic gas cell is split into two paths by the second polarizing beam splitter, which are received by the first photodetector and the second photodetector, respectively. The output signals of the first photodetector and the second photodetector are used for differential processing to extract the CPT resonance signal.

[0013] This invention also provides a measurement method for a millimeter-level CPT magnetometer based on magneto-optical rotation, which is implemented using the magnetometer optical path described in this invention and includes the following steps: Step S1: The atomic gas chamber and the laser are kept at a constant temperature to keep them at the working temperature; the laser is driven to generate linearly polarized polychromatic light, and the linearly polarized polychromatic light is converted into two linearly polarized polychromatic lasers with mutually perpendicular polarization directions through the polarization adjustment optical component; Step S2: Scan the driving current of the laser and adjust the power of the coupled microwave to match the frequency of the linearly polarized polychromatic light with the absorption spectrum of the working atom in the atomic gas chamber, and lock the driving current at the corresponding absorption peak. Step S3: Scan the frequency of the coupled microwaves to make the two mutually perpendicular linearly polarized multicolor lasers interact with the atoms, and use a pair of photodetectors to differentially detect the transmitted light intensity to obtain a CPT differential signal spectrum containing two resonance peaks. Step S4: Extract the microwave frequencies corresponding to the two resonance peaks from the CPT differential signal spectrum, calculate their frequency difference, and calculate the value of the magnetic induction intensity based on the linear relationship between the frequency difference and the magnetic induction intensity to be measured.

[0014] In step S1, by adjusting the position of the reflector in the polarization adjustment optical component, the optical path difference between the two mutually perpendicular linearly polarized multicolor laser beams is made to be one-quarter of a microwave wavelength, where the microwave wavelength is the wavelength corresponding to the splitting of the hyperfine energy level of the working atom's ground state.

[0015] The working atom is rubidium-87, and the absorption peak locked in step S2 is the Doppler absorption peak of the D1 line of rubidium-87 atom.

[0016] Among them, the two CPT resonance peaks obtained in step S3 correspond to the CPT resonance point frequency difference generated by the two different Λ-type three-level systems formed by Zeeman splitting of rubidium-87 atoms in a magnetic field.

[0017] Beneficial effects First, the optical path of this invention employs a polarization-adjusting optical component to convert the original single linearly polarized multicolor light into two mutually perpendicular linearly polarized multicolor laser beams. After interacting with atoms, differential detection of the magneto-optical effect signal is used, thereby effectively suppressing common-mode noise such as optical power in the laser, improving the signal-to-noise ratio of the CPT resonance signal, and enhancing the measurement accuracy and sensitivity of millimeter-level magnetic fields. This invention uses microwave-modulated dual-color lasers to interact with 87Rb, detecting the CPT resonance signal generated by nuclear spin splitting, enabling accurate measurement of millimeter-level magnetic fields.

[0018] Secondly, this invention converts a single laser beam into two orthogonally polarized beams through polarization adjustment and combines this with differential detection, laying the foundation for suppressing common-mode noise and improving the signal-to-noise ratio at the system level. The polarization adjustment section achieves precise quantum control of the relative phase between the two orthogonal beams. This key step can actively optimize the interference process between atoms and the light field, thereby directly generating a higher quality and better contrast CPT resonance signal, which is the core of improving sensor performance.

[0019] Third, this invention ensures the generation of a clear and easily detectable CPT resonance signal under a millimeter-level magnetic field by employing microwave-modulated laser interaction with rubidium-87 atoms. Specifically, utilizing the energy level structure of rubidium-87 atoms, two observable CPT resonance peaks can be naturally formed. Based on this, the differential detection method defined in claim 6 can effectively cancel the inherent optical power fluctuation noise and amplitude noise converted from frequency jitter in the laser itself, which are the main sources of interference in single-ended detection. Differential detection makes the final extracted resonance signal sensitive only to the optical rotation difference between the two orthogonal beams caused by the magnetic field, thereby greatly improving the signal purity.

[0020] Fourth, this invention presents a novel optical path structure for a CPT magnetometer capable of operating in millimeter-level magnetic fields. More importantly, through a synergistic design across the entire chain—from light source generation, polarization and phase modulation, and atomic interactions to differential signal extraction—it systematically solves the problem of low signal-to-noise ratio in existing technologies. The ultimate result is the simultaneous achievement of high measurement sensitivity and high measurement accuracy, providing a stable and reliable solution to fill the technological gap in the field of precision measurement of millimeter-level magnetic fields.

[0021] Fifth, this invention designs a set of polarization-adjusting optical components. Firstly, it can convert the original single-direction linearly polarized multicolor light into two mutually perpendicular beams of linearly polarized multicolor light. Secondly, it can adjust the optical path difference between the two mutually perpendicular multicolor beams, thereby quantum-controlling the interaction process between light and atoms and obtaining a CPT interference signal with a higher signal-to-noise ratio. This invention uses a pair of photodiodes to detect the magneto-optical signals of the two beams of linearly polarized multicolor light, effectively suppressing common-mode noise such as optical power noise (AM noise) and optical power noise from laser frequency conversion (FM-AM noise), thereby improving the measurement accuracy and sensitivity of the magnetometer.

[0022] Sixth, the method of this invention is based on the device of this invention. The measurement optical path uses a polarization-adjusting optical component to convert the original single linearly polarized multicolor light into two mutually perpendicular linearly polarized multicolor laser beams. After interacting with atoms, differential detection of the magneto-optical effect signal is used, thereby effectively suppressing common-mode noise such as optical power in the laser, improving the signal-to-noise ratio of the CPT resonance signal, and enhancing the measurement accuracy and sensitivity of the millimeter-level magnetic field. This invention uses microwave-modulated dual-color lasers to interact with 87Rb to detect the CPT resonance signal generated by nuclear spin splitting, enabling accurate measurement of the millimeter-level magnetic field. Attached Figure Description

[0023] Figure 1 This is a schematic diagram of the optical path of the milliter-level CPT magnetometer based on the magneto-optical effect of the present invention. The diagram shows: 1-light source section, 2-polarization adjustment section, 3-signal detection section; the light source section includes: 101-DC source, 102-microwave source, 103-Bias-Tee, 104-VCSEL laser; the polarization adjustment section includes: 201-first λ / 2 waveplate, 202-first PBS, 203-first λ / 4 waveplate, 204-second λ / 4 waveplate, 205-first reflector, 206-second reflector; the signal detection section includes: 301-second λ / 2 waveplate, 302-atomic gas cell, 303-second PBS, 304-first photodetector, 305-second photodetector.

[0024] Figure 2 This is a schematic diagram showing the relationship between the fixed-phase light field (f) and the variable-phase light field (v) of the present invention and the angles between them and the x and y axes.

[0025] Figure 3 For the present invention, multicolor laser and 87 Doppler absorption lines during Rb atom interactions.

[0026] Figure 4 For the present invention, dual-color laser and 87 Multiple three-level configurations are formed when Rb atoms interact with the hyperfine level of the D1 line.

[0027] Figure 5 This invention provides the CPT resonance signal under different magnetic induction intensities during magnetic field measurement. Detailed Implementation

[0028] The present invention will be further described below with reference to the accompanying drawings and specific embodiments.

[0029] This invention provides an optical path for a millimeter-level CPT magnetometer based on the magneto-optical effect, such as... Figure 1 As shown, it includes a light source section, a polarization adjustment section, and a signal detection section arranged in sequence.

[0030] The light source section includes a DC source 101, a microwave source 102, a Bias-Tee 103, and a VCSEL laser 104; the polarization adjustment section includes a first λ / 2 waveplate 201, a first PBS 202, a first λ / 4 waveplate 203, a second λ / 4 waveplate 204, a first reflector 205, and a second reflector 206; the signal detection section includes a second λ / 2 waveplate 301, an atomic gas cell 302, a second PBS 303, a first photodetector 304, and a second photodetector 305.

[0031] The microwave source outputs a microwave signal, and the DC power supply outputs a DC signal. The microwave signal and the DC signal are simultaneously input into the Bias-Tee. The Bias-Tee couples the microwave signal to the DC signal to obtain a mixed signal. The frequency of the microwave signal is approximately 3.417 GHz. The mixed signal drives a VCSEL laser to generate linearly polarized polychromatic light, and the propagation direction of the linearly polarized polychromatic light is along the z-axis. The linearly polarized multicolor light is input into the polarization adjustment section, and the first λ / 2 waveplate is rotated so that the intensity of the transmitted light and the reflected light after passing through the first PBS is the same. The propagation direction of the reflected light after passing through the first PBS is the x-axis. The planes of the first λ / 4 waveplate, the second λ / 4 waveplate, the first mirror, and the second mirror are parallel to the yoz plane, and the crystal axes of the first λ / 4 waveplate and the second λ / 4 waveplate are at 45° to the z-axis direction. The linearly polarized polychromatic light after being reflected by the first PBS becomes circularly polarized polychromatic light after passing through the first λ / 4 waveplate. Then, it is reflected back by the first mirror and passes through the first λ / 4 waveplate again. At this time, the circularly polarized polychromatic light becomes linearly polarized polychromatic laser, but it is rotated by 90° relative to the linearly polarized polychromatic light after being reflected by the first PBS for the first time. The linearly polarized polychromatic light that passes through the first λ / 4 waveplate twice passes through the first PBS again and is transmitted entirely from the first PBS to the second λ / 4 waveplate. After passing through the second λ / 4 waveplate, it is reflected by the second mirror and returns along the same path to pass through the second λ / 4 waveplate again. The polarization direction of the linearly polarized polychromatic light that passes through the second λ / 4 waveplate twice is rotated by 90° again. The reflected linearly polarized multicolor light after passing through the first PBS, after passing through the polarization adjustment section, is combined with the directly transmitted linearly polarized multicolor light after passing through the first PBS to form a vertically polarized multicolor light beam, such as... Figure 2 As shown, f is the transmitted linearly polarized polychromatic light after passing through the first PBS, and v is the reflected linearly polarized polychromatic light after passing through the first PBS. Adjust the position d of the first reflecting mirror in the polarization adjustment section so that the distance between the first reflecting mirror and the second reflecting mirror is... ,in ,for87 The microwave wavelength corresponding to the splitting of the hyperfine energy level of the Rb atom's ground state; The vertically linearly polarized polychromatic light after the polarization adjustment section passes through the second λ / 2 waveplate, the atomic gas cell, and the second PBS in sequence. The plane of the second λ / 2 waveplate is parallel to the xoy plane, and its crystal axis forms a 22.5° angle with the x-axis, such that... Figure 2 In ; The second PBS is placed in the same orientation as the first PBS; The first and second photodetectors receive the reflected and transmitted light from the second PBS, respectively, and perform differential detection on the signals from the first and second photodetectors. Theoretically, when CPT resonance does not occur, the intensity of the polychromatic light received by the two photodetectors is equal; therefore, the differential signal between the first and second photodetectors is 0 when CPT resonance does not occur. When CPT resonance occurs, then... Figure 2 The f-ray and v-ray in the photometer rotate sequentially, causing the differential signal between the first and second photodetectors to no longer be zero, thus obtaining the CPT resonance signal. This invention further employs the magneto-optical effect to obtain a CPT resonance signal with a better signal-to-noise ratio, thereby improving the measurement accuracy and sensitivity of the magnetometer.

[0032] This invention also provides a measurement method for the optical path of a millimeter-level CPT magnetometer based on magneto-optical rotation, comprising the following steps: Step 1: Perform constant temperature control on the atomic gas chamber and VCSEL laser respectively to ensure that the atomic gas chamber and VCSEL laser are at the correct operating temperature.

[0033] Step 2: Scan the current driving the VCSEL laser with a DC source and adjust the output power of the microwave source to obtain the following result. Figure 3 shown 87 The Doppler absorption peak of the D1 line of Rb atoms was then used to adjust the current of the DC source and lock it at... Figure 3 The current value corresponding to the Doppler absorption peak shown in the dashed box. Figure 4 for 87 A schematic diagram of the D1 line energy level of an Rb atom in a magnetic field. 87 The D1 line level of the Rb atom undergoes Zeeman splitting, and the energies of the individual Zeeman sublevels can be expressed by the Breit-Rabi formula: (1) in, , , 87 Rb atom D1 line parameters: , , The microwave frequency corresponding to the ground state energy level when the external magnetic field is zero. , , Planck's constant .

[0034] like Figure 4 As shown, when linearly polarized dichroic light and 87 When Rb atoms interact, the ground state , and excited state The system consists of a three-level system with thick solid lines (aΛ), ground state. , and excited state This forms a thin solid-line bΛ three-level system. The a and b double Λ configuration three-level systems can each achieve CPT resonance. Meanwhile, the ground state... , and excited state The formed Λ three energy levels and ground state , and excited state The CPT resonance signal generated by the Λ-configuration three-level system is relatively weak. The other three-level systems formed by the dashed lines either fail to generate CPT resonance due to excessive detuning or destructive interference. Therefore, in practical implementation, only the two Λ-configuration three-level systems, a and b, are considered.

[0035] When an atom is placed in a millimeter-level magnetic field, the CPT resonance frequency of the aΛ configuration gradually decreases, while the CPT resonance frequency of the bΛ configuration gradually increases, causing the CPT resonance spectral lines generated by the a and b three energy levels to gradually split. Let's assume... Under a magnetic field, the energies between the two ground state energy levels of the Λ configurations a and b are respectively and According to formula (1). and They are represented as follows: (2) (3) Therefore, the frequency difference of the CPT resonance points formed by the two Λ configurations a and b is... for: (4) in , , It is a constant, therefore, according to the measurement Calculated magnetic field value Substituting the value of the constant into the equation, we obtain the frequency difference. With magnetic induction intensity The ratio is approximately 27.85 kHz / mT. It can be seen that... , By subtracting, higher-order terms are eliminated, leaving only linear terms. Therefore, by measuring... By measuring the magnetic field, errors caused by the nonlinear Zeeman effect can be eliminated, thereby obtaining accurate values ​​of magnetic flux density.

[0036] Step 3: Scan the microwave frequency output by the microwave source and acquire the differential signals from the first and second photodetectors. This will yield the following result: Figure 5 The image shows the CPT resonance signal generated by the magneto-optical effect. Different magnetic induction intensities result in different spacing between the CPT resonance peaks. The corresponding microwave frequencies of the CPT resonance peaks (a and b) are measured to obtain the values ​​of the two CPT resonance signals. Thus, the accurate value of the external magnetic induction intensity can be calculated according to equation (4).

[0037] This invention includes, but is not limited to, the above embodiments. Any equivalent substitutions or partial improvements made under the spirit and principles of this invention shall be considered within the scope of protection of this invention.

Claims

1. An optical path for a milliter-level CPT magnetometer based on the magneto-optical effect, characterized in that, It includes a light source section, a polarization adjustment section, and a signal detection section arranged sequentially; The light source section is used to generate linearly polarized multicolor laser; The polarization adjustment section is used to convert a single linearly polarized multicolor laser from the light source section into two linearly polarized multicolor lasers with mutually perpendicular polarization directions, and to adjust the optical path difference between the two laser beams. The signal detection section includes an atomic gas cell and a differential photodetector unit, which is used to make the two mutually perpendicular linearly polarized multicolor laser beams interact with the atoms in the atomic gas cell and differentially detect the transmitted light signal to obtain the CPT resonance signal.

2. The optical path of the millitrile-level CPT magnetometer according to claim 1, characterized in that, The polarization adjustment section includes a first half-wave plate, a first polarizing beam splitter, a first quarter-wave plate, a second quarter-wave plate, a first reflecting mirror, and a second reflecting mirror arranged sequentially along the optical path; The first polarization beam splitter separates the incident linearly polarized multicolor laser into transmitted P-beams and reflected S-beams. The first quarter-wave plate and the first reflecting mirror constitute the first optical path, which is used to rotate the polarization direction of the S-light by 90 degrees and convert it into P-light and return it to the first polarization beam splitter. The second quarter-wave plate and the second reflector constitute a second optical path for receiving and processing the P-beam emitted from the first polarizing beam splitter. By adjusting the position of the first reflector, the optical path of the first optical path is changed, thereby adjusting the optical path difference between the two ultimately emitted linearly polarized multicolor laser beams that are perpendicular to each other.

3. The optical path of the millitrile-level CPT magnetometer according to claim 2, characterized in that, The position of the first reflector is adjusted so that the equivalent optical path difference between the first reflector and the second reflector is one-quarter of a microwave wavelength, where the microwave wavelength is the wavelength of the microwave signal corresponding to the splitting of the hyperfine energy level of the atomic ground state in the atomic gas chamber.

4. The optical path of the milliter-level CPT magnetometer according to any one of claims 1-3, characterized in that, The light source includes a laser, a microwave source, and a DC source; The microwave source is used to output a microwave signal with a frequency that matches the splitting frequency of the hyperfine level of the ground state of the target atom. The DC source is used to provide bias current to the laser; The microwave signal is coupled to the DC signal and together drive the laser to generate a linearly polarized multicolor laser containing two frequency components.

5. The optical path of the millitrile-level CPT magnetometer according to claim 4, characterized in that, The atomic chamber is filled with rubidium-87 atomic vapor.

6. The optical path of the milliter-level CPT magnetometer according to claim 2, 3, or 5, characterized in that, The signal detection section also includes a second half-wave plate and a second polarizing beam splitter prism; Two mutually perpendicular linearly polarized multicolor laser beams emitted from the polarization adjustment section pass through the second half-wave plate and then enter the atomic gas cell; The emitted light after passing through the atomic gas cell is split into two paths by the second polarizing beam splitter, which are received by the first photodetector and the second photodetector, respectively. The output signals of the first photodetector and the second photodetector are used for differential processing to extract the CPT resonance signal.

7. A measurement method for the optical path of a millimeter-level CPT magnetometer based on magneto-optical rotation, characterized in that, The method employs the magnetometer optical path as described in any one of claims 1-6, and includes the following steps: Step S1: The atomic gas chamber and the laser are kept at a constant temperature to keep them at the working temperature; the laser is driven to generate linearly polarized polychromatic light, and the linearly polarized polychromatic light is converted into two linearly polarized polychromatic lasers with mutually perpendicular polarization directions through the polarization adjustment optical component; Step S2: Scan the driving current of the laser and adjust the power of the coupled microwave to match the frequency of the linearly polarized polychromatic light with the absorption spectrum of the working atom in the atomic gas chamber, and lock the driving current at the corresponding absorption peak. Step S3: Scan the frequency of the coupled microwaves to make the two mutually perpendicular linearly polarized multicolor lasers interact with the atoms, and use a pair of photodetectors to differentially detect the transmitted light intensity to obtain a CPT differential signal spectrum containing two resonance peaks. Step S4: Extract the microwave frequencies corresponding to the two resonance peaks from the CPT differential signal spectrum, calculate their frequency difference, and calculate the value of the magnetic induction intensity based on the linear relationship between the frequency difference and the magnetic induction intensity to be measured.

8. The measurement method according to claim 7, characterized in that, In step S1, by adjusting the position of the reflector in the polarization adjustment optical component, the optical path difference between the two mutually perpendicular linearly polarized multicolor laser beams is made to be one-quarter of a microwave wavelength, where the microwave wavelength is the wavelength corresponding to the splitting of the hyperfine energy level of the working atom's ground state.

9. The measurement method according to claim 7, characterized in that, The working atom is rubidium-87, and the absorption peak locked in step S2 is the Doppler absorption peak of the D1 line of rubidium-87 atom.

10. The measurement method according to any one of claims 7-9, characterized in that, The two CPT resonance peaks obtained in step S3 correspond to the frequency difference of the CPT resonance points generated by the two different Λ-type three-level systems formed by Zeeman splitting of rubidium-87 atoms in a magnetic field.

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