A method for measuring electron spin exchange relaxation based on magnetic resonance curves

Abstract

A method for measuring electron spin exchange relaxation based on a magnetic resonance curve, firstly using a pumping laser to longitudinally polarize the electron spin, then applying a radio frequency magnetic field transversely and scanning the radio frequency magnetic field frequency, to obtain the line width of the electron magnetic resonance curve with respect to the longitudinal environmental magnetic field; scanning the transverse radio frequency magnetic field amplitude, measuring the slope of the magnetic resonance curve at the resonance frequency, and obtaining the radio frequency magnetic field amplitude corresponding to the maximum slope of the magnetic resonance curve at the resonance frequency. Through the dynamic evolution equation of electron spin polarization, a theoretical model of the radio frequency magnetic field amplitude corresponding to the line width of the magnetic resonance curve and the maximum slope at the resonance frequency of the curve is established, and the transverse and longitudinal relaxation of the electron is solved, and finally the electron spin exchange relaxation is obtained. The present invention can be applied to magnetic field environments ranging from zero magnetism to geomagnetic magnitude, and provides a method for measuring electron spin exchange relaxation within the geomagnetic magnitude magnetic field range, which has a wider range of application scenarios.

Description

Technical Field

[0001] The invention relates to an electron spin exchange relaxation measurement method based on a magnetic resonance curve, which can be used for measuring electron spin exchange relaxation in a magnetic field environment ranging from zero magnetic field to earth magnetic field level. Background Art

[0002] Based on optically pumped high-density alkali metal vapor and optical spin detection technology, a highly sensitive atomic magnetometer was born. Under high alkali metal density, decoherence caused by relaxation is usually the main limitation of the sensitivity of atomic magnetometers. The spin exchange relaxation-free magnetometer significantly suppresses the decoherence caused by spin exchange relaxation under conditions of high atomic density and zero magnetic field, making it a more sensitive magnetometer than superconducting interferometer devices. However, when the application environment is expanded to high magnetic field environments, such as aviation, ocean and other geomagnetic environments, spin exchange relaxation becomes the main limitation of magnetometer performance. In order to find the mechanism of suppressing spin exchange relaxation under high magnetic fields, it is necessary to accurately measure spin exchange relaxation. At present, the main spin exchange relaxation measurement method is to obtain the line width of the electron resonance curve from optical synchronous pumping or radio frequency magnetic field excitation, and use the quadratic relationship between spin exchange relaxation and magnetic field under low field for measurement. However, when the magnetic field increases, the quadratic relationship will no longer be consistent. Another measurement method is to extract relaxation information from the transient response of the system by applying pumping light pulses or magnetic pulse signals. This method requires the longitudinal relaxation time of electrons to be calibrated in a zero-field environment. The measurement accuracy depends on the accuracy of magnetic field compensation. At the same time, since the electron transient response process is extremely short, this method has high requirements on the sampling rate of the acquisition system. Electron spin exchange relaxation is the key to the sensitivity performance of atomic magnetometers in geomagnetic environments. However, there is currently a lack of measurement methods for electron spin exchange relaxation in geomagnetic environments. Summary of the invention

[0003] The technical problem solved by the present invention is: in view of the problem that the existing electron spin exchange relaxation measurement method can only be applied under low magnetic field, the low magnetic field refers to zero magnetic field or near-zero magnetic field, and the low magnetic field is usually obtained by compensating for the magnetic field of the geomagnetic magnitude, and a method for measuring electron spin exchange relaxation based on magnetic resonance curve is provided. The method can be applied in the magnetic field range from zero magnetic field to geomagnetic magnitude, has a wider range of application scenarios, provides an effective solution for directly measuring spin exchange relaxation in a geomagnetic environment, and effectively breaks through the limitation that the existing electron spin exchange relaxation measurement method can only be applied under low magnetic field.

[0004] The technical solution of the present invention is as follows:

[0005] A method for measuring electron spin exchange relaxation based on magnetic resonance curves, characterized in that it includes using laser polarization atomic ensembles to make alkali metal atoms have consistent electron spin orientations, then measuring the resonance line width by scanning the electron magnetic resonance curve, and measuring the radio frequency magnetic field amplitude corresponding to the slope maximum at the resonance frequency of the magnetic resonance curve by scanning the transverse radio frequency magnetic field amplitude, and using the electron relaxation information contained in the line width and the radio frequency magnetic field amplitude to solve the electron transverse and longitudinal relaxations, thereby obtaining electron spin exchange relaxation.

[0006] The following steps are involved:

[0007] Step 1, turn on the pump laser to polarize the atomic ensemble;

[0008] Step 2, scanning the transverse radio frequency magnetic field frequency to obtain a magnetic resonance curve and measuring the line width of the curve;

[0009] Step 3, scanning the transverse radio frequency magnetic field amplitude, and measuring the radio frequency magnetic field amplitude corresponding to the maximum slope value at the resonance frequency of the magnetic resonance curve;

[0010] Step 4: Use the line width and RF magnetic field amplitude to solve the electron spin exchange relaxation.

[0011] The step 1 includes: the pumping laser performs laser pumping on the atomic ensemble along the z-axis.

[0012] The step 2 includes: applying a radio frequency magnetic field along the y-axis, scanning the frequency of the radio frequency magnetic field, demodulating the in-phase component of the x-axis optical rotation angle signal to obtain a magnetic resonance curve of the Lorentz absorption line type, and using the curve Fitting is performed, where S is the demodulated signal amplitude, ω L is the RF magnetic field frequency, A, B, C are the undetermined fitting parameters, and the fitting parameter C is the line width Γ of the magnetic resonance curve.

[0013] The step 3 comprises: scanning the frequency of the radio frequency magnetic field, demodulating the orthogonal component of the x-axis optical rotation angle signal to obtain a magnetic resonance curve of the Lorentz dispersion line type, scanning the amplitude of the radio frequency magnetic field at the resonance frequency, measuring the slope of the magnetic resonance curve at the resonance frequency, and obtaining the amplitude of the radio frequency magnetic field corresponding to the maximum slope.

[0014] The step 4 comprises: establishing a mapping model of transverse and longitudinal relaxation to the line width of the magnetic resonance curve and the amplitude of the radio frequency magnetic field corresponding to the maximum value of the slope of the magnetic resonance curve through the theoretical expression of the amplitude of the radio frequency magnetic field corresponding to the line width of the magnetic resonance curve and the maximum value of the slope of the magnetic resonance curve, wherein the process is as follows:

[0015] The dynamic evolution equation of electron spin polarization is established using the BLOCH equation:

[0016]

[0017] Among them, S is the electron spin polarization vector, t is time, γ e is the electron gyromagnetic ratio, B is the environmental magnetic field vector, R op is the optical pumping rate, is the unit vector in the z direction, γ={γ 2 ,γ 2 ,γ 1} is the three-axis electron relaxation vector, γ 1 and γ 2 are the longitudinal relaxation and transverse relaxation of electrons respectively. By solving the BLOCH equation, the theoretical expression of the line width of the magnetic resonance curve is obtained as follows:

[0018]

[0019] Where Γ is the line width of the magnetic resonance curve, B y is the RF magnetic field amplitude, the slope of the magnetic resonance curve at the resonance frequency is proportional to the RF magnetic field amplitude B y By taking the derivative, we can get the RF magnetic field amplitude corresponding to the maximum slope, and its theoretical expression is:

[0020]

[0021] Among them, B′ y is the RF magnetic field amplitude corresponding to the maximum slope value. In summary, we get two theoretical expressions for the line width of the magnetic resonance curve and the RF magnetic field amplitude corresponding to the maximum slope value at the resonant frequency of the magnetic resonance curve. Combining the two equations, we can replace B in the expression of the line width of the magnetic resonance curve Γ with y Replace with B′ y , we get the expressions of the electron longitudinal relaxation and transverse relaxation about the line width of the magnetic resonance curve and the RF magnetic field amplitude corresponding to the maximum value of the slope of the magnetic resonance curve:

[0022]

[0023] Leveraging Relationships 0e =γ 2 -γ 1 , where γ se It is the electron spin exchange relaxation, and finally the electron spin exchange relaxation is solved.

[0024] The technical effects of the present invention are as follows: The present invention provides a method for measuring electron spin exchange relaxation based on a magnetic resonance curve. First, a pumping laser is used to longitudinally polarize the electron spin. Then, a radio frequency magnetic field is applied transversely and the radio frequency magnetic field frequency is scanned to obtain the line width of the electron magnetic resonance curve with respect to the longitudinal environmental magnetic field; the transverse radio frequency magnetic field amplitude is scanned to measure the slope of the magnetic resonance curve at the resonance frequency, and the radio frequency magnetic field amplitude corresponding to the maximum slope at the resonance frequency of the magnetic resonance curve is obtained. Through the dynamic evolution equation of electron spin polarization, a theoretical model of the radio frequency magnetic field amplitude corresponding to the line width of the magnetic resonance curve and the maximum slope at the resonance frequency of the curve is established, and the transverse and longitudinal relaxation of the electron is solved to finally obtain the electron spin exchange relaxation. The present invention is applicable to magnetic field environments ranging from zero magnetism to geomagnetic magnitude, and provides a method for measuring electron spin exchange relaxation within the geomagnetic magnitude magnetic field range, which has a wider range of application scenarios. BRIEF DESCRIPTION OF THE DRAWINGS

[0025] Figure 1 The present invention is a schematic flow chart of a method for measuring electron spin exchange relaxation based on magnetic resonance curves. Figure 1 The method includes step 1, starting the pumping laser and polarizing the atomic ensemble; step 2, scanning the transverse radio frequency magnetic field frequency to obtain a magnetic resonance curve and measuring the line width of the curve; step 3, scanning the transverse radio frequency magnetic field amplitude and measuring the radio frequency magnetic field amplitude corresponding to the maximum slope of the magnetic resonance curve at the resonance frequency; and step 4, using the line width and radio frequency magnetic field amplitude to solve the electron spin exchange relaxation. DETAILED DESCRIPTION

[0026] Below is the attached figure ( Figure 1 ) and Examples illustrate the present invention.

[0027] Figure 1 The figure is a schematic flow chart of a method for measuring electron spin exchange relaxation based on magnetic resonance curves according to the present invention. Figure 1 As shown, a method for measuring electron spin exchange relaxation based on magnetic resonance curves includes using laser polarization of an atomic ensemble to make alkali metal atoms have a consistent electron spin orientation, then measuring the resonance line width by scanning the electron magnetic resonance curve, and measuring the radio frequency magnetic field amplitude corresponding to the slope maximum at the resonance frequency of the magnetic resonance curve by scanning the transverse radio frequency magnetic field amplitude, and using the electron relaxation information contained in the line width and the radio frequency magnetic field amplitude to solve the electron transverse and longitudinal relaxations, thereby obtaining electron spin exchange relaxation.

[0028] Specifically, the method includes the following steps: Step 1, turning on the pumping laser to polarize the atomic ensemble; Step 2, scanning the transverse radio frequency magnetic field frequency to obtain a magnetic resonance curve and measuring the line width of the curve; Step 3, scanning the transverse radio frequency magnetic field amplitude, and measuring the radio frequency magnetic field amplitude corresponding to the maximum slope value at the resonance frequency of the magnetic resonance curve; Step 4, using the line width and radio frequency magnetic field amplitude to solve the electron spin exchange relaxation.

[0029] The step 1 includes: the pumping laser performs laser pumping on the atomic ensemble along the z-axis. The step 2 includes: applying a radio frequency magnetic field along the y-axis, scanning the frequency of the radio frequency magnetic field, demodulating the in-phase component of the x-axis optical rotation angle signal to obtain a magnetic resonance curve of the Lorentz absorption line type, and using the curve Fitting is performed, where S is the demodulated signal amplitude, ω L is the radio frequency magnetic field frequency, A, B, and C are the undetermined fitting parameters, and the fitting parameter C is the line width Γ of the magnetic resonance curve. The step 3 comprises: scanning the radio frequency magnetic field frequency, demodulating the orthogonal component of the x-axis optical rotation angle signal to obtain a magnetic resonance curve of the Lorentz dispersion line type, scanning the radio frequency magnetic field amplitude at the resonance frequency, measuring the slope of the magnetic resonance curve at the resonance frequency, and obtaining the radio frequency magnetic field amplitude corresponding to the slope maximum. The step 4 comprises: establishing a mapping model from transverse and longitudinal relaxation to the line width of the magnetic resonance curve and the radio frequency magnetic field amplitude corresponding to the slope maximum of the magnetic resonance curve through the theoretical expression of the magnetic resonance curve line width and the magnetic resonance curve slope maximum, and the process is:

[0030] The dynamic evolution equation of electron spin polarization is established using the BLOCH equation:

[0031]

[0032] Among them, s is the electron spin polarization vector, t is the time, γ e is the electron gyromagnetic ratio, B is the environmental magnetic field vector, R op is the optical pumping rate, is the unit vector in the z direction, γ={γ 2 ,γ 2 ,γ 1} is the three-axis electron relaxation vector, γ 1 and γ 2 are the longitudinal relaxation and transverse relaxation of electrons respectively. By solving the BLOCH equation, the theoretical expression of the line width of the magnetic resonance curve is obtained as follows:

[0033]

[0034] Where Γ is the line width of the magnetic resonance curve, B y is the RF magnetic field amplitude, the slope of the magnetic resonance curve at the resonance frequency is proportional to the RF magnetic field amplitude B y By taking the derivative, we can get the RF magnetic field amplitude corresponding to the maximum slope, and its theoretical expression is:

[0035]

[0036] Among them, B′ yis the RF magnetic field amplitude corresponding to the maximum slope value. In summary, we get two theoretical expressions for the line width of the magnetic resonance curve and the RF magnetic field amplitude corresponding to the maximum slope value at the resonant frequency of the magnetic resonance curve. Combining the two equations, we can replace B in the expression of the line width of the magnetic resonance curve Γ with y Replace with B′ y , we get the expressions of the electron longitudinal relaxation and transverse relaxation about the line width of the magnetic resonance curve and the RF magnetic field amplitude corresponding to the maximum value of the slope of the magnetic resonance curve:

[0037]

[0038] Leveraging Relationships se =γ 2 -γ 1 , where γ se It is the electron spin exchange relaxation, and finally the electron spin exchange relaxation is solved.

[0039] In view of the problem that the existing electron spin exchange relaxation measurement method can only be applied in low magnetic fields, the present invention proposes an electron spin exchange relaxation measurement method based on magnetic resonance curves that can be applied in the magnetic field range from zero magnetic field to geomagnetic level. This method has a wider range of application scenarios and provides an effective means for measuring spin exchange relaxation in geomagnetic fields. Figure 1 As shown, the specific method of the present invention is as follows:

[0040] (1) Turn on the pump laser to polarize the atomic ensemble. The pump laser is used to make the alkali metal atoms have a consistent electron spin orientation and heat the atomic ensemble to ensure a high atomic density.

[0041] (2) Scan the transverse RF magnetic field frequency to obtain the magnetic resonance curve and measure the line width of the curve. Apply the RF magnetic field along the y-axis, scan the RF magnetic field frequency, demodulate the in-phase component of the x-axis optical rotation angle signal to obtain the magnetic resonance curve of the Lorentz absorption line type, and use the curve Fitting is performed, where S is the demodulated signal amplitude, ω L is the RF magnetic field frequency, A, B, C are the undetermined fitting parameters, and the fitting parameter C is the line width Γ of the magnetic resonance curve.

[0042] (3) Scanning the RF magnetic field frequency, demodulating the orthogonal component of the x-axis optical rotation angle signal to obtain a magnetic resonance curve of the Lorentz dispersion line type, scanning the RF magnetic field amplitude at the resonance frequency, measuring the slope of the magnetic resonance curve at the resonance frequency, and obtaining the RF magnetic field amplitude corresponding to the maximum slope.

[0043] (4) Calculate spin exchange relaxation using line width and RF magnetic field amplitude. Based on the theoretical expressions of the line width of the magnetic resonance curve and the maximum value of the slope of the magnetic resonance curve corresponding to the RF magnetic field amplitude, a mapping model of transverse and longitudinal relaxation to the line width of the magnetic resonance curve and the maximum value of the slope of the magnetic resonance curve corresponding to the RF magnetic field amplitude is established. The process is as follows:

[0044] The dynamic evolution equation of electron spin polarization is established using the BLOCH equation:

[0045]

[0046] Where S is the electron spin polarization vector, B is the magnetic field vector, γ e is the electron gyromagnetic ratio, R op is the pumping rate, γ = {γ 2 ,γ 2 ,γ 1} is the three-axis relaxation vector, γ 1 , γ 2 They are longitudinal relaxation and transverse relaxation respectively. The first term on the right side of the equation is the Larmor precession behavior of the atom around the external magnetic field, the second term describes the polarization effect of the pump light along a specific axis z, and the third term represents the total relaxation of the atom. The total relaxation includes the effects of spin exchange relaxation, spin destruction relaxation, pump light, and detection light:

[0047] γ 1 =γ pump +γ probe +γ sd +γ wall

[0048] γ 2 =γ 1 +γ se

[0049] Among them, γ pump is the relaxation caused by the pump laser, γ probe To detect laser-induced relaxation, γ sd is the spin-destroying collision relaxation, γ 6all is the bubble wall collision relaxation, γ se These relaxations will cause the broadening of magnetic resonance lines. The general spin collision relaxation can be expressed as = is the atomic density of alkali metals, σ m is the corresponding collision cross section, is the average thermal motion speed. Spin exchange relaxation has a large collision cross section and is therefore the key to determining the size of total relaxation and affecting system performance.

[0050] To obtain the magnetic resonance line shape, assume that the z-axis magnetic field is B z , the corresponding Larmor frequency is ω L =γB z , apply a radio frequency field 2B in the y direction y cosωt, where B yis the RF magnetic field amplitude, ω is the RF field frequency, and t is time. Using the rotating wave approximation, in a rotating coordinate system rotating along the z-axis by ω, the analytical solution of the Bloch equation can be obtained:

[0051]

[0052]

[0053]

[0054] Among them, S′ x , S′ y , S′ z is the electronic polarizability of the three axes in the rotating coordinate system, Γ is S E ′,S′ y The line width Γ of the magnetic resonance curve depends on the detuning frequency:

[0055]

[0056] It can be found that the line width is related to the longitudinal relaxation γ 1 and transverse relaxation γ 2 In the laboratory coordinate system, the S C =S′ C cosωt+S′ y sinωt, where S C is the electronic polarization rate of the x-axis in the laboratory coordinate system, ω is the frequency of the radio frequency magnetic field, and t is the time. Through the phase-locked amplifier, S' is demodulated y , we get a magnetic resonance curve that is symmetrical about the Larmor frequency. We get the slope of the magnetic resonance curve at the resonance frequency:

[0057]

[0058] The slope is about B y The derivative of :

[0059]

[0060] The RF magnetic field amplitude B can be found y The RF magnetic field amplitude corresponding to the maximum slope value at the resonant frequency of the magnetic resonance curve is:

[0061]

[0062] The RF magnetic field amplitude corresponding to the slope maximum includes the longitudinal relaxation γ 1 and transverse relaxation γ 2 By combining it with the resonance line width, which also contains relaxation information, the B in the expression of the magnetic resonance curve line width Γ is converted to y Replace with B′y , the longitudinal relaxation γ 1 and transverse relaxation γ 2 Separation:

[0063]

[0064]

[0065] Experimentally, the line width Γ is measured from the magnetic resonance curve in the in-phase component of the signal demodulation, B′ y The RF magnetic field amplitude corresponding to the maximum value of the zero-point slope of the magnetic resonance curve is obtained. Finally, the relationship γ se =γ 2 -γ 1 Implementation se Fast measurement.

[0066] The contents not described in detail in the specification of the present invention belong to the prior art known to the professional and technical personnel in the field. It is pointed out here that the above description helps those skilled in the art to understand the invention, but does not limit the protection scope of the invention. Any equivalent replacement, modification and / or simplification of the above description without departing from the essence of the invention falls within the protection scope of the invention.

Claims

1. A method for measuring electron spin exchange relaxation based on magnetic resonance curves, characterized in that: The method includes using laser polarization to polarize the atomic ensemble so that the alkali metal atoms have a consistent electron spin orientation, then measuring the resonance line width by scanning the electron magnetic resonance curve, and measuring the radio frequency magnetic field amplitude corresponding to the slope maximum of the magnetic resonance curve at the resonance frequency by scanning the transverse radio frequency magnetic field amplitude, and using the electron relaxation information contained in the line width and radio frequency magnetic field amplitude to solve the electron transverse and longitudinal relaxation, thereby obtaining electron spin exchange relaxation.

2. The method for measuring electron spin exchange relaxation based on magnetic resonance curve according to claim 1, characterized in that: The following steps are involved: Step 1, turn on the pump laser to polarize the atomic ensemble; Step 2, scanning the transverse radio frequency magnetic field frequency to obtain a magnetic resonance curve and measuring the line width of the curve; Step 3, scanning the transverse radio frequency magnetic field amplitude, and measuring the radio frequency magnetic field amplitude corresponding to the maximum slope value at the resonance frequency of the magnetic resonance curve; Step 4: Use the line width and RF magnetic field amplitude to solve the electron spin exchange relaxation.

3. The method for measuring electron spin exchange relaxation based on magnetic resonance curve according to claim 2, characterized in that: The step 1 includes: the pumping laser performs laser pumping on the atomic ensemble along the z-axis.

4. The method for measuring electron spin exchange relaxation based on magnetic resonance curve according to claim 2, characterized in that: The step 2 includes: applying a radio frequency magnetic field along the y-axis, scanning the frequency of the radio frequency magnetic field, demodulating the in-phase component of the x-axis optical rotation angle signal to obtain a magnetic resonance curve of the Lorentz absorption line type, and using the curve Fitting is performed, where S is the demodulated signal amplitude, ω L is the RF magnetic field frequency, A, B, C are the undetermined fitting parameters, and the fitting parameter C is the line width Γ of the magnetic resonance curve.

5. The method for measuring electron spin exchange relaxation based on magnetic resonance curve according to claim 2, characterized in that: The step 3 comprises: scanning the frequency of the radio frequency magnetic field, demodulating the orthogonal component of the x-axis optical rotation angle signal to obtain a magnetic resonance curve of the Lorentz dispersion line type, scanning the amplitude of the radio frequency magnetic field at the resonance frequency, measuring the slope of the magnetic resonance curve at the resonance frequency, and obtaining the amplitude of the radio frequency magnetic field corresponding to the maximum slope.

6. The method for measuring electron spin exchange relaxation based on magnetic resonance curve according to claim 2, characterized in that: The step 4 comprises: establishing a mapping model of transverse and longitudinal relaxation to the line width of the magnetic resonance curve and the amplitude of the radio frequency magnetic field corresponding to the maximum value of the slope of the magnetic resonance curve through the theoretical expression of the amplitude of the radio frequency magnetic field corresponding to the line width of the magnetic resonance curve and the maximum value of the slope of the magnetic resonance curve, wherein the process is as follows: The dynamic evolution equation of electron spin polarization is established using the BLOCH equation: Among them, S is the electron spin polarization vector, t is time, γ e is the electron gyromagnetic ratio, B is the environmental magnetic field vector, R op is the optical pumping rate, is the unit vector in the z direction, γ={γ2,γ2,γ1} is the three-axis electron relaxation vector, γ1 and γ2 are the electron longitudinal relaxation and transverse relaxation respectively. By solving the BLOCH equation, the theoretical expression of the line width of the magnetic resonance curve is obtained as follows: Where Γ is the line width of the magnetic resonance curve, B y is the RF magnetic field amplitude, the slope of the magnetic resonance curve at the resonance frequency is proportional to the RF magnetic field amplitude B y By taking the derivative, we can get the RF magnetic field amplitude corresponding to the maximum slope, and its theoretical expression is: Among them, B ′ y is the RF magnetic field amplitude corresponding to the maximum slope value. In summary, we get two theoretical expressions for the line width of the magnetic resonance curve and the RF magnetic field amplitude corresponding to the maximum slope value at the resonant frequency of the magnetic resonance curve. Combining the two equations, we can replace B in the expression of the line width of the magnetic resonance curve Γ with y Replace with B ′ y , we get the expressions of electron longitudinal relaxation and transverse relaxation for the line width of the magnetic resonance curve and the RF magnetic field amplitude corresponding to the maximum value of the slope of the magnetic resonance curve: Leveraging Relationships se =γ2-γ1, where γ se It is the electron spin exchange relaxation, and finally the electron spin exchange relaxation is solved.

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