CN116087845A - Electron spin polarizability three-dimensional distribution measuring method based on electron paramagnetic resonance - Google Patents
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Abstract
The method for measuring the three-dimensional distribution of the spin polarizability of the electron based on electron paramagnetic resonance uses a longitudinal uniform magnetic field coil and a longitudinal gradient magnetic field coil to distinguish the transverse distribution of the spin polarizability of the electron, applies an oscillating magnetic field in the x direction to generate electron paramagnetic resonance with the spin, changes the size of the longitudinal uniform magnetic field, makes the spin of the electron at different positions away from the x axis resonate with the oscillating magnetic field, ensures that the amplitude of the spin angle of a resonance signal is in direct proportion to the relative polarizability of a resonance point, reflects the three-dimensional distribution of the spin polarizability of the electron by measuring the resonance signals at different spatial positions, does not apply a big magnetic field of Gaussian magnitude to cause the atomic energy level to split, and is favorable for measuring the three-dimensional distribution of the spin polarizability of the electron at high temperature and high pressure.
Description
Technical Field
The invention relates to an electron spin polarization three-dimensional distribution measurement method based on electron paramagnetic resonance, and belongs to the field of optical pumping atomic polarization.
Background
The sensitive elements of atomic magnetometers, atomic gyroscopes, atomic clocks and other devices based on optical pumping atomic polarization are alkali metal air chambers. Due to the absorption of pumping light by alkali metals, there is a severe gradient in electron spin polarizability, which has a great influence on the coherence of electron spin and nuclear spin. Accurately measuring the three-dimensional distribution of electron polarizability becomes a problem to be solved.
At present, most three-dimensional distribution researches of electron polarizability are finite element simulation based on a Bloch-Diffusion equation, the simulation result is seriously dependent on preset parameters, and different simulation results can be generated by unreal preset parameters. There are studies on the transmittance response longitudinal polarization distribution using pumping light, but this method cannot accurately measure the lateral distribution of polarization. In the previous study of electron paramagnetic resonance measurement electron spin polarization, the proposal relies on a large magnetic field to generate energy level cleavage and measure the atomic layout number, and has measurement defects for an atomic gas chamber with high temperature and high air pressure.
Disclosure of Invention
The invention solves the problems that: the invention provides an electron spin polarization three-dimensional distribution measuring method based on electron paramagnetic resonance, which uses a longitudinal uniform magnetic field coil and a longitudinal gradient magnetic field coil to distinguish the transverse distribution of electron spin polarization, applies an oscillating magnetic field in the x direction to generate electron paramagnetic resonance with the electron spin, changes the size of the longitudinal uniform magnetic field, makes the electron spin at different positions away from the x axis resonate with the oscillating magnetic field, ensures that the amplitude of the resonance signal rotation angle is in direct proportion to the relative polarization of a resonance point, reflects the three-dimensional distribution of the electron spin polarization by measuring resonance signals at different spatial positions, does not apply a big magnetic field of Gaussian magnitude to generate cleavage at atomic energy level, and is favorable for measuring the three-dimensional distribution of the electron spin polarization at high temperature and high pressure.
The technical scheme of the invention is as follows:
the electron spin polarization rate three-dimensional distribution measuring method based on electron paramagnetic resonance is characterized in that a longitudinal uniform magnetic field coil and a longitudinal gradient magnetic field coil are used for distinguishing the transverse distribution of the electron spin polarization rate, an oscillating magnetic field is applied in the x direction and the electron spin generates electron paramagnetic resonance, the size of the longitudinal uniform magnetic field is changed, and different positions away from the x axis are causedThe electron spin of the electron-beam resonance device and the oscillating magnetic field are subjected to resonance, the amplitude of the resonance signal rotation angle is in direct proportion to the relative polarizability of the resonance point, and the three-dimensional distribution of the electron spin polarizability is reflected by measuring the resonance signals of different spatial positions. The spatial resolution of the method is less than 1mm 3 。
The method comprises the following steps:
step 1, applying a bias magnetic field B in a z-axis direction perpendicular to the detection light direction z0 And gradient magnetic field B z gradient ，dB z gradient Dx=k, where k is the magnetic field gradient and the total gradient magnetic field is B z (x)＝B z0 +B z gradient (x) The electron spin precession frequency distributed in the x-axis direction, i.e. in the direction of the probe light, is ω spin (x)＝γ e (B z0 +kx)/q, where q is an electron spin ensemble slow down factor, gamma e Is electron spin ensemble gyromagnetic ratio;
step 2, measuring the transmitted light intensity of the detection light;
step 3, applying an oscillating magnetic field in the x direction to generate resonance with electron spin;
step 4, change B z0 The electron spin resonance point x= (ωq/γ) is shifted from one side to the other side along the direction x of the alkali metal gas chamber by the magnetic field intensity value of (a) e -B z0 ) K, wherein ω is the frequency of the x-direction oscillating magnetic field, recording the resonance intensity of each resonance point, the resonance intensity being proportional to the electron spin polarization;
step 5, changing the position of the detection light on the yoz plane, and repeatedly testing the transmitted light intensity and the resonance intensity;
and 6, dividing the resonance intensity of each position by the transmission light intensity of the detection light to obtain the three-dimensional distribution of the electron spin polarization rate.
The bias magnetic field in the step 1 is a direct current uniform magnetic field.
In the step 2, in the process of measuring the rotation angle by adopting a balance difference method, the output signal is in direct proportion to the rotation angle or the transmitted light intensity, and in order to ensure the comparability of the rotation angles at different measuring positions, the transmitted light intensity of the detection light is measured at first, and the output signal is normalized at the later stage.
The oscillating frequency of the oscillating magnetic field applied in the step 3 is gamma e B z0 Near/q to facilitate resonance with the electron spin.
The resonance intensity in the step 4 is obtained by demodulating the output signal by the lock-in amplifier.
The step 2 comprises extracting x-axis component information of electron spin ensemble polarizability<P x >：
Wherein the method comprises the steps of<S x >The optical rotation angle signal detected by the detection light is represented by I, the transmitted light intensity is represented by a constant proportionality coefficient, and l is the width of the inner space of the alkali metal gas chamber on the x axis.
The device for measuring the transmitted light intensity comprises a polarization beam splitter prism, wherein the input side of the polarization beam splitter prism is connected with transmitted light penetrating through an alkali metal air chamber, the reflection side of the polarization beam splitter prism is connected with the negative input end of a differential amplifier through a first photoelectric detector, the transmission side of the polarization beam splitter prism is connected with the positive input end of the differential amplifier, and the output end of the differential amplifier is connected with a data acquisition system.
The invention has the following technical effects: the invention discloses a three-dimensional distribution measuring method of electron spin polarization based on electron paramagnetic resonance, which is based on different precession frequencies of electron spin under different longitudinal magnetic fields, so that a longitudinal uniform magnetic field coil and a longitudinal gradient magnetic field coil are used for distinguishing transverse distribution of electron spin polarization, an oscillating magnetic field is applied in the x direction, the oscillating frequency of the oscillating magnetic field is close to Larmor precession frequency of the electron spin, the magnitude of the longitudinal uniform magnetic field is changed, the electron spin at different positions away from the x axis can resonate with the oscillating magnetic field, and the amplitude of a resonance signal rotation angle is in direct proportion to the magnitude of the electron spin polarization of a resonance point, so that the three-dimensional distribution of the transverse polarization can be measured. The incidence position of the detection light on the yoz plane is changed to carry out repeated tests, and the three-dimensional distribution condition of the polarization rate of the electron spin in the atomic gas chamber can be measured. The method can be used for three-dimensional distribution research of atomic vapor electron spin polarization rate of systems such as an optical pump magnetometer, a SERF atomic gyroscope, an optical pumping atomic clock and the like.
Compared with the prior art, the invention has the advantages that: the transverse distribution of the electron spin polarizability can be measured by distinguishing the transverse distribution of the electron spin polarizability by using a longitudinal uniform magnetic field coil and a longitudinal gradient magnetic field coil. The balanced differential optical rotation angle detection scheme after magnetic field modulation is adopted, and has higher signal-to-noise ratio compared with the optical absorption detection scheme. The atomic energy level is split without applying a Gaussian magnitude large magnetic field, and the three-dimensional distribution of the spin polarizability of electrons at high temperature and high pressure can be measured.
Drawings
FIG. 1 is a schematic flow chart of a method for measuring three-dimensional distribution of electron spin polarizability based on electron paramagnetic resonance in which the invention is implemented. In FIG. 1, the steps of 1, applying a gradient magnetic field and a direct current magnetic field in the z direction are included; step 2, measuring the transmitted light intensity of the detection light; step 3, applying an oscillating magnetic field in the x direction to generate resonance with electron spin; step 4, changing the intensity of the direct current uniform magnetic field to enable the resonance plane of the electron spin to move from one side to the other side along the x direction of the air chamber, and recording the resonance intensity of each resonance point; step 5, changing the position of the detection light on the yoz plane, and repeatedly testing the transmitted light intensity and the resonance intensity; and 6, dividing the resonance intensity of each position by the transmission light intensity of the detection light to obtain the three-dimensional distribution of the electron spin polarization rate.
Fig. 2 is a schematic diagram of an electron spin polarizability three-dimensional distribution measuring device based on electron paramagnetic resonance. Fig. 2 includes a resonant magnetic field along the x-axis, a gradient magnetic field Bz along the z-axis, a polarization distribution along the x-direction, a pumping light beam, and a probe light beam, and in a cartesian coordinate system, the pumping light incidence direction is parallel to the z-axis, and the probe light incidence direction is parallel to the x-axis. Fig. 2 includes a PBS (polarization beam splitter, polarizing beam splitter prism), two PDs (photodetectors), a differential amplifier, and a data acquisition system.
Detailed Description
The invention is described below with reference to the figures (fig. 1-2) and examples.
FIG. 1 is a schematic flow chart of a method for measuring three-dimensional distribution of electron spin polarizability based on electron paramagnetic resonance in which the invention is implemented. Fig. 2 is a schematic diagram of an electron spin polarizability three-dimensional distribution measuring device based on electron paramagnetic resonance. Referring to fig. 1 to 2, the electron spin polarization three-dimensional distribution measuring method based on electron paramagnetic resonance uses a longitudinal uniform magnetic field coil and a longitudinal gradient magnetic field coil to distinguish the transverse distribution of electron spin polarization, applies an oscillating magnetic field in the x direction to generate electron paramagnetic resonance with electron spin, changes the size of the longitudinal uniform magnetic field, makes the electron spin at different positions from the x axis resonate with the oscillating magnetic field, and the amplitude of the spin angle of a resonance signal is proportional to the relative polarization of a resonance point, and reflects the three-dimensional distribution of electron spin polarization by measuring the resonance signals at different spatial positions. The spatial resolution is less than 1mm 3 。
The method comprises the following steps: step 1, applying a bias magnetic field B in a z-axis direction perpendicular to the detection light direction z0 And gradient magnetic field B z gradient ，dB z gradient Dx=k, where k is the magnetic field gradient and the total gradient magnetic field is B z (x)＝B z0 +B z gradient (x) The electron spin precession frequency distributed in the x-axis direction, i.e. in the direction of the probe light, is ω spin (x)＝γ e (B z0 +kx)/q, where q is an electron spin ensemble slow down factor, gamma e Is electron spin ensemble gyromagnetic ratio; step 2, measuring the transmitted light intensity of the detection light; step 3, applying an oscillating magnetic field in the x direction to generate resonance with electron spin; step 4, change B z0 The electron spin resonance point x= (ωq/γ) is shifted from one side to the other side along the direction x of the alkali metal gas chamber by the magnetic field intensity value of (a) e -B z0 ) K, wherein ω is the frequency of the x-direction oscillating magnetic field, recording the resonance intensity of each resonance point, the resonance intensity being proportional to the electron spin polarization; step 5, changing the position of the detection light on the yoz plane, and repeatedly testing the transmitted light intensity and the resonance intensity; and 6, dividing the resonance intensity of each position by the transmission light intensity of the detection light to obtain the three-dimensional distribution of the electron spin polarization rate.
The bias magnet in the step 1The field is a direct current uniform magnetic field. In the step 2, in the process of measuring the rotation angle by adopting a balance difference method, the output signal is in direct proportion to the rotation angle or the transmitted light intensity, and in order to ensure the comparability of the rotation angles at different measuring positions, the transmitted light intensity of the detection light is measured at first, and the output signal is normalized at the later stage. The oscillating frequency of the oscillating magnetic field applied in the step 3 is gamma e B z0 Near/q to facilitate resonance with the electron spin. The resonance intensity in the step 4 is obtained by demodulating the output signal by the lock-in amplifier.
The step 2 comprises extracting x-axis component information of electron spin ensemble polarizability<P x >：
Wherein the method comprises the steps of<S x >The optical rotation angle signal detected by the detection light is represented by I, the transmitted light intensity is represented by a constant proportionality coefficient, and l is the width of the inner space of the alkali metal gas chamber on the x axis. The device for measuring the transmitted light intensity comprises a polarization beam splitter prism, wherein the input side of the polarization beam splitter prism is connected with transmitted light penetrating through an alkali metal air chamber, the reflection side of the polarization beam splitter prism is connected with the negative input end of a differential amplifier through a first photoelectric detector, the transmission side of the polarization beam splitter prism is connected with the positive input end of the differential amplifier, and the output end of the differential amplifier is connected with a data acquisition system.
The invention provides an electron spin polarization rate three-dimensional distribution measurement method based on electron paramagnetic resonance. The transverse distribution of electron spin polarizability is distinguished using a longitudinal uniform magnetic field coil from a longitudinal gradient magnetic field coil. An oscillating magnetic field is applied in the x direction to generate electron paramagnetic resonance with electron spin. The magnitude of the longitudinal uniform magnetic field is changed, so that electron spins at different positions from the x-axis resonate with the oscillating magnetic field, and the amplitude of the rotation angle of the resonance signal is in direct proportion to the relative polarization rate of the resonance point. The three-dimensional distribution of electron spin polarizability is reflected by measuring resonance signals at different spatial positions.
The electron spin polarizability three-dimensional distribution measurement principle and the coordinate system based on electron paramagnetic resonance are set as shown in the following figure 2. The kinetic equation of the polarization of optically pumped atoms and the larmor precession of atoms under external magnetic fields can be described approximately by the following Bloch equation:
in the Cartesian coordinate system of FIG. 2, the pumping light direction is parallel to the z-axis and the probe light direction is parallel to the x-axis; t is time; electron spin ensemble polarization<P>＝<P x ,P y ,P z >Wherein P is x ,P y ,P z Three coordinate axis components of electron polarization rate; gamma ray e Is the electron spin ensemble gyromagnetic ratio; q is an electron spin ensemble slow-down factor; pumping rate R of the pulse laser; external magnetic field B =<B x (t),B y (t),B z (t)>Triaxial component B x (t),B y (t),B z (t); to describe relaxation processes of atomic longitudinal and transverse polarizability, a longitudinal relaxation rate Γ of the electron spin is introduced 1 Transverse relaxation rate Γ 2 . The equation describes the dynamic evolution of the electron spin ensemble under larmor precession in an optical pumping, atomic relaxation, and magnetic field.
Wherein the method comprises the steps of<P ± >＝<P x >±<P y >，<B ± >(t)＝<B x >(t)±<B y >(t). The longitudinal component of the electron spin is
Applying an oscillating magnetic field B in the x-axis of the system x (t)＝B 1 cos(ωt)，B 1 For the amplitude of the oscillating magnetic field, ω is the angular velocity of the oscillating magnetic field, and no magnetic field is applied on the y-axis, i.e. B y (t) =0, z-axis applied direct current magnetic field B z (t)＝B z0 The magnetic field response of the system x-direction polarization rate can be obtained by taking the magnetic field response (2) into the system<P x >：
Wherein the method comprises the steps of
When the magnetic field applied by the z axis and the oscillating magnetic field B applied by the x axis x (t)＝B 1 When cos (ωt) resonates, i.e. γ e B z0 =ωq, the resonance signal reaches a maximum:
by being in a similar principle to that of nuclear magnetic resonance imaging, by being in a magnetic field B z By adding a spatial gradient, the information of the spatial variation of the spin polarization of the electrons along the direction of the detection laser can be obtained, as shown in fig. 2. Applying a bias magnetic field B in a z-axis perpendicular to the direction of the detection laser z0 And gradient magnetic field B z gradient The magnetic field gradient was dB z gradient Dx=k, the total gradient magnetic field is B z (x)＝B z0 +B z gradient (x) A. The invention relates to a method for producing a fibre-reinforced plastic composite With such a gradient, the precession frequency of the electron spins distributed in the x-direction is ω spin (x)＝γ e (B z0 +kx)/q. The gradient magnetic field is kept unchanged, and the frequency of the x-direction oscillating field is set to omega. At this time, the electron spin resonance point is x= (ωq/γ) e -B z0 ) /k, scan B z0 The size of (2) is such that the resonance point moves along the detection laser from one side of the atomic gas cell to the other. The applied magnetic field is kept unchanged, and when electron spins and the applied oscillating magnetic field generate resonance,<P x >is only equal to the longitudinal polarization of the electron spin<P z > 0 Correlated and proportional. The detection light is a beam of linearly polarized light with parallel x-axis, and electron spin can be extracted by adopting a balanced differential method<P x >Component information:
wherein the method comprises the steps of<S x >The optical rotation angle signal detected by the detection light is represented, I is the projected light intensity, and a is a constant proportionality coefficient. And extracting oscillation amplitude of each resonance point along the direction of the detection light by using a phase-locking amplification technology and dividing the oscillation amplitude by corresponding transmission light intensity I to obtain the relative distribution of the longitudinal polarization rate of the electron spin. Since the diameter of the probe beam is only a few millimeters or less, the spatial resolution of the method is less than 1mm 3 。
The method needs to realize three-dimensional distribution measurement of electron spin polarization rate based on electron paramagnetic resonance through 6 steps.
Step one: applying a gradient magnetic field and a DC magnetic field in the z direction
Applying a bias magnetic field B in a z-axis perpendicular to the direction of the detection laser z0 And gradient magnetic field B z gradient The magnetic field gradient was dB z gradient Dx=k, the total gradient magnetic field is B z (x)＝B z0 +B z gradient (x) A. The invention relates to a method for producing a fibre-reinforced plastic composite With such a gradient, the precession frequency of the electron spins distributed in the x-direction is ω spin (x)＝γ e (B z0 +kx)/q。
Step two: measuring transmitted light intensity of probe light
In the process of measuring the rotation angle by adopting the balance difference method, the output signal is in direct proportion to the rotation angle and the transmitted light intensity. In order to ensure comparability of the rotation angles at different measuring positions, the transmission light intensity of the detection light is measured at first, and the output signal is normalized for the later period.
Step three: the oscillation magnetic field is applied in the x direction and the electron spin generates resonance
The applied oscillation frequency should be at gamma e B z0 Near/q to facilitate resonance with the electron spin.
Step four: changing the intensity of the z-axis direct current uniform magnetic field to enable the resonance plane of the electron spin to move from one side to the other side along the x direction of the air chamber, wherein the electron spin resonance point is x= (ωq/γ) e -B z0 ) And/k. Recording resonance of each resonance pointStrength. The resonance intensity is proportional to the electron spin polarizability, which can be obtained by demodulating the output signal by a lock-in amplifier.
Step five: changing the position of the probe light on the yoz plane, repeatedly testing the transmitted light intensity and the resonance intensity
Step six: and dividing the resonance intensity of each position by the transmission light intensity of the detection light to obtain the three-dimensional distribution of the spin polarizability of the electrons.
The transverse distribution of electron spin polarizability is distinguished using a longitudinal uniform magnetic field coil from a longitudinal gradient magnetic field coil. An oscillating magnetic field is applied in the x-direction, the oscillation frequency of which should be close to the larmor precession frequency of the electron spins. The magnitude of the longitudinal uniform magnetic field is changed, so that electron spins at different positions from the x-axis resonate with the oscillating magnetic field, and the amplitude of the rotation angle of the resonance signal is in direct proportion to the relative polarization rate of the resonance point. The three-dimensional distribution of electron spin polarizability can be reflected by measuring resonance signals at different spatial locations.
What is not described in detail in the present specification belongs to the prior art known to those skilled in the art. It is noted that the above description is helpful for a person skilled in the art to understand the present invention, but does not limit the scope of the present invention. Any and all such equivalent substitutions, modifications and/or deletions as may be made without departing from the spirit and scope of the invention.
Claims (9)
1. The method is characterized in that a longitudinal uniform magnetic field coil and a longitudinal gradient magnetic field coil are used for distinguishing transverse distribution of electron spin polarization, an oscillating magnetic field is applied in the x direction and electron spin generates electron paramagnetic resonance, the size of the longitudinal uniform magnetic field is changed, electron spin at different positions away from the x axis and the oscillating magnetic field generate resonance, the amplitude of a resonance signal rotation angle is in direct proportion to the relative polarization of a resonance point, and the three-dimensional distribution of electron spin polarization is reflected by measuring resonance signals at different spatial positions.
2. The method for measuring the three-dimensional distribution of the spin polarizability of electrons based on the electron paramagnetic resonance according to claim 1, wherein the spatial resolution is less than 1mm 3 。
3. The method for measuring the three-dimensional distribution of the spin polarizability of electrons based on the electron paramagnetic resonance according to claim 1, comprising the steps of:
step 1, applying a bias magnetic field B in a z-axis direction perpendicular to the detection light direction z0 And gradient magnetic field B z gradient ，dB z gradient Dx=k, where k is the magnetic field gradient and the total gradient magnetic field is B z (x)＝B z0 +B z gradient (x) The electron spin precession frequency distributed in the x-axis direction, i.e. in the direction of the probe light, is ω spin (x)＝γ e (B z0 +kx)/q, where q is an electron spin ensemble slow down factor, gamma e Is electron spin ensemble gyromagnetic ratio;
step 2, measuring the transmitted light intensity of the detection light;
step 3, applying an oscillating magnetic field in the x direction to generate resonance with electron spin;
step 4, change B z0 The electron spin resonance point x= (ωq/γ) is shifted from one side to the other side along the direction x of the alkali metal gas chamber by the magnetic field intensity value of (a) e -B z0 ) K, wherein ω is the frequency of the x-direction oscillating magnetic field, recording the resonance intensity of each resonance point, the resonance intensity being proportional to the electron spin polarization;
step 5, changing the position of the detection light on the yoz plane, and repeatedly testing the transmitted light intensity and the resonance intensity;
and 6, dividing the resonance intensity of each position by the transmission light intensity of the detection light to obtain the three-dimensional distribution of the electron spin polarization rate.
4. The method for measuring the three-dimensional distribution of the spin polarizability of electrons based on the electron paramagnetic resonance according to claim 3, wherein the bias magnetic field in the step 1 is a uniform direct current magnetic field.
5. The method according to claim 3, wherein the step 2 includes measuring the rotation angle by a balance difference method, wherein the output signal is proportional to the rotation angle or the transmitted light intensity, and the transmitted light intensity of the probe light is measured first to normalize the output signal at a later stage to ensure the comparability of the rotation angle at different measurement positions.
6. The method for measuring three-dimensional distribution of spin polarizability of electron based on electron paramagnetic resonance according to claim 3, wherein the oscillating frequency of the oscillating magnetic field applied in the step 3 is at γ e B z0 Near/q to facilitate resonance with the electron spin.
7. The method for measuring the three-dimensional distribution of the spin polarizability of electrons based on the electron paramagnetic resonance according to claim 3, wherein the resonance intensity in the step 4 is obtained by demodulating the output signal by a lock-in amplifier.
8. The method for three-dimensional distribution measurement of electron spin polarizability based on electron paramagnetic resonance according to claim 3, wherein the step 2 comprises extracting the x-axis component information of electron spin ensemble polarizability by the following formula<P x >：
Wherein the method comprises the steps of<S x >The optical rotation angle signal detected by the detection light is represented by I, the transmitted light intensity is represented by a constant proportionality coefficient, and l is the width of the inner space of the alkali metal gas chamber on the x axis.
9. The electron spin polarization three-dimensional distribution measurement method based on electron paramagnetic resonance according to claim 3, wherein the measurement device of the transmitted light intensity comprises a polarization beam splitter prism, the input side of the polarization beam splitter prism is connected with the transmitted light passing through the alkali metal gas chamber, the reflection side of the polarization beam splitter prism is connected with the negative input end of the differential amplifier through the first photoelectric detector, the transmission side of the polarization beam splitter prism is connected with the positive input end of the differential amplifier, and the output end of the differential amplifier is connected with the data acquisition system.
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