Method for accurate determination of electron spin fermi contact field and polarizability

Abstract

The application relates to a method for accurately measuring electron spin Fermi contact field and polarization rate. A spin coupling system decoupling magnetic field ten times of nuclear spin Fermi contact field is applied in the z direction, a uniaxial magnetometer sensitive to longitudinal magnetic field is constructed by using nuclear spin, and the longitudinal magnetic field is measured by detecting the precession frequency of the nuclear spin. The rotation direction of circularly polarized pumping laser is converted into sigma + The rotation direction of circularly polarized pumping laser is converted into sigma ‑ The precession frequency difference of nuclear spin under two kinds of pumping laser is measured, and the change amount of the longitudinal magnetic field is converted into double electron spin Fermi contact field. The measurement of the electron spin Fermi contact field is converted into the measurement of the precession frequency of the nuclear spin, and compared with the traditional measurement method, the measurement precision is higher. The polarization rate of the electron spin is linearly related to the Fermi contact field, and the polarization rate of the electron spin can be accurately calculated. The method can be used for measuring the electron spin Fermi contact field and the polarization rate of the electron spin of atomic spin gyroscopes, nuclear magnetic resonance gyroscopes and other instruments.

Description

Technical Field

[0001] This invention belongs to the field of optical pump atom polarization technology, specifically a method for accurately measuring electron spin Fermi contact field and polarizability. Background Technology

[0002] In the testing of atomic spin gyroscopes and nuclear magnetic resonance gyroscopes based on optically pumped atomic polarization, it is necessary to accurately calibrate the Fermi contact field and electron spin polarizability of the electron spin. Furthermore, the precise calculation of certain physical constants also requires accurate values ​​for these parameters. However, current measurements of the Fermi contact field and electron spin polarizability have relatively large errors (greater than 10%), making the accurate measurement of these parameters a pressing issue.

[0003] There are currently three methods for measuring the electron spin Fermi contact field and polarizability: one method is based on the measurement of the slowing factor Q, which is related to the electron spin polarizability. However, due to the existence of the polarization gradient, the relationship between the slowing factor Q and the electron spin polarizability is not clear. The second method is based on the absorption of pump light by the electron spin. However, since the scattering and absorption of pump laser by the bubble wall cannot be completely measured, this method has a large measurement error. The third method is based on the transient response of the electron spin during pumping and relaxation. This method requires the use of optical modulation devices, which is more complex to implement, and it does not consider the polarization gradient, resulting in fitting errors. Summary of the Invention

[0004] The problem solved by this invention is that it proposes a precise method for measuring the electron spin Fermi contact field and polarizability. By applying a magnetic field in the z-direction to decouple the electron spin from the nuclear spin, a magnetometer based on nuclear spin is constructed. The method of reversing electron spin polarization is used to convert the measurement of the electron spin Fermi contact field into the measurement of the nuclear spin precession frequency. The electron spin Fermi contact field is then divided by the fully polarized Fermi contact constant to obtain the electron spin polarizability, which is more accurate than traditional measurement methods.

[0005] The technical solution of the present invention is as follows:

[0006] A method for accurately determining the electron spin Fermi contact field and polarizability, characterized by comprising the following steps:

[0007] Step 1: Apply a DC magnetic field in the z-direction to decouple the electron spin from the nuclear spin;

[0008] Step 2: Apply left-handed circularly polarized pump-polarized electron spin and nuclear spin in the z-direction;

[0009] Step 3: Apply an alternating magnetic field that resonates with the nuclear spin in the x-direction to induce a transverse component in the nuclear spin;

[0010] Step 4: Use electron spin as an in-situ magnetometer to measure the precession frequency of nuclear spin;

[0011] Step 5: Change the rotation direction of the pump light in the z-direction to right-hand circular polarization, and measure the nuclear spin precession frequency again;

[0012] Step 6: Calculate the Fermi contact field and polarizability of the electron spin using the frequency difference between the two measurements.

[0013] Step 1 includes: based on the precession frequency coupling effect between electron spin and nuclear spin under a weak magnetic field, which affects the Larmor precession frequency of electron spin and nuclear spin, setting 1uT≤Bz≤1mT, where Bz is the DC magnetic field applied in the z direction, i.e., the decoupling magnetic field, and the nuclear spin precession frequency Ω under this decoupling magnetic field. n The expression is as follows:

[0014]

[0015] =γ n (B z +λM e P z e )

[0016]

[0017]

[0018]

[0019] Where ω e ω n a and b are both real intermediate variables, and Sign[b] represents the sign of b. The term represents the coupling effect between electron spin and nuclear spin, γ e It is the electron spin gyromagnetic ratio, γ n It is the nuclear spin gyromagnetic ratio; Q is the electron spin slowing factor, and Be is the electron spin-sensing magnetic field. Represents the electron spin Fermi contact field. It is the electron spin polarizability, λM e It is a constant related to the atomic density of alkali metals. It is the transverse relaxation rate of electrons. It is an electron polarization magnetic field. It is a nuclear polarization magnetic field.

[0020] Step 2 includes: electron spin in left-handed circularly polarized light σ + Polarization occurs under the pumping action, and nuclear spins are hyperpolarized through spin-exchange collisions with electron spins.

[0021] Step 3 includes: according to the precession frequency of the detected nuclear spin, the nuclear spin is deviated from the longitudinal direction, a magnetic field resonating with the nuclear spin is applied, and the resonant magnetic field is withdrawn after the nuclear spin deviates from the longitudinal direction.

[0022] Step 4 includes: the nuclear spin undergoes Larmor precession under the combined action of the decoupling magnetic field and the electron spin Fermi contact field. The electron spin senses the magnetic field generated by the nuclear spin precession and rotates around the z-axis, generating transverse polarization of the electron spin. The incident linearly polarized light in the x-direction extracts the optical rotation angle of the linearly polarized light generated by the transverse polarization of the electron spin, and the optical rotation angle information is extracted using the balanced difference method. Nuclear spin precession information for more than 10 cycles is collected. At this time, the left-handed circularly polarized light σ + Pump-induced nuclear spin precession frequency The expression is as follows:

[0023]

[0024] Step 5 includes: changing the rotation direction of the pump light in the z-direction, and converting the left-handed circularly polarized light σ... + Change to right-hand circularly polarized light σ - Electron spin polarization Contact field with Fermi Reverse the direction and measure the nuclear spin precession frequency again; at this time, σ - Nuclear spin precession frequency under right-hand circularly polarized pump The expression is as follows:

[0025]

[0026] Step 6 includes: dividing the frequency difference between the two precessions by twice the nuclear spin gyromagnetic ratio to obtain the electron spin Fermi contact field. Fermi contact field Dividing by the fully polarized Fermi contact constant yields the electron spin polarizability. The formula is as follows:

[0027]

[0028]

[0029] The technical effects of this invention are as follows: The method for accurately measuring the electron spin Fermi contact field and polarizability involves applying a spin-coupled ensemble decoupling magnetic field ten times larger than the nuclear spin Fermi contact field in the z-axis. A uniaxial magnetometer is used to construct a sensitive longitudinal magnetic field (i.e., the Z-axis magnetic field Bz) using nuclear spin. The longitudinal magnetic field is measured by detecting the precession frequency of the nuclear spin. The spin direction of the circularly polarized pump laser is determined by σ. + Transform into σ -This method measures the difference in precession frequency of nuclear spin under two pump lasers, converting it into a change in the longitudinal magnetic field, i.e., twice the electron spin Fermi contact field. Transforming the measurement of the electron spin Fermi contact field into a measurement of the nuclear spin precession frequency offers higher measurement accuracy compared to traditional methods. Since the electron spin polarizability has a linear relationship with its Fermi contact field, precise calculations of the electron spin polarizability are possible. This method can be used for measuring the electron spin Fermi contact field and electron spin polarizability in instruments such as atomic spin gyroscopes and nuclear magnetic resonance gyroscopes.

[0030] The advantages of this invention compared to existing technologies are as follows: A decoupling magnetic field is applied in the z-axis to decouple the electron spin from the nuclear spin, thus constructing a magnetometer based on nuclear spin. The measurement of the Fermi contact field of the electron spin is transformed into a measurement of the precession frequency of the nuclear spin using a method of reversing electron spin polarization. The electron spin Fermi contact field is then divided by the fully polarized Fermi contact constant to obtain the electron spin polarizability. Compared to traditional measurement methods, this frequency-based method is more accurate and has stronger anti-interference capabilities; furthermore, the frequency difference measurement method greatly suppresses common-mode noise. Attached Figure Description

[0031] Figure 1 This is a schematic diagram of the process for accurately measuring the electron spin Fermi contact field and polarizability of the present invention. Figure 1 The process includes the following steps: Step 1, applying a DC magnetic field in the z-direction to decouple the electron spin from the nuclear spin; Step 2, applying a left-handed circularly polarized pump light in the z-direction to polarize the electron spin and the nuclear spin; Step 3, applying an AC magnetic field resonating with the nuclear spin in the x-direction to generate a transverse component in the nuclear spin; Step 4, using the electron spin as an in-situ magnetometer to measure the precession frequency of the nuclear spin; Step 5, changing the direction of the pump light in the z-direction to right-handed circular polarization and measuring the precession frequency of the nuclear spin again; Step 6, calculating the Fermi contact field and polarizability of the electron spin based on the frequency difference between the two measurements.

[0032] Figure 2 This is a schematic diagram illustrating the principle of the method for accurately measuring the electron spin Fermi contact field and polarizability of the present invention. Figure 2 This includes the manifestations of nuclear spin, electron spin, and quenched gas in a spherical gas cell within the Cartesian coordinate system xyz, σ + Pump light refers to either positively circularly polarized pump light or left-handed circularly polarized pump light, σ - The pump light refers to either negatively circularly polarized pump light or right-handed circularly polarized pump light. The direction of the Bz magnetic field and the direction of the pump light are both along the z-axis, i.e., longitudinal. Bz is the z-axis magnetic field. σ represents the left-handed circularly polarized pump light + The nuclear spin precession frequency, σ represents the right-hand circularly polarized pump light -The nuclear spin precession frequency is measured by measuring the nuclear spin precession frequency difference. It can measure the electron spin Fermi contact field. Size and electron spin polarization λM e It is a constant related to the atomic density of alkali metals (belonging to the Fermi contact constant of fully polarized metals). γ n It is the nuclear spin-gyromagnetic ratio. Detailed Implementation

[0033] The following is in conjunction with the attached diagram ( Figures 1-2 The invention will be described in the following sections and examples.

[0034] Figure 1 This is a schematic diagram of the process for accurately measuring the electron spin Fermi contact field and polarizability of the present invention. Figure 2 This is a schematic diagram illustrating the principle of the method for accurately measuring the electron spin Fermi contact field and polarizability of this invention. (Reference) Figures 1 to 2 As shown, a method for accurately measuring the Fermi contact field and polarizability of electron spin is characterized by the following steps: Step 1, applying a DC magnetic field in the z-direction to decouple the electron spin from the nuclear spin; Step 2, applying left-handed circularly polarized pump light in the z-direction to polarize the electron spin and the nuclear spin; Step 3, applying an AC magnetic field resonating with the nuclear spin in the x-direction to generate a transverse component of the nuclear spin; Step 4, using the electron spin as an in-situ magnetometer to measure the precession frequency of the nuclear spin; Step 5, changing the direction of the pump light in the z-direction to right-handed circular polarization and measuring the precession frequency of the nuclear spin again; Step 6, calculating the Fermi contact field and polarizability of the electron spin by the frequency difference between the two measurements.

[0035] Step 1 includes: based on the precession frequency coupling effect between electron spin and nuclear spin under a weak magnetic field, which affects the Larmor precession frequency of electron spin and nuclear spin, setting 1uT≤Bz≤1mT, where Bz is the DC magnetic field applied in the z direction, i.e., the decoupling magnetic field, and the nuclear spin precession frequency Ω under this decoupling magnetic field. n The expression is as follows:

[0036]

[0037]

[0038]

[0039]

[0040] Where ω e ω n a and b are both real intermediate variables, and Sign[b] represents the sign of b. The term represents the coupling effect between electron spin and nuclear spin, γ e It is the electron spin gyromagnetic ratio, γ n It is the nuclear spin gyromagnetic ratio; Q is the electron spin slowing factor, and Be is the electron spin-sensing magnetic field. Represents the electron spin Fermi contact field. It is the electron spin polarizability, λM e It is a constant related to the atomic density of alkali metals. It is the transverse relaxation rate of electrons. It is an electron polarization magnetic field. It is a nuclear polarization magnetic field.

[0041] Step 2 includes: electron spin in left-handed circularly polarized light σ + Polarization occurs under the pumping action, and the nuclear spin is hyperpolarized through spin-exchange collisions with the electron spin. Step 3 includes: according to the precession frequency of the detected nuclear spin, the nuclear spin is deviated from the longitudinal direction by applying a magnetic field that resonates with the nuclear spin. After the nuclear spin deviates from the longitudinal direction, it leaves the resonant magnetic field. Step 4 includes: the nuclear spin undergoes Larmor precession under the combined action of the decoupling magnetic field and the electron spin Fermi contact field. The electron spin senses the magnetic field generated by the nuclear spin precession and rotates around the z-axis, generating transverse polarization of the electron spin. The incident linearly polarized light in the x-direction extracts the transverse polarization of the electron spin to generate the optical rotation angle of the linearly polarized light. The optical rotation angle information is extracted using the balanced difference method. Nuclear spin precession information for more than 10 cycles is collected. At this time, the left-handed circularly polarized light σ + Pump-induced nuclear spin precession frequency The expression is as follows:

[0042]

[0043] Step 5 includes: changing the rotation direction of the pump light in the z-direction, and converting the left-handed circularly polarized light σ... + Change to right-hand circularly polarized light σ - Electron spin polarization Contact field with Fermi Reverse the direction and measure the nuclear spin precession frequency again; at this time, σ - Nuclear spin precession frequency under right-hand circularly polarized pump The expression is as follows:

[0044]

[0045] Step 6 includes: dividing the frequency difference between the two precessions by twice the nuclear spin gyromagnetic ratio to obtain the electron spin Fermi contact field. Fermi contact field Dividing by the fully polarized Fermi contact constant yields the electron spin polarizability. The formula is as follows:

[0046]

[0047]

[0048] The dynamic equations for Larmor precession of optically pumped electron spin polarization and nuclear spin hyperpolarization under an external magnetic field can be approximated by the following Bloch equations:

[0049]

[0050]

[0051] exist Figure 2 In a Cartesian coordinate system, the pump beam incident direction is parallel to the z-axis, and the probe beam incident direction is parallel to the x-axis; t is time; electron spin polarization. in The three coordinate axes represent the electronic spin polarization components, and the nuclear spin polarization... in The three coordinate axes represent the components of nuclear spin polarization; λM e P e For electron spin Fermi contact field; λM n P n For nuclear spin Fermi contact field; γ e It is the electron spin gyromagnetic ratio, γ n It is the nuclear spin gyromagnetic ratio; Q is the electron spin slowing factor; R p The pump rate of the pumping laser is given by the applied external magnetic field, B = [B]. x B y B z ] T B x B y B z The three coordinate axis components represent the applied external magnetic field; to describe the relaxation process of the longitudinal and transverse polarizability of atoms, the longitudinal relaxation rate of electron spin is introduced. Electron spin transverse relaxation rate nuclear spin longitudinal relaxation rate nuclear spin transverse relaxation rate The spin-exchange collision rate is the rate at which nuclear spin is transferred to electron spin. Let P be the spin-exchange collision rate from electron spin to nuclear spin. This equation describes the dynamic evolution of the electron-spin-nuclear spin coupling ensemble under optical pumping, atomic relaxation, and Larmor precession in a magnetic field. From equation (1), we can obtain that the nuclear spin P in the state of electron-spin coupling is... n Precession frequency Ω c for:

[0052]

[0053] Where ω e ω n a and b are real intermediate variables, and Sign[b] represents the sign of b.

[0054]

[0055]

[0056]

[0057] In the above formula The term represents the coupling effect between electron spin and nuclear spin. This coupling can be weakened by applying a z-axis decoupling magnetic field. When the decoupling magnetic field B... z When the nuclear spin is greater than 1 μT and less than 1 mT, the nuclear spin and electron spin are decoupled. In the decoupled state, the precession rate Ω of the nuclear spin... n for:

[0058]

[0059] From equation (4), it can be concluded that σ + Left-handed circularly polarized electron spin For the positive direction, the electron spin is controlled by σ. + Nuclear spin precession rate under optical polarization for:

[0060]

[0061] From equation (4), it can be concluded that σ - Right-handed circularly polarized electron spin For the opposite direction, the electron spin is reversed by σ. - Nuclear spin precession rate under optical polarization for:

[0062]

[0063] The Fermi contact field of electron spin can be obtained by the following equation:

[0064]

[0065] The polarizability of electron spin is:

[0066]

[0067] This method requires six steps to accurately determine the electron spin Fermi contact field and polarizability.

[0068] Step 1: Apply a DC magnetic field in the z-direction to decouple the electron spin from the nuclear spin.

[0069] Electron spin and nuclear spin exhibit a precession frequency coupling effect under a weak magnetic field, which affects the Larmor precession frequencies of both electron and nuclear spins. This decoupling magnetic field should be greater than 1 μT and less than 1 mT. The precession frequency Ω of the nuclear spin under this decoupling magnetic field is... n for

[0070]

[0071] Step 2: Apply σ in the z-direction + Left-handed circularly polarized pump-polarized electron spin and nuclear spin

[0072] Electron spin in σ + Polarization is generated under the pumping action of left-handed circularly polarized light, and nuclear spin is hyperpolarized through spin-exchange collisions with electron spin.

[0073] Step 3: Apply an alternating magnetic field in the x-axis that resonates with the nuclear spin, causing the nuclear spin to generate a transverse component.

[0074] To detect the precession frequency of nuclear spin, it is necessary to deflect the nuclear spin from its longitudinal direction. A magnetic field that resonates with the nuclear spin is applied, and the nuclear spin deflects from its longitudinal direction and then leaves the resonant magnetic field.

[0075] Step 4: Use electron spin as an in-situ magnetometer to measure the precession frequency of nuclear spin.

[0076] Nuclear spins undergo Larmor precession under the combined influence of the decoupling magnetic field and the electron spin Fermi contact field. The electron spin senses the magnetic field generated by the nuclear spin precession and rotates around the z-axis, resulting in transverse electron spin polarization. The incident linearly polarized light in the x-direction is used to extract the optical rotation angle of the linearly polarized light, and this angle is extracted using a balanced difference method. Nuclear spin precession information for more than 10 cycles is collected. At this point, σ... + The nuclear spin precession frequency under right-handed circularly polarized pumping is:

[0077]

[0078] Step 5: Change the rotation direction of the pump light in the z-direction to σ. - Right-handed circular polarization, nuclear spin precession frequency measured again.

[0079] Change the rotation direction of the pump light in the z-direction to σ. - With right-handed circular polarization, the electron spin polarizability is opposite to that of the Fermi contact field; the nuclear spin precession frequency is measured again. At this point, σ... - The nuclear spin precession frequency under right-handed circularly polarized pumping is:

[0080]

[0081] Step Six: Calculate the Fermi contact field and polarizability of the electron spin using the frequency difference between the two measurements.

[0082] Dividing the frequency difference between the two precessions by twice the nuclear spin gyromagnetic ratio yields the Fermi contact field of the electron spin. Dividing this Fermi contact field by the fully polarized Fermi contact constant yields the polarizability of the electron spin.

[0083] The Fermi contact field of electron spin can be obtained by the following equation:

[0084]

[0085] The polarizability of electron spin is:

[0086]

[0087] A magnetic field is applied in the z-axis to decouple electron spin from nuclear spin, thus constructing a nuclear spin-based magnetometer. The Fermi contact field measurement of electron spin is converted into a measurement of the precession frequency of nuclear spin using a method of reversing electron spin polarization. The electron spin Fermi contact field is then divided by the fully polarized Fermi contact constant to obtain the electron spin polarizability, which is more accurate than traditional measurement methods.

[0088] Contents not described in detail in this specification are prior art known to those skilled in the art. It is hereby indicated that the above description is intended to help those skilled in the art understand this invention, but does not limit the scope of protection of this invention. Any equivalent substitutions, modifications, improvements, and / or simplifications of the above descriptions that do not depart from the essential content of this invention fall within the scope of protection of this invention.

Claims

1. A method for accurate determination of the electron spin fermi contact field and the polarizability of an electron spin, characterized in that, The method comprises the following steps: Step 1, applying a direct current magnetic field in the z direction to decouple the electron spin from the nuclear spin; Step 2, applying left-handed circularly polarized pumping light in the z direction to polarize the electron spin and the nuclear spin; Step 3, applying an alternating current magnetic field in the x direction which resonates with the nuclear spin to make the nuclear spin produce a transverse component; Step 4, measuring the precession frequency of the nuclear spin by taking the electron spin as an in-situ magnetometer; Step 5, changing the handedness of the pumping light in the z direction to right-handed circular polarization, and measuring the precession frequency of the nuclear spin again; Step 6, calculating the Fermi contact field and the polarizability of the electron spin by the frequency difference of the two measurements; The step 1 includes: according to the effect of precession frequency coupling of electron spin and nuclear spin under weak magnetic field, the effect will affect the Larmor precession frequency of electron spin and nuclear spin, set 1uT≤Bz≤1mT, wherein Bz is the z direction applied direct current magnetic field, that is, the decoupling magnetic field, under the decoupling magnetic field, the precession frequency of nuclear spin Ω n The expression is as follows: where ω e , ω n , a and b are real intermediate variables, and Sign[b] represents the sign of b, represents the coupling effect between electron spin and nuclear spin, γ e is the electron spin gyromagnetic ratio, γ n is the nuclear spin gyromagnetic ratio; Q is the electron spin slowing-down factor, Be is the electron spin experienced magnetic field, represents the electron spin Fermi contact field, is the electron spin polarizability, λM e is a constant related to the alkali metal atom density, is the electron transverse relaxation rate, is the electron polarizing magnetic field, is the nuclear polarizing magnetic field.

2. The method of precise measurement of the electron spin fermi contact field and polarizability according to claim 1, characterized in that, The step 2 includes: the electronic spin is polarized under the pumping of left circularly polarized light σ + , and the nuclear spin is hyperpolarized through the spin exchange collision of the electronic spin.

3. The method of precise measurement of the electron spin fermi contact field and polarizability according to claim 2, characterized in that, The step 3 comprises the following steps: according to the need of detecting the precession frequency of the nuclear spin, making the nuclear spin deviate from the longitudinal direction by applying a magnetic field which resonates with the nuclear spin, and withdrawing the resonant magnetic field after the nuclear spin deviates from the longitudinal direction.

4. The method of precise measurement of the electron spin fermi contact field and polarizability according to claim 3, characterized in that, The step 4 includes: the nuclear spin makes Larmor precession under the joint action of the decoupling magnetic field and the electron spin Fermi contact field, the electron spin senses the magnetic field generated by the nuclear spin precession, rotates around the z axis to produce electron spin transverse polarization, the x direction incident linearly polarized light extracts the transverse polarization of the electron spin to produce the optical rotation angle of linearly polarized light, and the optical rotation angle information is extracted by using the balanced difference method, and the nuclear spin precession information of more than 10 cycles is collected, at this time, the left circularly polarized light σ + Nuclear spin precession frequency under pumping The expression is as follows:

5. The method of precise measurement of the electron spin fermi contact field and polarizability according to claim 4, characterized in that, The step 5 includes: changing the handedness of the z-direction pumping light, changing the left circularly polarized light σ + to the right circularly polarized light σ - , the electron spin polarization rate and the Fermi contact field , and then measuring the nuclear spin precession frequency again, at this time σ - the nuclear spin precession frequency under the right circularly polarized pumping The expression is as follows:

6. The method of precise measurement of the electron spin fermi contact field and polarizability according to claim 5, characterized in that, The step 6 includes: the frequency difference of two precessions divided by twice the nuclear spin gyromagnetic ratio, resulting in the electron spin Fermi contact field This Fermi contact field Divided by the fully polarized Fermi contact constant, resulting in the electron spin polarization The formula is as follows:

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