CN112683996A - Method for measuring spin exchange relaxation rate based on SERF inertia measurement device - Google Patents
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- 238000005259 measurement Methods 0.000 title claims description 33
- 238000000034 method Methods 0.000 title claims description 25
- 239000007789 gas Substances 0.000 claims description 17
- 150000001340 alkali metals Chemical class 0.000 claims description 13
- 229910052783 alkali metal Inorganic materials 0.000 claims description 10
- 239000011261 inert gas Substances 0.000 claims description 4
- 238000005086 pumping Methods 0.000 claims description 4
- 230000010287 polarization Effects 0.000 description 3
- 230000035945 sensitivity Effects 0.000 description 2
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Abstract
A half-height half-width of a corresponding frequency response curve under different bias magnetic field conditions is obtained through fitting of a frequency response formula, a first total relaxation rate of an incomplete SERF state and a second total relaxation rate of a complete SERF state are calculated by utilizing a relation between the half-height half-width and the total relaxation rates, and the two total relaxation rates are subtracted to obtain the spin exchange relaxation rate.
Description
Technical Field
The invention relates to the field of atomic spin inertia measurement devices, in particular to a method for measuring spin exchange relaxation rate based on an SERF inertia measurement device.
Background
Because the atoms in the two hyperfine energy levels precess in opposite directions, spin-exchange collisions redistribute the alkali metal atoms between the ground-state zeeman sublevels and cause relaxation, affecting polarization. Only by completely eliminating the relaxation caused by spin-exchange collisions can the atomic inertia measurement device achieve ultra-high sensitivity to slowly varying magnetic fields, such as those generated by the earth or magnetic anomalies. Therefore, accurate measurement of the Spin-Exchange Relaxation rate that is not completely eliminated in the SERF inertial measurement unit is of great importance to improve the sensitivity of precision measurements (SERF is Spin-Exchange Relaxation-Free). It is now common to calculate the relaxation rate R-nsv using the formula of relaxation rate, where n is the density of a certain gas contained in a gas chamber, s is the effective collision cross section between an alkali metal and the gas, and v is the relative thermal velocity between the alkali metal and the gas, and the accuracy of calculation is limited by the accuracy of density measurement, only an approximate value can be calculated, and accurate measurement in real time cannot be achieved.
Disclosure of Invention
Aiming at the defects or shortcomings of the prior art, the invention provides a method for measuring spin exchange relaxation rate based on a SERF inertia measurement device, which obtains the half-height half-width of the corresponding frequency response curve under different bias magnetic field conditions through frequency response formula fitting, calculates the first total relaxation rate of an incomplete SERF state and the second total relaxation rate of a complete SERF state by using a relational expression between the half-height half-width and the total relaxation rates, and obtains the spin exchange relaxation rate by subtracting the two total relaxation rates, thereby being beneficial to accurately measuring the spin exchange relaxation rate which is not completely eliminated in the SERF inertia measurement device and providing a foundation for the development of a high-precision atomic spin inertia measurement device.
The technical solution of the invention is as follows:
a method for measuring spin exchange relaxation rate based on SERF inertia measurement device is characterized by comprising the following steps:
step 1, applying bias magnetic fields Bz with different sizes in the z-axis direction of a gas chamber of an SERF inertia measuring device, and measuring the frequency response Sx of the SERF inertia measuring device;
step 2, fitting by using a frequency response formula, and obtaining half-height half-width delta omega of corresponding frequency response curves under different Bz conditions through fitting curves;
step 3, calculating a first Rtot of the incomplete SERF state and a second Rtot of the complete SERF state by utilizing a relational expression between the delta omega and the total relaxation rate Rtot;
step 4, calculating the spin exchange relaxation rate Rrel according to the following formula: rrel-first Rtot-second Rtot.
The Bz in the step 1 is respectively as follows:
and
wherein
A magnetic field generated by inert gas nuclei in the gas chamber,
a magnetic field generated by electrons of alkali metal in the gas chamber, in the first case, the external magnetic field sensed by the electrons is
Now not a complete SERF state, there is a spin-exchange relaxation rate RrelNot equal to 0, first Rtot＝ROP+RSD+Rrel(ii) a Second caseIn this case, the external magnetic field sensed by the electron is B ═ 0, which is the complete SERF state, Rrel0, second Rtot＝ROP+RSDWherein R isOPFor pumping power, RSDThe total relaxation rates under the two conditions are subtracted to obtain the spin exchange relaxation rate Rrel.
The Sx measurement in the step 1 adopts the following mode: applying magnetic field in y-axis direction of air chamber
Wherein B 'is a magnetic field vector, B' is an intrinsic quantity of a magnetic field applied in the y-axis direction of the gas chamber, omega is the frequency of an applied electric signal, t is time,
is a y-axis unit vector.
The frequency response formula in step 2 is as follows:
in the formula, S0In order to balance the electron spin polarizability,
γeis the gyromagnetic ratio of electrons, I is the nuclear spin of atoms, and different B are obtained by fitting a curvezUnder the condition, the half-height and half-width delta omega of the corresponding frequency response curve.
By fitting a curve to obtain
A first Δ ω of, and
second Δ ω below.
The relation between Δ ω and the total relaxation rate Rtot in step 3 is as follows: Δ ω ═ Rtotand/Q, wherein Q is the slowing factor for alkali metals.
The first Rtot is obtained by using the first Δ ω, and the second Rtot is obtained by using the second Δ ω.
The invention has the following technical effects: the invention relates to a method for measuring spin exchange relaxation rate based on a SERF inertia measurement device, which obtains the half-height half-width of a corresponding frequency response curve under different bias magnetic field conditions through frequency response formula fitting, calculates the first total relaxation rate of an incomplete SERF state and the second total relaxation rate of a complete SERF state by utilizing a relation between the half-height half-width and the total relaxation rates, and obtains the spin exchange relaxation rate by subtracting the two total relaxation rates.
Compared with the prior art, the invention has the advantages that: (1) according to the method, the bias magnetic field is applied, the precession frequency of the alkali metal atoms under different bias magnetic fields is measured, fitting is carried out according to a frequency response formula, the half-height half-width value of a frequency response curve is obtained, different total relaxivity is obtained by utilizing different half-height half-width values, the spin exchange relaxivity can be obtained through the difference value between different total relaxivity, compared with the existing method, external influence factors are reduced, the polarization of the atoms cannot be damaged, and meanwhile the instantaneity and the accuracy are guaranteed. (2) The method is reasonable, the experimental operation is simple, and a foundation is provided for the development of a high-precision atomic spin inertia measurement device.
Drawings
Fig. 1 is a schematic flow chart of a method for measuring spin-exchange relaxation rate based on a SERF inertial measurement unit. Fig. 1 includes the following steps: step 1, applying bias magnetic fields with different sizes, and measuring frequency response (for example, applying bias magnetic fields Bz with different sizes in the z-axis direction of a gas chamber of an SERF inertia measuring device by using the SERF inertia measuring device, and measuring the frequency response Sx of the SERF inertia measuring device); step 2, fitting to obtain the half-width at half maximum of the frequency response curve (for example, fitting by using a frequency response formula to obtain the half-width at half maximum Δ ω of the corresponding frequency response curve under different Bz conditions); step 3, calculate the corresponding total relaxation rate (e.g.,
the first Rtot of the total relaxation rate of,
second Rtot) of the total relaxation rate; step 4, a spin-exchange relaxation rate (for example, the first Rtot — the second Rtot ═ the spin-exchange relaxation rate Rrel) is calculated.
Detailed Description
The invention is described below with reference to the accompanying drawings (fig. 1) and examples.
Fig. 1 is a schematic flow chart of a method for measuring spin-exchange relaxation rate based on a SERF inertial measurement unit. Referring to fig. 1, a method for measuring spin-exchange relaxation rate based on a SERF inertial measurement unit is characterized by comprising the following steps: step 1, applying bias magnetic fields Bz with different sizes in the z-axis direction of a gas chamber of an SERF inertia measuring device, and measuring the frequency response Sx of the SERF inertia measuring device; step 2, fitting by using a frequency response formula, and obtaining half-height half-width delta omega of corresponding frequency response curves under different Bz conditions through fitting curves; step 3, calculating a first Rtot of the incomplete SERF state and a second Rtot of the complete SERF state by utilizing a relational expression between the delta omega and the total relaxation rate Rtot; step 4, calculating the spin exchange relaxation rate Rrel according to the following formula: rrel-first Rtot-second Rtot.
The Bz in the step 1 is respectively as follows:
and
wherein
A magnetic field generated by inert gas nuclei in the gas chamber,
for producing electrons of alkali metals in gas chambersA magnetic field generated, in the first case, by electrons, by an external magnetic field
Now not a complete SERF state, there is a spin-exchange relaxation rate RrelNot equal to 0, first Rtot＝ROP+RSD+Rrel(ii) a In the second case, the external magnetic field experienced by the electron is B ═ 0, which is the complete SERF state, Rrel0, second Rtot＝ROP+RSDWherein R isOPFor pumping power, RSDThe total relaxation rates under the two conditions are subtracted to obtain the spin exchange relaxation rate Rrel. The Sx measurement in the step 1 adopts the following mode: applying magnetic field in y-axis direction of air chamber
Wherein B 'is a magnetic field vector, B' is an intrinsic quantity of a magnetic field applied in the y-axis direction of the gas chamber, omega is the frequency of an applied electric signal, t is time,
is a y-axis unit vector. The frequency response formula in step 2 is as follows:
in the formula, S0In order to balance the electron spin polarizability,
γeis the gyromagnetic ratio of electrons, I is the nuclear spin of atoms, and different B are obtained by fitting a curvezUnder the condition, the half-height and half-width delta omega of the corresponding frequency response curve. By fitting a curve to obtain
A first Δ ω of, and
second Δ ω below. The relation between Δ ω and the total relaxation rate Rtot in step 3 is as follows: Δ ω ═ Rtotand/Q, wherein Q is the slowing factor for alkali metals. The first Rtot is obtained by using the first Δ ω, and the second Rtot is obtained by using the second Δ ω.
The invention relates to a spin exchange relaxation rate measuring method based on a SERF inertia measuring device, which can accurately measure the spin exchange relaxation rate which is not completely eliminated in the SERF inertia measuring device. The method is realized by applying different bias magnetic fields BzMeasuring the frequency response S of the inertial measurement unitxCalculating the corresponding total relaxation rate R through formula fitting and half-height and half-width delta omega of the frequency response curvetotUsing the total relaxation rate R under different conditionstotObtaining the spin exchange relaxation rate R from the differencerel. The method is reasonable, the experimental operation is simple, the spin exchange relaxation rate which is not completely eliminated in the SERF inertia measurement device can be accurately measured, and a foundation is provided for the development of a high-precision atomic spin inertia measurement device.
A method for measuring spin exchange relaxation rate based on SERF inertia measurement device is characterized in that: the method comprises the following steps:
step (1): applying bias magnetic field B of different magnitudes in Z directionzMeasuring the frequency response S of a high-precision atomic spin inertia measuring apparatusx。
Step (2): according to the frequency response S obtained in the step (1)xFitting is carried out according to a frequency response formula, and the half height and half width delta omega of a frequency response curve.
And (3): according to the half-height half-width delta omega obtained in the step (2), the corresponding total relaxation rate Rtot。
And (4): according to the total relaxation rate R obtained in the step (3)totCalculating the spin exchange relaxation rate Rrel。
Bias magnetic field B with different magnitudes in the step (1)zAre respectively as
And
wherein
The magnetic field generated for the inert gas nuclei,
a magnetic field generated for alkali metal electrons. In the first case, the electron experiences an external magnetic field of
Now not a complete SERF state, there is a spin-exchange relaxation rate Rrel≠0，Rtot＝ROP+RSD+Rrel. In the second case, the external magnetic field sensed by the electron is B ═ 0, which is the SERF state, Rrel＝0，Rtot＝ROP+RSDWherein R isOPFor pumping power, RSDThe total relaxation rates in the two cases are subtracted to obtain the spin exchange relaxation rate.
In the step (1), one is applied in the y direction
The magnetic field, changing ω, measures the system frequency response.
The frequency response fitting formula in the step (2) is as follows:
wherein S is0In order to balance the electron spin polarizability,
γeis the gyromagnetic ratio of electrons, I is the nuclear spin of atoms, and different B are obtained by fitting a curvezThe half-height and half-width of the corresponding frequency response curve under the condition delta omega.
The half-height half-width Delta omega and the total relaxation rate R of the frequency response curve in the step (3)totThe relationship of (A) is as follows:
Δω＝Rtot/Q，
wherein Q is the slowing factor for alkali metals.
In the step (3), the
And
total relaxation rate R corresponding to each of the two casestotR in both casestotBy subtraction, the spin-exchange relaxation rate R is obtainedrel. The invention measures the precession frequency of the alkali metal atoms under different bias magnetic fields by applying the bias magnetic field, reduces external influence factors compared with the prior method, cannot damage the polarization of the atoms, and simultaneously ensures real-time property and accuracy. The method is reasonable, the experimental operation is simple, and a foundation is provided for the development of a high-precision atomic spin inertia measurement device.
Those skilled in the art will appreciate that the invention may be practiced without these specific details. It is pointed out here that the above description is helpful for the person skilled in the art to understand the invention, but does not limit the scope of protection of the invention. Any such equivalents, modifications and/or omissions as may be made without departing from the spirit and scope of the invention may be resorted to.
Claims (7)
1. A method for measuring spin exchange relaxation rate based on SERF inertia measurement device is characterized by comprising the following steps:
step 1, applying bias magnetic fields Bz with different sizes in the z-axis direction of a gas chamber of an SERF inertia measuring device, and measuring the frequency response Sx of the SERF inertia measuring device;
step 2, fitting by using a frequency response formula, and obtaining half-height half-width delta omega of corresponding frequency response curves under different Bz conditions through fitting curves;
step 3, calculating a first Rtot of the incomplete SERF state and a second Rtot of the complete SERF state by utilizing a relational expression between the delta omega and the total relaxation rate Rtot;
step 4, calculating the spin exchange relaxation rate Rrel according to the following formula: rrel-first Rtot-second Rtot.
2. The SERF inertial measurement unit-based method for measuring spin-exchange relaxation rate according to claim 1, wherein Bz in step 1 is respectively:
and
wherein
A magnetic field generated by inert gas nuclei in the gas chamber,
a magnetic field generated by electrons of alkali metal in the gas chamber, in the first case, the external magnetic field sensed by the electrons is
Now not a complete SERF state, there is a spin-exchange relaxation rate RrelNot equal to 0, first Rtot＝ROP+RSD+Rrel(ii) a In the second case, the external magnetic field experienced by the electron is B ═ 0, which is the complete SERF state, Rrel0, second Rtot＝ROP+RSDWherein R isOPFor pumping power, RSDThe total relaxation rates under the two conditions are subtracted to obtain the spin exchange relaxation rate Rrel.
3. SERF inertial measurement unit-based according to claim 1Method for measuring the spin-exchange relaxation rate, characterized in that the measurement of Sx in step 1 is performed in the following way: applying magnetic field in y-axis direction of air chamber
Wherein B 'is a magnetic field vector, B' is an intrinsic quantity of a magnetic field applied in the y-axis direction of the gas chamber, omega is the frequency of an applied electric signal, t is time,
is a y-axis unit vector.
4. The SERF inertial measurement unit-based method for measuring spin-exchange relaxation rate according to claim 1, wherein the frequency response formula in step 2 is as follows:
in the formula, S0In order to balance the electron spin polarizability,
γeis the gyromagnetic ratio of electrons, I is the nuclear spin of atoms, and different B are obtained by fitting a curvezUnder the condition, the half-height and half-width delta omega of the corresponding frequency response curve.
5. The SERF inertial measurement unit-based method for measuring spin-exchange relaxation rate according to claim 4, wherein the fitting curve is used to obtain
A first Δ ω of, and
second Δ ω below.
6. The SERF inertial measurement unit-based method for measuring spin-exchange relaxation rate according to claim 5, wherein the relation between Δ ω and the total relaxation rate Rtot in step 3 is as follows: Δ ω ═ Rtotand/Q, wherein Q is the slowing factor for alkali metals.
7. The SERF inertial measurement unit-based method for measuring spin-exchange relaxation rate according to claim 6, characterized in that the first Rtot is obtained with a first Δ ω and the second Rtot is obtained with a second Δ ω.
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