CN112683996B - Method for measuring spin-exchange relaxation rate based on SERF inertial measurement device - Google Patents
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- 238000005259 measurement Methods 0.000 title claims abstract description 43
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- 229910052783 alkali metal Inorganic materials 0.000 claims description 10
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- 238000005086 pumping Methods 0.000 claims description 4
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Abstract
A method for measuring spin-exchange relaxation rate based on SERF inertial measurement unit includes obtaining half-width of corresponding frequency response curve under different bias magnetic field conditions by fitting frequency response formula, calculating first total relaxation rate of incomplete SERF state and second total relaxation rate of complete SERF state by using relation between half-width and total relaxation rate, subtracting two total relaxation rates to obtain spin-exchange relaxation rate, providing basis for developing high-precision atomic spin inertial measurement unit.
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 a SERF inertia measurement device, which is used for obtaining half-width of corresponding frequency response curves under different bias magnetic field conditions through fitting of a frequency response formula, calculating a first total relaxation rate of an incomplete SERF state and a second total relaxation rate of a complete SERF state by using a relation between the half-width and the total relaxation rate, and subtracting the two total relaxation rates to obtain the spin-exchange relaxation rate, 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 developing the atomic spin inertia measurement device with high precision.
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 energy levels and cause relaxation, affecting polarization. Only if the relaxation caused by spin-exchange collisions is completely eliminated, the atomic inertial measurement unit can reach ultra-high sensitivity to slowly varying magnetic fields, such as those generated by earth or magnetic anomalies. Therefore, accurately measuring Spin-exchange relaxation rates that are not completely eliminated in a SERF inertial measurement unit is of great importance to improving the sensitivity of precision measurements (SERF is Spin-Exchange Relaxation-Free Spin-Free relaxation). Currently, the relaxation rate r= nsv is generally calculated by using a relaxation rate formula, where n is the density of a certain gas contained in the gas chamber, s is the effective collision cross section between an alkali metal and the gas, 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 a rough value can be calculated, and cannot be accurately measured in real time.
Disclosure of Invention
Aiming at the defects or shortcomings in the prior art, the invention provides a method for measuring spin-exchange relaxation rate based on a SERF inertial measurement device, which is used for obtaining half-width of corresponding frequency response curves under different bias magnetic field conditions through fitting a frequency response formula, calculating a first total relaxation rate of an incomplete SERF state and a second total relaxation rate of a complete SERF state by using a relation between the half-width and the total relaxation rate, and subtracting the two total relaxation rates to obtain the spin-exchange relaxation rate, thereby being beneficial to accurately measuring the spin-exchange relaxation rate which is not completely eliminated in the SERF inertial measurement device and providing a basis for developing a high-precision atomic spin inertial measurement device.
The technical scheme of the invention is as follows:
a method of measuring spin-exchange relaxation rate based on a SERF inertial measurement unit, comprising the steps of:
step 1, applying bias magnetic fields Bz with different magnitudes in the direction of the z axis of a gas chamber by using a SERF inertial measurement device, and measuring the frequency response Sx of the SERF inertial measurement device;
step 2, fitting by using a frequency response formula, and obtaining half-width at half-height delta omega of corresponding frequency response curves under different Bz conditions through fitting curves;
step 3, calculating a first Rtot in an incomplete SERF state and a second Rtot in a complete SERF state by using a relation between delta omega and a total relaxation rate Rtot;
step 4, calculating the spin-exchange relaxation rate Rrel according to the following formula: rrel = first Rtot-second Rtot.
Bz in the step 1 is respectively:or->Wherein->Magnetic field generated by inert gas nuclei in the gas chamber, ">A magnetic field generated by alkali metal electrons in the gas cell; in the first case, the external magnetic field felt by the electrons is +.>In this case, not in the complete SERF state, there is a spin-exchange relaxation rate R rel Not equal to 0, first R tot ＝R OP +R SD +R rel The method comprises the steps of carrying out a first treatment on the surface of the In the second case, the external magnetic field sensed by electrons is b=0, and is in the complete SERF state, R rel =0, second R tot ＝R OP +R SD Wherein R is OP For pumping rate, R SD For spin destruction, two conditionsAnd subtracting the total relaxation rate under the condition to obtain the spin-exchange relaxation rate Rrel.
The Sx measurement in the step 1 adopts the following mode: applying a magnetic field in the y-axis direction of the air cellWherein B 'is a magnetic field vector, B' is an intrinsic quantity of a magnetic field applied in the y-axis direction of the air chamber, ω is a frequency of an applied electric signal, t is time,/->Is a y-axis unit vector.
The frequency response formula in the step 2 is as follows:
wherein S is 0 In order to balance the spin polarizability of electrons,γ e is the gyromagnetic ratio of electrons, I is the nuclear spin of atoms, and different B are obtained by fitting curves z Corresponding to half-width at half-width deltaomega of the frequency response curve under the condition.
Obtained by fitting a curveFirst Δω below, and ∈ ->A second Δω below.
The relation between Δω and the total relaxation rate Rtot in the step 3 is as follows: Δω=r tot Q, wherein Q is the slow down factor of the alkali metal.
The first Rtot is obtained by the first Δω, and the second Rtot is obtained by the second Δω.
The invention has the following technical effects: the method for measuring the spin-exchange relaxation rate based on the SERF inertial measurement device is reasonable, the experimental operation is simple, the spin-exchange relaxation rate which is not completely eliminated in the SERF inertial measurement device can be accurately measured, and a foundation is provided for the development of the high-precision atomic spin inertial measurement device.
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, half-width at half-height values of a frequency response curve are obtained, different total relaxation rates are obtained by using different half-width at half-height values, and the spin-exchange relaxation rate can be obtained through the difference value between the different total relaxation rates. (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 measuring 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 embodying the present invention. The following steps are included in fig. 1: step 1, applying bias magnetic fields with different magnitudes, and measuring frequency response (for example, using a SERF inertial measurement device, applying bias magnetic fields Bz with different magnitudes in the z-axis direction of a gas chamber of the SERF inertial measurement device, and measuring frequency response Sx of the SERF inertial measurement device); step 2, fitting to obtain half-width at half-height of the frequency response curve (for example, fitting by using a frequency response formula to obtain half-width at half-width delta omega of the corresponding frequency response curve under different Bz conditions); step 3, the corresponding total relaxation rate is calculated (e.g.,first Rtot, < ->A second Rtot of the total relaxation rate of (2); step 4, a spin-exchange relaxation rate (e.g., first Rtot-second rtot=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 embodying the present invention. Referring to fig. 1, a method for measuring spin-exchange relaxation rate based on a SERF inertial measurement unit, comprising the steps of: step 1, applying bias magnetic fields Bz with different magnitudes in the direction of the z axis of a gas chamber by using a SERF inertial measurement device, and measuring the frequency response Sx of the SERF inertial measurement device; step 2, fitting by using a frequency response formula, and obtaining half-width at half-height delta omega of corresponding frequency response curves under different Bz conditions through fitting curves; step 3, calculating a first Rtot in an incomplete SERF state and a second Rtot in a complete SERF state by using a relation between delta omega and a total relaxation rate Rtot; step 4, calculating the spin-exchange relaxation rate Rrel according to the following formula: rrel = first Rtot-second Rtot.
Bz in the step 1 is respectively:or->Wherein->Magnetic field generated by inert gas nuclei in the gas chamber, ">In the first case, the external magnetic field sensed by the electrons is +.>At this time do notIs in a complete SERF state, with spin-exchange relaxation rate R rel Not equal to 0, first R tot ＝R OP +R SD +R rel The method comprises the steps of carrying out a first treatment on the surface of the In the second case, the external magnetic field sensed by electrons is b=0, and is in the complete SERF state, R rel =0, second R tot ＝R OP +R SD Wherein R is OP For pumping rate, R SD The spin-exchange relaxation rate Rrel can be obtained by subtracting the total relaxation rates in both cases from the spin-destruction rate. The Sx measurement in the step 1 adopts the following mode: applying a magnetic field in the y-axis direction of the 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 air chamber, ω is a frequency of an applied electric signal, t is time,/->Is a y-axis unit vector. The frequency response formula in the step 2 is as follows:
wherein S is 0 In order to balance the spin polarizability of electrons,γ e is the gyromagnetic ratio of electrons, I is the nuclear spin of atoms, and different B are obtained by fitting curves z Corresponding to half-width at half-width deltaomega of the frequency response curve under the condition. Obtained by fitting a curveFirst Δω below, and ∈ ->A second Δω below. The relation between Δω and the total relaxation rate Rtot in the step 3 is as follows: Δω=r tot Q, wherein Q is the slow down factor of the alkali metal.The first Rtot is obtained by the first Δω, and the second Rtot is obtained by the second Δω.
The invention relates to a measuring method of spin-exchange relaxation rate based on a SERF inertial measurement device, which can accurately measure the spin-exchange relaxation rate which is not completely eliminated in the SERF inertial measurement device. The method is implemented by applying different bias magnetic fields B z Measuring the frequency response S of an inertial measurement unit x The corresponding total relaxation rate R is calculated by fitting a formula and calculating the half-width at half-maximum delta omega of the frequency response curve tot By using the total relaxation rate R under different conditions tot To obtain the spin-exchange relaxation rate R rel . The method is reasonable, the experimental operation is simple, the spin-exchange relaxation rate which is not completely eliminated in the SERF inertial measurement device can be accurately measured, and a foundation is provided for the development of the high-precision atomic spin inertial measurement device.
A method for measuring spin-exchange relaxation rate based on a SERF inertial measurement unit, characterized by: the method comprises the following steps:
step (1): applying bias magnetic fields B with different magnitudes in z direction z Measuring the frequency response S of a high-precision atomic spin inertial measurement unit x 。
Step (2): according to the frequency response S obtained in step (1) x Fitting according to a frequency response formula, wherein the half-width at half-maximum delta omega of the frequency response curve is obtained.
Step (3): according to the half-width at half-maximum Deltaω obtained in step (2), the corresponding total relaxation rate R tot 。
Step (4): according to the total relaxation rate R obtained in the step (3) tot Calculating spin-exchange relaxation rate R rel 。
The bias magnetic fields B with different magnitudes in the step (1) z Respectively isOr->Wherein->Magnetic field generated for inert gas nuclei, +.>A magnetic field generated for alkali metal electrons. In the first case, the external magnetic field felt by the electrons is +.>In this case, not in the complete SERF state, there is a spin-exchange relaxation rate R rel ≠0，R tot ＝R OP +R SD +R rel . In the second case, the external magnetic field sensed by electrons is b=0, and is in the SERF state, R rel ＝0，R tot ＝R OP +R SD Wherein R is OP For pumping rate, R SD The spin-exchange relaxation rate can be obtained by subtracting the total relaxation rate in the two cases.
In the step (1), one is applied in the y directionThe magnetic field, ω, is varied and the system frequency response is measured.
The frequency response fitting formula in the step (2) is as follows:
wherein S is 0 In order to balance the spin polarizability of electrons,γ e is the gyromagnetic ratio of electrons, I is the nuclear spin of atoms, and different B are obtained by fitting curves z The half-width at half-height delta omega of the corresponding frequency response curve under the condition.
The half-width at half-maximum delta omega and the total relaxation rate R of the intermediate frequency curve in the step (3) tot The relation of (2) is as follows:
Δω＝R tot /Q，
wherein Q is the slowing factor of the alkali metal.
The step (3) is performedAnd->The corresponding total relaxation rate R in both cases tot R in both cases tot By subtracting, the spin-exchange relaxation rate R is obtained rel . According to the method, the bias magnetic field is applied to measure the precession frequency of the alkali metal atoms under different bias magnetic fields, so that compared with the existing method, external influence factors are reduced, the polarization of the atoms is not damaged, and the instantaneity and the accuracy are ensured. The method is reasonable, the experimental operation is simple, and a foundation is provided for the development of a high-precision atomic spin inertia measuring device.
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 (3)
1. A method of measuring spin-exchange relaxation rate based on a SERF inertial measurement unit, comprising the steps of:
step 1, applying bias magnetic fields Bz with different magnitudes in the direction of the z axis of a gas chamber by using a SERF inertial measurement device, and measuring the frequency response Sx of the SERF inertial measurement device;
step 2, fitting by using a frequency response formula, and obtaining half-width at half-height delta omega of corresponding frequency response curves under different Bz conditions through fitting curves;
step 3, calculating a first Rtot in an incomplete SERF state and a second Rtot in a complete SERF state by using a relation between delta omega and a total relaxation rate Rtot;
step 4, calculating the spin-exchange relaxation rate Rrel according to the following formula: rrel = first Rtot-second Rtot;
bz in the step 1 is respectively:or->Wherein->Magnetic field generated by inert gas nuclei in the gas chamber, ">A magnetic field generated by alkali metal electrons in the gas cell; in the first case, the external magnetic field felt by the electrons is +.>In this case, not in the complete SERF state, there is a spin-exchange relaxation rate R rel Not equal to 0, first R tot ＝R OP +R SD +R rel The method comprises the steps of carrying out a first treatment on the surface of the In the second case, the external magnetic field sensed by electrons is b=0, and is in the complete SERF state, R rel =0, second R tot ＝R OP +R SD Wherein R is OP For pumping rate, R SD The spin-exchange relaxation rate Rrel can be obtained by subtracting the total relaxation rates under the two conditions;
the Sx measurement in the step 1 adopts the following mode: applying a magnetic field in the y-axis direction of the air cellThe left side B 'of the medium-sized sign is a magnetic field vector, the right side B' of the medium-sized sign is the intrinsic quantity of the magnetic field applied in the y-axis direction of the air chamber, omega is the frequency of the applied electric signal, t is time, and>is a y-axis unit vector;
the frequency response formula in the step 2 is as follows:
wherein S is 0 In order to balance the spin polarizability of electrons,γ e is the gyromagnetic ratio of electrons, I is the nuclear spin of atoms, and different R's are obtained through fitting curves z Half-width at half-height delta omega of corresponding frequency response curve under condition 0 Is the alkali metal atom precession frequency;
the relation between Δω and the total relaxation rate Rtot in the step 3 is as follows: Δω=r tot Q, wherein Q is the slow down factor of the alkali metal.
2. The method for measuring spin-exchange relaxation rate based on SERF inertial measurement unit according to claim 1, wherein the spin-exchange relaxation rate is obtained by fitting a curveFirst Δω below, and ∈ ->A second Δω below.
3. A method of measuring spin-exchange relaxation rate based on a SERF inertial measurement unit according to claim 2, characterized in that a first Rtot is obtained with a first Δω and a second Rtot is obtained with a second Δω.
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