CN116859305A - Relaxation time measurement method of Rb-Xe spin exchange system based on dark state sweep frequency method - Google Patents
Relaxation time measurement method of Rb-Xe spin exchange system based on dark state sweep frequency method Download PDFInfo
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Abstract
The invention discloses a relaxation time measuring method of an Rb-Xe spin exchange system based on a dark state sweep frequency method, which relates to the technical field of Rb-Xe spin exchange systems and has the technical scheme that: at the position of 87 Rb‑ 129 In the case of the Xe spin-exchange system, 87 rb and Rb 129 Accurate measurement of Xe relaxation time is important for magnetic resonance gyro and magnetometer related applications. In response to this requirement, the pump light and excitation magnetic field pair was analyzed 87 Influence of Rb relaxation time in dark state 87 Rb and Rb 129 Xe spin exchange process and provides a dark state sweep frequency measurement method based on theoretical analysis. Realize the alignment of 87 Rb and Rb 129 Measurement of longitudinal relaxation time of Xe. Compared with the previous measuring method, the dark state sweep method can thoroughly eliminate the pump lightThe influence of the magnetic field gradient sensor has the advantage of high accuracy and is simple and convenient to operate. The invention has higher reference value for the performance analysis and calibration of the magnetic resonance gyroscope and the magnetometer.
Description
Technical Field
The invention relates to the technical field of Rb-Xe spin exchange systems, in particular to a relaxation time measuring method of an Rb-Xe spin exchange system based on a dark state sweep method.
Background
87 Rb- 129 The Xe spin-exchange system is widely applied to the precise measurement fields such as weak magnetic detection and nuclear magnetic resonance gyroscopes. Accurate measurement of parameters in the system is important for prototype performance analysis, e.g 87 Measurement of Rb and relaxation time is an important basis for evaluating the ultimate performance of magnetometers and nuclear magnetic resonance gyroscopes. For the following 87 Rb and Rb 129 Xe has a relaxation time divided into a transverse relaxation time T 2 And longitudinal relaxation time T 1 Wherein T is 1 The measurement ratio T of (2) 2 The measurement of (2) is more reflective of the characteristics of the system and, therefore, how to measure 87 Rb and Rb 129 Longitudinal relaxation time T of Xe 1 Is always an important issue in this field.
Currently, for 87 The main methods of Rb relaxation time measurement are optical pulse method and spin noise method. Wherein the optical pulse method uses pumping light with the duration of microsecond magnitude and detection light to alternately irradiate the air chamber, and the change of the detection light intensity is reflected 87 Polarization and coherence of Rb atoms, thus measuring 87 Longitudinal and transverse relaxation times of Rb. For example, franzen proposed "dark state relaxation" in 1959, modified multiple times for measurement 87 The relaxation time of Rb, the ODSE method proposed by M Gharavipour et al on this basis can also be used for measuring 87 Relaxation time of Rb. On the one hand, the optical pulse method requires accurate control of the duration time and the interval of the pumping light and the detection light in the experimental process, so that the method has higher requirements on test equipment such as a laser light source, a photoelectric detector and the like. On the other hand, the optical pulse method alternately turns on and off the pump light, and thus cannot completely eliminate the influence of the pump light on the system state. The spin noise law is utilized 87 Rb spin noise spectra to calculate its relaxation time, e.g., G.E. Katsoprinakis et al prepared the air cell to near SERF state and then fitted with the line width of the spin noise spectra to obtain 87 Relaxation information of Rb. However, this method requires a high level of air space, and in the near-SERF state, 87 the relaxation time of Rb varies with the magnitude of the external magnetic field, so this approach is difficult to meet the relaxation time test requirements in magnetometers or nuclear magnetic resonance gyroscopes operating at larger magnetic fields.
129 The relaxation time measurement method of Xe mainly includes an inversion recovery method and an exponential fitting method. Wherein the principle of the inversion recovery method is to use pi pulse to make 129 The polarization direction of Xe is reversed in 129 Applying pi/2 pulses during the return of the polarization direction of Xe to the thermal equilibrium state, measured perpendicular to the main magnetic field 129 The polarization of Xe is obtained by adjusting the time interval between pi pulses and pi/2 pulses 129 Relaxation time information of Xe. Although the inversion recovery method is simple to operate, it is often necessary to let 129 The polarization of Xe is reversed several times and is therefore very time-consuming.
The exponential fitting rule is to apply a high-frequency excitation field in the direction of the z-axis of the main magnetic field so that it can be applied in 129 Direct monitoring of Xe relaxation process 129 The variation of the polarization magnitude of Xe can thus be obtained in a single relaxation process 129 Relaxation information of Xe. However, when the method is used for demodulating the signals on the x axis and the y axis, the phase of the signals needs to be continuously adjusted, so that the measuring and signal processing processes are complex.
Aiming at the technical problems, the applicant invents a relaxation time measuring method of an Rb-Xe spin exchange system based on a dark state sweep method.
Disclosure of Invention
The invention aims to provide a relaxation time measuring method of an Rb-Xe spin exchange system based on a dark state sweep frequency method, which is used for measuring compared with the traditional measuring method 87 Rb and Rb 129 The effect of pump light can be completely stripped when Xe relaxes, thereby eliminating the measurement caused by XeError, simple signal processing process and relatively simple operation.
The technical aim of the invention is realized by the following technical scheme: the relaxation time measuring method of the Rb-Xe spin exchange system based on the dark state sweep frequency method specifically comprises the following steps:
s1: establishing a Bloch equation and solving the Bloch equation to obtain:
s2: measurement of 87 Transverse relaxation time of Rb
S3: at a known positionUnder the condition of (a), the excitation field B needs to be continuously adjusted 1 At different B 1 Sweep frequency under the condition of intensity to obtain the half-width delta omega of the signal 1/2 And B is connected with 1 Fitting the intensity by the following method 87 Longitudinal relaxation time of Rb->
S4: measurement of 129 Longitudinal relaxation time of Xe
Further, the specific step of S2 is:
s2-1: the pumping light is turned on to uniformly irradiate the air chamber for more than 10 minutes, so that the air chamber is filled with the air 129 The Xe is fully polarized;
s2-2: turning off the pump light and starting to sweep the frequency;
s2-3: by the formula
Obtaining 87 Transverse relaxation time of Rb
Further, the specific step of S4 is:
s4-1: at the position of 129 After the Xe is fully polarized, the pumping light is turned off to carry out continuous sweep;
s4-2: switching off the pumping light to carry out continuous sweep frequency;
s4-3: for a pair of 87 Center frequency ω of Rb swept Signal Rb And peak value A Rb Fitting the e index to obtain 129 Longitudinal relaxation time information of Xe.
Further, the excitation magnetic field is connected with 129 The larmor precession frequency of Xe is consistent; pulse duration is such that 129 The polarization direction of Xe is just reversed.
In summary, the beneficial effects of the invention are as follows: the magnetic field brought by the pumping light can be thoroughly eliminated by the dark state sweep frequency methodGradient effects and no need to separate the signals in the x-axis and y-axis directions during signal processing; in addition, the method pair is usedThe measurement does not require laser pulse modulation, but is performed +.>In the process of (1) 129 The Xe initial state has no requirement and small disturbance, so that compared with the traditional method, the dark state sweep frequency method has lower requirements on equipment and experimental conditions, the data processing process is simpler, and the accuracy of measurement is ensured and the practicability is higher.
Drawings
FIG. 1 is a schematic diagram of an experimental apparatus in an embodiment of the invention;
FIG. 2 is a schematic illustration of an embodiment of the present invention 87 Signal amplitude plot of Rb continuous swept frequency signal (200 times);
FIG. 3 is a graph of fitting results of a single sweep signal in an embodiment of the present invention;
FIG. 4 shows the line widths Δω of the first 50 sets of swept signals in an embodiment of the invention 1/2 Fitting the result;
FIG. 5 is a schematic illustration of an embodiment of the present inventionAnd pump light power P pump Is a relationship diagram of (1);
FIG. 6 shows a line width Δω in an embodiment of the invention 1/2 Along with the sweep frequency field B 1 Fitting the intensity variation;
FIG. 7 shows a swept signal peak A in an embodiment of the invention Rb (t) and the swept center frequency ω Rb E-exponential fit result plot of (t);
FIG. 8 is a graph showing the peak value A of the swept signal in an embodiment of the invention Rb (t) and the swept center frequency ω Rb A linear fit of (t);
FIG. 9 is a reverse rotation in an embodiment of the invention 129 Relaxation is carried out under the condition of Xe polarization direction, and e of sweep frequency signal is measuredFitting the number to a result graph;
FIG. 10 is a diagram of B in an embodiment of the invention 1 Fitting of e-index of the swept signal at 1.65 nT.
Detailed Description
The invention is described in further detail below with reference to fig. 1-10.
Examples: the relaxation time measuring method of the Rb-Xe spin exchange system based on the dark state sweep method, as shown in fig. 1 to 10, specifically comprises the following steps:
s1: establishing a Bloch equation and solving the equation;
the interaction of the external magnetic field and polarized atoms is shown as larmor precession of the atomic magnetic moment around the external magnetic field direction. Taking into account this interaction and the depolarization (relaxation) process of the atoms at the same time, and assuming that a static magnetic field B exists in the z-axis (longitudinal direction) z ＝B 0 Then the well-known Bloch equation in the magnetic resonance field can be obtained:
wherein M is x ，M y And M z The macroscopic magnetic moment M of the atomic system is the component in the x, y and z directions,andis their time derivative, gamma is gyromagnetic ratio, M 0 Is the longitudinal magnetic moment in steady state, T 1 And T 2 Longitudinal and transverse relaxation times of polarized atoms, respectively. To detect macroscopic magnetic moment M in the transverse direction x And M y An excitation field bx=b can be applied in the x-direction 1 cos (ωt) is transformed into rotational coordinates:
M x ＝M′ x cos(ωt)+M′ y sin(ωt) (2.1)
M y ＝-M′ x sin(ωt)+M′ y cos(ωt) (2.2)
at this time, excitation field B x Can also be decomposed into two magnetic field components B which are co-directional and counter-directional to the Larmor precession + And B - . Due to the reverse component B - Substantially unable to resonate with polarized atoms, and therefore consider only the homeotropic component B + And solving the Bloch equation to obtain:
wherein Δω is the excitation field B x Is equal to the oscillation frequency omega and atomic larmor precession frequency The detuning amount between the two is obtained by the method 87 Rb and Rb 129 Relaxation time information of Xe.
S2: measurement of 87 Transverse relaxation time of Rb
For the following 87 Rb requires the measurement of the transverse relaxation time using the dark-state sweep methodBefore the measurement of its longitudinal relaxation time +.>First, the +.A can be made by combining the formulas (3.1) and (3.2)>Then there are:
in the formula (4), the field strength B is due to the excitation field 1 Far less than B 0 Thus, it isMuch less than 1, so that the approximate degeneracy of formula (4) can be obtained:
let M ⊥ The linewidth (half width) of the signal is Δω 1/2 Then it can be obtained by the formula (4.1):
thus, using dark state sweep method in measurement 87 Transverse relaxation time of RbIn this case, it is unnecessary to distinguish the transverse macroscopic magnetic moment M' x And M' y By direct measurement of M ⊥ Linewidth acquisition of a signal 87 Transverse relaxation time of Rb->
S3: measurement of 87 Longitudinal relaxation time of Rb
At a known positionUnder the condition of (a) using an excitation field B 1 For signal line width delta omega 1/2 Can be calculated from the power spread of (2) 87 Longitudinal relaxation time of Rb->From equation (4), Δω is obtained 1/2 The analytical solution of (2) is:
wherein the method comprises the steps ofAt different field strengths B 1 The corresponding signal half width delta omega is measured 1/2 The value of eta can be obtained by fitting the formula (10) and then calculated to obtain +.>
S4: measurement of 129 Longitudinal relaxation time of Xe
When the pump light is turned off, although 87 Rb and Rb 129 Xe begins to enter the relaxation process, but spin-exchange collisions between the two continue to occur. Due to 129 The relaxation time of Xe is much longer than 87 Rb, therefore 87 The Rb polarization decays rapidly, at this time 129 Xe will self-collideTransfer of body polarization to 87 Rb at this time 87 The polarization strength PRbb of Rb satisfies:
wherein Γ is se For spin-exchange pumping rate, due to the aboveFar greater than Γ se Thus, equation (11) can be approximated as:
as can be seen, in Γ se Andare all constant and therefore during relaxation 87 Polarization intensity P of Rb Rb And (3) with 129 Polarization intensity P of Xe Xe In a linear relationship, i.e. M Rb And M is as follows Xe In a linear relationship. In addition, in the case of the optical fiber, 129 polarization of Xe also produces an equivalent magnetic field B in the z-axis Xe ：
Wherein, kappa 0 To enhance the factor, mu 0 Vacuum permeability g s Is Landmax factor, mu B Is Bohr's magneton Xe Is that 129 Particle concentration of Xe. Equivalent magnetic field B Xe And B in the z-axis 0 Will change after superposition 87 Larmor precession frequency of RbThe amount of frequency shift generated is:
δω＝γB Xe ∝P Xe (13)
with the formulas (11.1) and (13), the embodiment can pass through after turning off the pump light 87 Signal peak and frequency shift of Rb to reflect 129 Polarization intensity of Xe, thereby obtaining 129 Relaxation time information of Xe. At the position of 129 During the relaxation of Xe, its polarization and the equivalent magnetic field size in the z-axis over time satisfy the following rules:
wherein P is 0 And B 0 The polarization intensity and the equivalent magnetic field size when the pump light is turned off and the sweep is started (time 0). Thus, the expression (13) and the expression (14.1) can be obtained 87 Resonance center frequency ω of Rb Rb The method meets the following conditions:
wherein omega 0 Is the center frequency corresponding to the moment of switching off the pumping light, and the longitudinal magnetic field B z ＝B 0 +B Xe 。Is that 129 After sufficient relaxation of Xe, i.e. B Xe Center frequency corresponding to=0. Furthermore, it can be obtained by the formula (11.1) 87 Rb swept Signal Peak A Rb Is a trend of change:
simultaneously (15) and (16), the embodiment can also obtain 87 Center frequency ω of Rb swept Signal Rb And peak value A Rb In a linear stateThe system is as follows:
as can be readily seen from the above analysis, for 87 Center frequency ω of Rb swept Signal Rb And peak value A Rb E, performing exponential fitting to obtain 129 Longitudinal relaxation time of Xe
The present example verifies by experiment:
as shown in FIG. 1, the experimental device used in this example has a square air chamber with a side length of 20mm filled with 87 Rb and Rb 129 Xe gas and buffer gas N 2 . The air chamber is placed inside the heating frame at 90 ℃ and three sets of coils are distributed around the heating frame for providing magnetic fields in three directions of x, y and z axes. The coil is provided with 5 layers of cylindrical magnetic shielding barrels which are used for shielding external magnetic field disturbance, and small holes are formed in the z-axis direction and the x-axis direction of the magnetic shielding barrels for respectively allowing pumping light and detection light to pass through the air chamber.
The pump light in the experiment comes from a UniQuanta DFB 801-795-180204 laser, the power is adjustable, and the center frequency is 795nm; the probe light was from a UniQuanta DFB 801-780-150901 laser with a fixed power of 500 μW and a center frequency of 780nm. The pumping light is emitted from the laser, passes through the beam expanding and collimating system, the polarizer and the 1/4 wave plate in sequence, is converted into left-hand circularly polarized light and enters the air chamber to be used for making alkali metal atoms in the air chamber 87 Rb polarization. The detection light enters the air chamber along the x-axis after passing through the 1/2 wave plate and the polarizer, and is polarized in the air chamber 87 The Rb atomic interaction generates an optical rotation effect, and then the Rb atomic interaction enters a balance detector through beam splitting of a Wollaston prism, so as to obtain Faraday rotation angle information of the detection light. Finally, a signal control and processing system composed of a collection card, a lock-in amplifier, a computer and the like is used for controlling the on and off of the pumping laser and recording and processing dataAnd (5) analyzing.
1. The experimental process comprises the following steps: first, in order to obtain 87 Sweep signal of Rb requires turning on transverse magnetic field B x And in the sweep interval [ omega ] 1 ,ω 2 ]Continuously changing its oscillation frequency omega in the transverse magnetic field B x Is driven by the power of (a), 87 the amplitude of the Rb paramagnetic resonance (EPR) signal reflects its transverse magnetic moment M ⊥ The change curve of the recorded signal amplitude along with time is the sweep frequency signal curve. Further, as shown in FIG. 2, for measurement 87 Trend of Rb formants and center frequency can be compared with 87 Rb continuous frequency sweep, i.e. in the sweep interval [ omega ] 1 ,ω 2 ]Continuously varying the transverse magnetic field B in a periodic and repeated manner x Is a frequency of (a) is a frequency of (b). In order to meet the requirements of the data processing stage, the sweep interval [ omega ] needs to be ensured at the moment 1 ,ω 2 ]Should be slightly larger than the width of 87 Resonance center frequency ω of Rb Rb Is described. In this test, the sweep interval [ omega ] 1 ,ω 2 ]Each sweep process recorded 60 data points, each set of continuous sweep processes comprised 200 single sweeps, with the total time taken for the continuous sweep process being approximately 1506s.
Measurement of 87 Transverse relaxation time of RbWhen the pump light is started, the air chamber is uniformly irradiated for more than 10 minutes, so that the air chamber is filled with the pump light 129 The Xe is sufficiently polarized to ensure a high signal to noise ratio at the sweep, and then the pump light is turned off and the sweep is started. Finally, fitting by using formula (4) 87 Half-width delta omega of Rb sweep frequency signal 1/2 The transverse relaxation time is obtained by the calculation of (5)>As can be seen from FIG. 2, each sweep curve can be fitted to obtain the line width Δω 1/2 And is used for calculating +.>In addition, the peak value of the sweep frequency signal is along with 129 The relaxation of Xe is continuously reduced, the center frequency is continuously shifted, and the change trend of Xe accords with the reasoning results of the formula (15) and the formula (16).
To verify the pump power pair 87 Transverse relaxation time of RbThe experiment is carried out under the condition of switching on the pump light, and the transverse relaxation time +.>Measurement of 87 Longitudinal relaxation time of Rb->When it is needed to continuously adjust B 1 At different B 1 Sweep frequency under the condition of intensity to obtain the signal half-width delta omega 1/2 And B is connected with 1 Fitting the intensity by using the method (10) to calculate the longitudinal relaxation time +.>
Finally, for the purpose of measurement 129 Longitudinal relaxation time of XeIs needed to be at 129 And after the Xe is fully polarized, the pumping light is turned off for continuous sweep frequency. It is also possible to apply a pulsed excitation field +.>(pi pulse) the oscillation frequency of the excitation magnetic field and 129 the Larmor precession frequency of Xe is consistent, and the pulse duration is adjusted to lead the Larmor precession frequency of Xe to be consistent 129 The polarization direction of Xe is just inverted, and then the pump light is turned off for continuous sweep. Along with 129 Xe relaxation, its polarization strength is continuously reduced,thus also leading to 87 The intensity and formant frequency of the Rb swept signal are constantly changing. For a pair of 87 Center frequency ω of Rb swept Signal Rb And peak value A Rb Fitting the e index to obtain 129 Longitudinal relaxation time information of Xe.
2. Analysis of experimental data:
to obtain 87 The transverse relaxation time of Rb, as shown in FIG. 3, is calculated by the formula (4) pair 87 Rb sweep data was fitted. Because the signal to noise ratio of the frequency far from the resonance center frequency in the frequency sweeping process is low, the half-width delta omega of the signal is reduced 1/2 Since the calculation of (c) does not greatly contribute, the present embodiment performs interpolation processing in the vicinity of the data peak in order to obtain the value of the signal half-width as accurately as possible.
In order to satisfy the expression (4.1) approximation condition as much as possible, the present embodiment selects the expression represented by B 1 Continuous sweep experiments were performed with =4.95 nT. As shown in fig. 4, after data fitting is performed on the first 50 sweep curves of continuous sweep data by using the single fitting method in fig. 3, the line width fitting results of the first 50 sweep curves are obtained. Although the signal-to-noise ratio is continuously reduced with relaxation, the fitting line width thereof can be stably obtained. Finally, the present embodiment calculates according to the expression (5) 87 Transverse relaxation time of Rb
As can be seen from the fitting results of fig. 3: when the sweep frequency signal is fitted by the formula (4), a certain error exists. The analysis is carried out according to the form of the formula (4), the curves on the left side and the right side of the signal peak value are symmetrical, and the data obtained by the experiment show certain asymmetry. This non-alignment results mainly from three factors:
first of all, the first one, 87 rb has two hyperfine zeeman level formants of f=1 and f=2 near the formants, corresponding gyromagnetic ratio γ 1 And gamma is equal to 2 Very close, and therefore a situation where the measured value is higher than the fitted result is observed on the right side of the swept signal peak, which also results in 87 Resonance signal of RbOne of the main reasons for the asymmetry of the numbers.
Second, in solving Bloch equation (1) in section 2.1, it is necessary to apply an excitation field B on the x-axis 1 Into two rotating magnetic field components B rotating in the xy plane clockwise and counter-clockwise respectively + And B-, the present embodiment considers only the and 87 component B of Rb larmor precession direction same direction + . However, in practice, another component B-opposite thereto will also be true 87 The resonance signal of Rb produces a weak effect that leads to asymmetry in the signals on the x-axis and y-axis, and thus to 87 Asymmetry of the resonance signal of Rb.
Third, the third step of, in the case of a vehicle, 87 the Rb sweep process is always accompanied by 129 Dynamic relaxation of Xe, thus 87 The peak and center frequencies corresponding to the Rb resonance signal will change in real time, which also results in some degree of asymmetry in the swept frequency signal.
3. Pump light power pairInfluence of (2)
To study the pump light pairIs required to perform the following steps under the condition of switching on the pump light 87 Rb is swept, as shown in FIG. 5, the present embodiment has been tested under different pump powers, and obtained +.>With pump light power P pump Is a trend of change in (c).
From the results shown in figure 5 of the drawings,and pump light power P pump The relationship of (2) is not a simple linear relationship as shown in the expression (9.1), but rather it is smoothed as the pump light power is increased. The reason for this is that when the pump light passes through the air chamber, it is 87 Rb atom absorption thereby destroying 87 The depolarization of Rb atoms is equivalent to the introduction of an additional relaxation mechanism resulting in R in formula (9.1) other And also with the pump light power. Therefore, the influence of the pump light on the system can cause 87 The Rb relaxation time measurement becomes more complex, which is not beneficial to practical application, and the dark state sweep algorithm proposed in this embodiment can thoroughly eliminate the influence of the pump light band on the system, which is also one of the significant advantages of the method.
4. 87 Longitudinal relaxation time of Rb
To obtain 87 Longitudinal relaxation time of RbThe embodiment respectively uses different sweep fields B 1 Sweep frequency is carried out under the condition of intensity, and fitting is carried out through the formula (4) to obtain the line width:
table 1: different sweep fields B 1 Measured under intensity conditions 87 Rb Signal linewidth
| B 1 (nT) | 4.95 | 8.25 | 11.55 | 14.85 | 55 |
| Linewidth (Hz) | 435 | 442 | 457 | 474 | 956 |
As shown in fig. 6, fitting is performed by using the equation (10) to obtain η= 3.624 ×10 -4 (nT-2), substituting gyromagnetic ratio gamma= 6.998Hz/nT to obtain
By comparison with the transverse relaxation time, it can be seen that 87 Longitudinal relaxation time of RbGreater than transverse relaxation timeThe reason for this is that some decoherence mechanisms of the system are only destroyed 87 The phase of Rb larmor precession results in 87 The transverse component of the Rb macroscopic polarization vector decays more rapidly than the longitudinal component, ultimately resulting in a transverse relaxation rate Γ 2 Greater than the longitudinal relaxation rate Γ 1 . Their relationship can be expressed as:
wherein R is se For relaxation rate due to atomic spin exchange, q se R is an amount related to the atomic polarizability and the number of nuclear spin quanta ΔB Is the relaxation rate caused by the magnetic field gradient. Thus, it finally appears as 87 Transverse relaxation time of RbLess than longitudinal relaxation time->This example shows that R is at 90 DEG C se /q se Estimated to be about 475/s, and in this experiment R after switching off the pump light ΔB Close to zero. Will->Substituting 5.87ms into the formula (18), and calculating to obtain Γ 2 =645/s, i.e.)>The calculation result and +.4.1 section>The measured values of (2) have deviation due to more complex error factors still existing in the experimental process, such as fluctuation of an experimental temperature control system, calibration error of a coil constant, and the like, 87 Difference of Rb two sub-level relaxation time and 87 and an estimation error of Rb atomic number density. Therefore, the method is continuously optimized for each error factor on the basis of the dark state sweep frequency method, and the measurement accuracy can be further improved.
5. 129 Longitudinal relaxation time of Xe
For each set of data, the present embodiment can be implemented by applying the signal peak value A Rb (t) and center frequency ω Rb (t) performing e-exponential fitting to obtainIn addition, the present embodiment is provided with the following steps 129 Xe free relaxation, also in inversion 129 Turning off the pump light after Xe polarization 129 Xe is relaxed and its longitudinal relaxation time +.>
First, as shown in FIG. 7, in the present embodiment, at B 1 Sweep frequency when=4.95 nT, and use signal peak value a according to (15) and (16) respectively Rb (t) and center frequency ω Rb (t) performing an e-exponential fit.
The fitting result in FIG. 8 is well in line with the theoretical derivation of equation (17), verifying the signal peak A Rb (t) and center frequency ω Rb (t) linear relationship. In addition, as shown in fig. 9, the present embodiment does not directly turn off the pump light 129 Xe free relaxation, also in inversion 129 Turning off the pump light after Xe polarization 129 Xe is relaxed and its longitudinal relaxation time is determined 129 Xe=515.8 s. The difference is less than 1% compared with the test result under the condition that no inversion occurs, so that the method can be considered to be used for measurement 129 Xe longitudinal relaxation timeIs not sensitive to the initial state.
Next, as shown in fig. 10, the present embodiment is also shown at B 1 The above measurement procedure was repeated with =1.65nt, at 129 Free relaxation and inversion of Xe 129 Longitudinal relaxation time when Xe is relaxed after polarization direction520s and 510.2s, respectively, the fitting result still shows higher stability despite the reduced signal-to-noise ratio of the sweep signal at this time.
And, since the dark state sweep method is essentially used 87 Signal measurement of Rb 129 Longitudinal relaxation time of Xe, the method is specific to 129 The relaxation state disturbance of Xe is small, so that when the e-exponential fitting is performed on the sweep frequency signal, the fitting result has extremely high fitting goodness (R square is larger than 0.9998).
The present embodiment is only for explanation of the present invention and is not to be construed as limiting the present invention, and modifications to the present embodiment, which may not creatively contribute to the present invention as required by those skilled in the art after reading the present specification, are all protected by patent laws within the scope of claims of the present invention.
Claims (4)
1. The relaxation time measuring method of the Rb-Xe spin exchange system based on the dark-state sweep frequency method is characterized by comprising the following steps: the method specifically comprises the following steps:
s1: establishing a Bloch equation and solving the Bloch equation to obtain:
s2: measurement of 87 Transverse relaxation time of Rb
S3: at a known positionUnder the condition of (a), the excitation field B needs to be continuously adjusted 1 At different B 1 Sweep frequency under the condition of intensity to obtain the half-width delta omega of the signal 1/2 And B is connected with 1 Fitting the intensity by the following method 87 Longitudinal relaxation time of Rb->
S4: measurement of 129 Longitudinal relaxation time of Xe
2. The method for measuring the relaxation time of the Rb-Xe spin-exchange system based on the dark-state sweep method according to claim 1, wherein the method comprises the following steps: the specific steps of the S2 are as follows:
s2-1: the pumping light is turned on to uniformly irradiate the air chamber for more than 10 minutes, so that the air chamber is filled with the air 129 The Xe is fully polarized;
s2-2: turning off the pump light and starting to sweep the frequency;
s2-3: by the formula
Obtaining 87 Transverse relaxation time of Rb
3. The method for measuring the relaxation time of the Rb-Xe spin-exchange system based on the dark-state sweep method according to claim 1, wherein the method comprises the following steps: the specific steps of the S4 are as follows:
s4-1: at the position of 129 After the Xe is fully polarized, the pumping light is turned off to carry out continuous sweep;
s4-2: switching off the pumping light to carry out continuous sweep frequency;
s4-3: for a pair of 87 Center frequency ω of Rb swept Signal Rb And peak value A Rb Fitting the e index to obtain 129 Longitudinal relaxation time information of Xe.
4. The method for measuring the relaxation time of an Rb-Xe spin-exchange system based on a dark state sweep method according to claim 3, wherein the method comprises the following steps: the excitation magnetic field 129 The larmor precession frequency of Xe is consistent; pulse duration is such that 129 The polarization direction of Xe is just reversed.
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