Expand this Topic clickable element to expand a topic
Skip to content
Optica Publishing Group
Journal Home About Issues in Progress Current Issue All Issues Feature Issues

Method to quickly estimate T1 value by suppressing spin exchange relaxation and magnetic field gradient relaxation in atomic sensors

Xuelei Wang, Jianli Li, Chunyu Qu, Yu Cheng, and Junjie Zhang

Open Access Open Access

Abstract

The accuracy of atomic sensor is determined by the transverse nuclear spin relaxation time (T2). As the longitudinal nuclear spin relaxation time (T1) is the upper limit of T2, it becomes an important metric for evaluating the merits of alkali vapor cells. However, the conventional method for measuring T1 of pulse delay takes dozens of minutes, which will increase the effect of random errors during the testing process. In order to solve this problem, a method to quickly estimate the value of T1 is proposed by suppressing the influence of spin exchange relaxation and magnetic field gradient relaxation terms on T2. Experimental results indicate that the accuracy is maintained at above 95%, and the testing time is reduced to less than 5%.

© 2024 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement

1. Introduction

In the field of atomic sensors [1], there are several mature applications, such as atomic clocks [2], atomic magnetometers [3,4], and atomic gyroscopes [5]. The nuclear magnetic resonance gyroscope stands out as a new gyroscope that combines the precision of optical gyroscopes with the compact size and cost-effectiveness of micro-electro-mechanical system (MEMS) gyroscopes [6].

The measurement accuracy of NMR gyroscope depends on T2 in atomic vapor cell [7]. Suppressing the nuclear spin relaxation rate in alkali vapor cell is crucial to improving the measurement accuracy of NMR gyroscopes. T1 is one of the important indicators for evaluating the performance of alkali metal vapor cell. Once T1 is determined, the transverse nuclear spin relaxation rate can be suppressed by manipulating external conditions such as light, heat, and magnetism, so that T2 is infinitely close to the T1 value.

Research of alkali metal vapor cells mainly focuses on interatomic interaction mechanisms and anti-nuclear spin relaxation coatings. [8–10]. As more experimental studies are conducted, the demand for testing the quality of alkali metal vapor cell samples has increased [11–13]. The conventional method for measuring nuclear spin relaxation time in alkali metal vapor cells involves using the free induction decay (FID) method to measure T2 and the delayed pulse method to measure T1. However, traditional T1 testing method requires a significant amount of testing time, usually tens of minutes. And with the prolongation of the nuclear spin relaxation time, the T1 test often takes even longer, thus resulting in significant time and energy waste during the research process. Furthermore, the long experimental operation can amplify the influence of the external environment on test errors. Therefore, it is essential to determine T1 value quickly and accurately to improve the performance testing of alkali metal vapor cells.

The original way of estimating T1 using optical shutter to suppress the optical-induced spin-exchange relaxation rate ignores the effect of the magnetic field inhomogeneity on the transverse nuclear spin relaxation. In contrast, the NMRG needs to apply a main magnetic field B0 of 10,000 nT, and the inhomogeneous distribution of the main magnetic field in the vapor cell as well as the inhomogeneous distribution of the external ambient magnetic field in the center of the vapor cell can cause the occurrence of transverse nuclear spin relaxation.

Therefore, the goal of rapid estimation of the longitudinal nuclear spin relaxation time is achieved by suppressing the nuclear spin relaxation induced by the magnetic inhomogeneous distribution of the ambient magnetic field in the center of the vapor cell through magnetic gradient coils, and suppressing the nuclear spin relaxation induced by the spin-exchange optical pumping action through optical shutters, both of which work together.

2. Theoretical analysis

The angular random walk (ARW) and angular rate uncertainty of an atom spin gyroscope are respectively expressed as [14]:

$$\textrm{ARW = }{\left( {{\textrm{T}_\textrm{2}} \times \textrm{SNR} \times \sqrt {\Delta f} } \right)^{ - 1}},$$
$$\delta \omega \sim {\left( {{\textrm{T}_2}\sqrt {{\tau / {{\textrm{T}_2}}}} {S / N}} \right)^{ - 1}},$$
where T2 represents the transverse spin relaxation time of Xe, SNR indicates the signal-to-noise ratio, $\Delta f$ denotes the repetition rate of the feedback loop, and $\tau $ refers to the time constant of the low-pass filter. Notably, the performance of the atom spin gyroscope is largely determined by T2. Therefore, it is necessary to conduct a theoretical analysis of the relaxation rate and its suppression methods.

T1 is the upper limit of T2. An accurate measurement of T1 is conducive to better characterizing the performance of the alkali vapor cell.

$${\Gamma _2} = \frac{1}{{{\textrm{T}_2}}} = {\Gamma _{\textrm{Xe - Rb}}}\textrm{ + }{\Gamma _{\textrm{vdW}}}\textrm{ + }{\Gamma _{\textrm{wall}}}\textrm{ + }{\Gamma _{\Delta \textrm{B}}} \cong \frac{1}{{{\textrm{T}_1}}} + {\Gamma _{\Delta \textrm{B}}},$$
$${\Gamma _{\textrm{Xe - Rb}}} = {n_{\textrm{Rb}}}{\sigma _{\textrm{Xe - Rb}}}\nu ,$$
where ${\Gamma _{\textrm{Xe - Rb}}}$ is the relaxation rate due to the binary collisions between Xe and Rb atoms, ${\Gamma _{\textrm{vdW}}}$ is the relaxation rate due to the three-body collisions formed by Rb-Xe van der Waals molecules, ${\Gamma _{\textrm{wall}}}$ is the relaxation rate resulting from the collisions with cell walls, and ${\Gamma _{\Delta \textrm{B}}}$ is the relaxation rate due to the magnetic field inhomogeneity in the alkali vapor cell, ${n_{\textrm{Rb}}}$ is the number density of Rb, ${\sigma _{\textrm{Xe - Rb}}}$ is the spin-exchange cross section, and $\nu$ is the mean thermal velocity in the alkali-noble gas collision [15,16].
$${\mathrm{\Gamma }_{\textrm{vdW}}} = \mathrm{\Gamma }_{\textrm{vdW}}^{(S)} + \mathrm{\Gamma }_{\textrm{vdW}}^{(F)} = {\mathrm{\Gamma }_\alpha }({{f_S} + v(P){f_F}} ),$$
$$\mathrm{\Gamma }_{\textrm{vdW}}^{(S)} = {f_S}{\mathrm{\Gamma }_\alpha } = \frac{{{f_S}{\gamma _\textrm{M}}}}{{2{n_{{\textrm{N}_2}}}}}{n_A},$$
$${\mathrm{\Gamma }_\alpha } = \frac{{\phi _\alpha ^2}}{{2{T_{\textrm{vdW}}}}} \equiv \frac{{{n_\textrm{A}}}}{{2{n_{{\textrm{N}_2}}}}}{\gamma _\textrm{M}},$$
$${f_S} = \frac{1}{{1 + \omega _{\textrm{hf}}^2\tau _\textrm{c}^2}},$$
$$\mathrm{\Gamma }_{\textrm{vdW}}^{(F)} = {f_F}{\mathrm{\Gamma }_\alpha }v(P) = \frac{{{f_F}{\gamma _\textrm{M}}}}{{2{n_{{\textrm{N}_2}}}}}v(P){n_A},$$
$${f_F} = 1 - {f_S} = \frac{{\omega _{\textrm{hf}}^2{\tau ^2}}}{{1 + \omega _{\textrm{hf}}^2{\tau ^2}}},$$
where $\mathrm{\Gamma }_{\textrm{vdW}}^{(S)}$ and $\mathrm{\Gamma }_{\textrm{vdW}}^{(F)}$ are the spin-exchange rate due to the short-lived and long-lived vdW molecules, ${f_S}$ and ${f_F}$ are the fraction of short-lived and long-lived vdW molecules, ${\mathrm{\Gamma }_\alpha }$ is the spin-exchange strength of the vdW process [16–18], ${n_\textrm{A}}$ and ${n_{{\textrm{N}_2}}}$ are the Rb density and N2 density, ${\gamma _\textrm{M}}$ is the proportional coefficient, ${\omega _{hf}} \approx 2\mathrm{\pi } \times {10^9}\textrm{Hz}$ is the ground-state hyperfine splitting of 87Rb atoms.
$${\Gamma _{\textrm{wall}}} = \left( {\frac{S}{V}} \right)\frac{{{{\overline V }_{Xe}}}}{2}{({\gamma {{\overline H }_l}\tau_s^0} )^2}{e^{\frac{{\alpha E}}{{{\textrm{k}_\textrm{B}}P}}}},$$
where S/V represents the internal surface area and volume ratio, γ indicates the gyromagnetic ratio of Xe, α denotes a constant, kB refers to the Boltzmann constant, and $\bar{H}$ stands for the effective local magnetic dipole field on the inner wall of the alkali metal vapor cell, $\tau_s^{0}$ means the high-temperature viscosity time of 10−13 s, E indicates the adsorption energy, P denotes the pressure of N2, and ${\bar{V}_{\textrm{Xe}}} = \sqrt {{{8{k_\textrm{B}}T} / {\mathrm{\pi }M}}}$ represents the Xe velocity, which is proportional to $\sqrt T$ [19].

In a cubic cell of side length L, the transverse relaxation rate due to the magnetic field inhomogeneity is given by [20,21]:

$${\Gamma _{\Delta \textrm{B}}} \approx \frac{{{\gamma ^2}{L^4}}}{{120D}}{|{\nabla {B_z}} |^2},$$
where $L$ is the length of cube cell, the D is the diffusion coefficients of noble gas.
$$D = \frac{{0.0101{T^{1.75}}\sqrt {\frac{\textrm{1}}{{{\textrm{M}_\textrm{A}}}}\textrm{ + }\frac{\textrm{1}}{{{\textrm{M}_\textrm{B}}}}} }}{{P{{\left[ {{{\left( {\sum {{\mathrm{\nu }_\textrm{A}}} } \right)}^{{1 / 3}}} + {{\left( {\sum {{\mathrm{\nu }_\textrm{B}}} } \right)}^{{1 / 3}}}} \right]}^2}}},$$
where P is the total pressure of gases, T is the temperature, MA and MB is the molecular weight of binary gas Xe and N2. $\sum {{\mathrm{\nu }_\textrm{A}}}$ and $\sum {{\mathrm{\nu }_\textrm{B}}}$ is the molecular diffusion volume [22].

By suppressing the nuclear spin relaxation caused by magnetic field inhomogeneity and the relaxation due to the spin-exchange optical pumping during the FID test, through this method, T2 can be made infinitely close to the true value of T1. This will significantly reduce the time required for our experiments and minimize the impact of random errors during long-term data acquisition.

3. Experimental setup

Figure 1 shows the system setup of a typical dual-beam NMRG. The alkali vapor cell filled with 5 Torr 129Xe, 20 Torr 131Xe, and 300 Torr N2, which is placed in the center of the device and is tightly wrapped in the oven to ensure a more uniform heat transfer. A flexible heating film is utilized to heat the vapor cell of 3mm × 3mm × 3 mm, and a platinum resistor is utilized to measure the temperature, both of which work together to ensure that the vapor cell can operate at 120 °C.

 figure: Fig. 1.

Fig. 1. Schematic of the experimental setup for measurements.

Download Full Size | PDF

The pump light is selected at the Rb D1 line 794.98 nm, 2 mW/cm2, propagating along the Z-axis, and the probe beam is selected at the Rb D2 line 780.20 nm, 0.5 mW/cm2, emitted by another semiconductor laser, propagating in the X-axis direction orthogonal to the pump light.

Two orthogonally distributed beams pass through the cell through the light transmission hole in the magnetically shielded barrel. The pump light is split into two parts by a polarization beam splitter (PBS). The reflected light is coupled into the fiber for pre-experimental wavelength calibration, the transmitted light is adjusted and stabilized by a noise eater, the circularly polarized light is obtained by a quarter-wave plate for pumping, and finally, the presence or absence of light is controlled by means of a light shutter.

A photodetector is utilized to obtain the intensity of the light passing through the vapor cell. The magnitude of the transmitted light intensity can be utilized to indicate the intensity of the pump light absorption by the atoms in the vapor cell. The signal from the photodetector is acquired by a signal processing system.

The probe beam is emitted by another semiconductor laser and propagates in the x-axis direction orthogonal to the pump light. The linearly polarized probe light is split by a PBS, and the reflected light is coupled into the fiber for pre-experimental wavelength calibration of the probe light. The noise attenuator stabilizes the light intensity of the transmitted light and the shutter controls the presence or absence of probe light. The signal from the optical detector is sent to the signal processing system for demodulation to obtain the atomic signal inside the vapor cell.

In the experiment, a static magnetic field along the z-axis is applied to the triaxial coil inside the shielded barrel and an oscillating magnetic field along the x-axis direction, the y-axis signal is obtained through modulation and demodulation. The signal amplitude and transverse relaxation rate are obtained by the data acquisition system.

4. Results and discussion

In Eq. (3), it is evident that the disparity between the transverse and longitudinal relaxation rates of nuclear spins is primarily determined by the impact of magnetic field inhomogeneity. To gain a better understanding of how this difference fluctuates with varying temperatures and optical powers, experimental research is required. By altering the temperature, the optical depth OD will also change, and as the temperature increases, the absorption of light by valence electrons will alter accordingly.

It can be seen from Fig. 2(a) that the relaxation rate is linearly related to the atomic number density for high temperatures (rubidium atomic number density n > 2 × 1013 cm−3). However, this relationship breaks down as the atomic number density decreases due to the dominance of wall collision relaxation rate at low temperatures (rubidium atomic number density n < 2 × 1013 cm−3) and the dominance of spin exchange relaxation rate at high temperatures. Figure 2(b) shows that the difference between the transverse and longitudinal relaxation rates increases with an increase in temperature. Furthermore, the higher the pumping optical power, the more pronounced this difference becomes. This difference is due to the magnetic field inhomogeneity, which arises from the gradient in the magnetic field at the center of the vapor cell caused by the external or internal magnetic signal. The relaxation rate difference at different pump powers gradually increases with increasing temperature, suggesting that light absorption enhances the rubidium-induced magnetic field inhomogeneity. This is also evidenced by the increase in the difference between the transverse and longitudinal relaxation rates with increasing temperature.

 figure: Fig. 2.

Fig. 2. (a) Variation of transverse and longitudinal relaxation rates with temperature for different pumping optical powers, (b) Variation of the difference between transverse and longitudinal relaxation rates with temperature for different pumping optical powers.

Download Full Size | PDF

The magnetic gradient coil is utilized to correct the magnetic field inhomogeneity in the system, as depicted in Fig. 3. The graph shows that the transverse relaxation time of 129Xe increases from 7s to approximately 8s at 120 °C after the correction.

 figure: Fig. 3.

Fig. 3. Compensation of the magnetic field gradients present in the system by means of gradient coils.

Download Full Size | PDF

 figure: Fig. 4.

Fig. 4. T2 is measured by utilizing an optical shutter to control the duty cycle of the pump light action time to suppress the influence of spin exchange relaxation.

Download Full Size | PDF

As shown in Fig. 4, when performing T2 testing using the FID method, the pumping light is only turned on at specific times to observe the magnitude of the nuclear spins’ macroscopic magnetic moment at that moment. This allows us to avoid the impact of spin exchange on nuclear spin relaxation when the pumping light is turned off. Table 1 shows that the upper and lower magnitudes are not strictly symmetrical about zero. Therefore, to obtain the required fit value, we take half the difference between the upper and lower magnitudes.

Tables Icon

Table 1. The moment when the optical shutter is opened and the magnitude of the nuclear spin magnetic moment observed at the corresponding moment.

View Table | View all tables in this article

Table 1 presents the experimental results obtained by applying an optical shutter for 0.5s after turning it off for 3s. To ensure the accuracy of the fitting, 11 data points were selected. To minimize the impact of the light on the nuclear spin relaxation, the duty cycle of the optical shutter should be kept as low as possible.

It can be seen from Fig. 5(a) that the fitted transverse relaxation rate deviates from the expected trend as the optical shutter on time is reduced when the optical shutter off duration is fixed at 3 seconds. This deviation occurs because the optical shutter is a mechanical device with a response time on the order of tens of milliseconds, which means that the relaxation due to the spin-exchange optical pumping cannot be fully suppressed by decreasing the optical shutter on duration infinitely. To determine the transverse relaxation rate at the limit of zero optical shutter opening time, a curve can be fitted using the data in Fig. 5(b) which is the selected part of the linear segment of Fig. 5(a) that shows the relationship between the optical shutter opening duration and the transverse relaxation rate, and then extrapolated to the point where the opening duration is zero.

 figure: Fig. 5.

Fig. 5. Effect of optical shutter opening and closing duty cycle on transverse relaxation rate.

Download Full Size | PDF

 figure: Fig. 6.

Fig. 6. Delayed pulse method for T1, (a) conventional test method using a combination of π pulses plus 1/2 π pulse, (b) delayed pulse method using an optical shutter.

Download Full Size | PDF

 figure: Fig. 7.

Fig. 7. Measurement T1 by time-delayed pulse method using optical shutter.

Download Full Size | PDF

 figure: Fig. 8.

Fig. 8. The fitting exponential decay curves of different methods.

Download Full Size | PDF

As shown in Fig. 6, to minimize the effect of the intermediate process light on the nuclear magnetic moment, an optical shutter is used to turn off the pumping light between pulses. This eliminates the influence of spin exchange relaxation of the pumping light during the process. Additionally, to avoid the inaccurate determination of the π-pulse duration affecting the experimental results, only a 1/2 π-pulse is used to measure the initial amplitude of the magnetic moment after a delayed time.

As shown in Fig. 7, by fitting an exponential function to the amplitude of the nuclear spin moment at various delay times, we can obtain the estimate value of T1. This allows us to evaluate the error between the values of T2 and T1 obtained by controlling the time share of the optical shutter opening.

As shown in Fig. 8, T2 is the transverse relaxation time that is obtained through a normal Free Induction Decay (FID) measurement. T2ΔB is T2 after compensating for the magnetic field inhomogeneity of the system through the magnetic gradient coil. T2pump is T2 obtained by controlling the on or off of the pumping light through the optical shutter. T2probe is the T2 obtained by synchronously controlling the probe light and the pumping light to turn on and off through the optical shutters. T1 is the longitudinal relaxation time measured using the delayed pulse method.

From the data presented in Table 2, compensating for the magnetic field inhomogeneity by a magnetic gradient coil on the original basis can lead to a reduction of the transverse relaxation rate by approximately 17.57%. Furthermore, suppressing the relaxation due to the spin-exchange optical pumping by using optical shutters can lead to a reduction of the transverse relaxation rate by approximately 28.74%. Finally, the longitudinal relaxation time T1 measured by the delayed pulse method is used as the true value. By suppressing spin exchange relaxation with an optical shutter, an error of 0.79% between the T2 and the true T1 value can be observed. The error between the obtained relaxation time and the true T1 value may be due to human error during experimental operation. By suppressing the effect of optical pumping and magnetic inhomogeneity on nuclear spin relaxation during the T2 test, the obtained T2 value can be made infinitely close to the actual T1 value with an accuracy of approximately 99.21%. Furthermore, the testing time is reduced to less than 5% of the original test method, significantly shortening the test time and improving testing efficiency.

Tables Icon

Table 2. Comparison between T2 and T1 values.

View Table | View all tables in this article

5. Conclusions

By using optical shutters to control the time duty cycle of the optical on and off, we can significantly reduce the data acquisition time required for longitudinal relaxation tests to just 5% of the original time. Although this reduction in time may result in a slight increase in test error of below 5%, it greatly improves the efficiency of longitudinal nuclear spin relaxation time tests. This method facilitates the calibration of alkali metal vapor cells performance in NMR gyroscopes and supports a variety of studies involving nuclear spins.

Funding

Agricultural Science and Technology Innovation Program (2021ZD0300403); National Science Fund for Distinguished Young Scholars (62225102); National Natural Science Foundation of China (42388101).

Disclosures

The authors declare no conflicts of interest.

Data Availability

Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

References

1. J. Kitching, S. Knappe, and E. A. Donley, “Atomic sensors - a review,” IEEE Sens. J. 11(9), 1749–1758 (2011). [CrossRef]  

2. F. Gong, Y. Y. Jau, K. Jensen, et al., “Electrolytic fabrication of atomic clock cells,” Rev. Sci. Instrum. 77(7), 711–714 (2006). [CrossRef]  

3. D. Robbes, “Highly sensitive magnetometers—a review,” Sens. Actuators, A 129(1-2), 86–93 (2006). [CrossRef]  

4. S. Zou, H. Zhang, X. Y. Chen, et al., “In-situ triaxial residual magnetic field measurement based on optically-detected electron paramagnetic resonance of spin-polarized potassium,” Measurement 187, 110338 (2022). [CrossRef]  

5. J. C Fang and J. Qin, “Advances in atomic gyroscopes: A view from Inertial navigation applications,” Sensors 12(5), 6331–6346 (2012). [CrossRef]  

6. R. M. Noor and A. M. Shkel, “MEMS components for NMR atomic sensors,” J. Microelectromech. Syst. 27(6), 1148–1159 (2018). [CrossRef]  

7. S. H. Yim, D. Y. Lee, S. Lee, et al., “Experimental setup to fabricate Rb–Xe gas cells for atom spin gyroscopes,” AIP ADV 12(1), 015025 (2022). [CrossRef]  

8. B. Driehuys, G. D. Cates, and W. Happer, “Surface Relaxation Mechanisms of Laser-Polarized 129Xe,” Phys. Rev. Lett. 74(24), 4943–4946 (1995). [CrossRef]  

9. E. Ulanski and W. Zhen, “Observation of large frequency shifts of the electron paramagnetic resonance of 87Rb atoms due to collisions with cell walls coated with RbH salt,” Phys. Rev. A 89(5), 053431 (2014). [CrossRef]  

10. A. T. Nicol, “Effect of several surface treatments on xenon nuclear polarization and relaxation in optically pumped Rb-Xe systemsm,” Phys. Rev. B 29(5), 2397–2403 (1984). [CrossRef]  

11. Y. Y. Li, Z. G. Wang, S. L. Jin, et al., “Rapid longitudinal relaxation measurement of hyperpolarized 129Xe by a highly sensitive atomic magnetometer,” AIP Adv. 7(2), 025017 (2017). [CrossRef]  

12. X. Zhan, Q. Y. Jiang, Z. G. Wang, et al., “Efficient longitudinal relaxation time measurement of 129Xe via bias-approach,” AIP Adv. 8(9), 095104 (2018). [CrossRef]  

13. Y. Zhang, J. T. Zheng, Z. Y. Yu, et al., “Measurement of longitudinal nuclear spin relaxation time in NMR gyroscope by real-time monitoring,” AIP Adv. 12(9), 095221 (2022). [CrossRef]  

14. J. C. Allred, R. N. Lyman, T. W. Kornack, et al., “High-sensitivity atomic magnetometer unaffected by spin-exchange relaxation,” Phys. Rev. Lett. 89(13), 130801 (2002). [CrossRef]  

15. D. Y. Lee, S. Lee, and S. H. Yim, “Measurement of a 129Xe transverse relaxation rate without the influence of Rb polarization-induced magnetic gradient,” Appl. Opt. 60(24), 7290–7296 (2021). [CrossRef]  

16. W. Happer, E. Miron, S. Schaefer, et al., “Polarization of the nuclear spins of noble-gas atoms by spin exchange with optically pumped alkali-metal atoms,” Phys. Rev. A 29(6), 3092–3110 (1984). [CrossRef]  

17. X. Zeng, Z. Wu, T. Call, et al., “Experimental determination of the rate constants for spin exchange between optically pumped K, Rb, and Cs atoms and 129Xe nuclei in alkali-metal–noble-gas van der Waals molecules,” Phys. Rev. A 31(1), 260–278 (1985). [CrossRef]  

18. S. Appelt, A. B. -A. Baranga, C. J. Erickson, et al., “Theory of spin-exchange optical pumping of 3 He and 129Xe,” Phys. Rev. A 58(2), 1412–1439 (1998). [CrossRef]  

19. W. A. Fitzsimmons, L. L. Tankersley, and G. K. Walters, “Nature of surface-induced nuclear-spin relaxation of gaseous He 3,” Phys. Rev. 179(1), 156–165 (1969). [CrossRef]  

20. D. -Y. Lee, S. Lee, M. M. Kim, et al., “Magnetic-field-inhomogeneity-induced transverse-spin relaxation of gaseous 129Xe in a cubic cell with a stem,” Phys. Rev. A 104(4), 042819 (2021). [CrossRef]  

21. Y. J. Yu, S. H. Min, and H. S. Moon, “Comparative Measurement of Transverse Nuclear Magnetization of Polarized 129Xe and 131Xe by Spin-exchange Optical Pumping,” Curr. Opt. Photonics 4, 466–471 (2020). [CrossRef]  

22. X. Liu, C. Chen, T. L. Qu, et al., “Transverse spin relaxation and diffusion-constant measurements of spin-polarized 129Xe nuclei in the presence of a magnetic field gradient,” Sci. Rep. 6(1), 24122 (2016). [CrossRef]  

Data Availability

Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

Cited By

Optica participates in Crossref's Cited-By Linking service. Citing articles from Optica Publishing Group journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (8)
Fig. 1.
Fig. 1. Schematic of the experimental setup for measurements.

View in Article | Download Full Size | PDF

Fig. 2.
Fig. 2. (a) Variation of transverse and longitudinal relaxation rates with temperature for different pumping optical powers, (b) Variation of the difference between transverse and longitudinal relaxation rates with temperature for different pumping optical powers.

View in Article | Download Full Size | PDF

Fig. 3.
Fig. 3. Compensation of the magnetic field gradients present in the system by means of gradient coils.

View in Article | Download Full Size | PDF

Fig. 4.
Fig. 4. T2 is measured by utilizing an optical shutter to control the duty cycle of the pump light action time to suppress the influence of spin exchange relaxation.

View in Article | Download Full Size | PDF

Fig. 5.
Fig. 5. Effect of optical shutter opening and closing duty cycle on transverse relaxation rate.

View in Article | Download Full Size | PDF

Fig. 6.
Fig. 6. Delayed pulse method for T1, (a) conventional test method using a combination of π pulses plus 1/2 π pulse, (b) delayed pulse method using an optical shutter.

View in Article | Download Full Size | PDF

Fig. 7.
Fig. 7. Measurement T1 by time-delayed pulse method using optical shutter.

View in Article | Download Full Size | PDF

Fig. 8.
Fig. 8. The fitting exponential decay curves of different methods.

View in Article | Download Full Size | PDF

Tables (2)

Tables Icon

Table 1. The moment when the optical shutter is opened and the magnitude of the nuclear spin magnetic moment observed at the corresponding moment.

View Table | View all tables in this article
Tables Icon

Table 2. Comparison between T2 and T1 values.

View Table | View all tables in this article

Equations (13)

Equations on this page are rendered with MathJax. Learn more.

ARW =  ( T 2 × SNR × Δ f ) − 1 ,
δ ω ∼ ( T 2 τ / T 2 S / N ) − 1 ,
Γ 2 = 1 T 2 = Γ Xe - Rb  +  Γ vdW  +  Γ wall  +  Γ Δ B ≅ 1 T 1 + Γ Δ B ,
Γ Xe - Rb = n Rb σ Xe - Rb ν ,
Γ vdW = Γ vdW ( S ) + Γ vdW ( F ) = Γ α ( f S + v ( P ) f F ) ,
Γ vdW ( S ) = f S Γ α = f S γ M 2 n N 2 n A ,
Γ α = ϕ α 2 2 T vdW ≡ n A 2 n N 2 γ M ,
f S = 1 1 + ω hf 2 τ c 2 ,
Γ vdW ( F ) = f F Γ α v ( P ) = f F γ M 2 n N 2 v ( P ) n A ,
f F = 1 − f S = ω hf 2 τ 2 1 + ω hf 2 τ 2 ,
Γ wall = ( S V ) V ¯ X e 2 ( γ H ¯ l τ s 0 ) 2 e α E k B P ,
Γ Δ B ≈ γ 2 L 4 120 D | ∇ B z | 2 ,
D = 0.0101 T 1.75 1 M A  +  1 M B P [ ( ∑ ν A ) 1 / 3 + ( ∑ ν B ) 1 / 3 ] 2 ,
Select as filters
Select Topics Cancel
Top
       
© Copyright 2024 | Optica Publishing Group. All rights reserved, including rights for text and data mining and training of artificial technologies or similar technologies.
Privacy | Terms of Use