Measuring the enhancement factor of the hyperpolarized Xe in nuclear magnetic resonance gyroscopes

In atomic gyroscopes, measuring the effective noble-gas magnetic field enables the determination of the noble-gas polarization. The enhancement factor is introduced to relate the effective magnetic field and the polarization in a certain magnetic-field environment. Earlier experiments concentrate on the strong magnetic-field environment for measuring the spin-exchange cross section precisely, so the results on the enhancement factor in the weak magnetic field are still insufficient. In our nuclear magnetic resonance gyroscope based on Cs-${}^{129}\mathrm{Xe}$ and -${}^{131}\mathrm{Xe}$, the magnetic field is usually set to 1–10 $\mu \mathrm{T}$. In this paper, we measure the effective magnetic field and the polarization of Xe atoms to estimate the Cs-Xe enhancement factor in the weak magnetic field of 2.5 $\mu \mathrm{T}$ and give the estimation of the Cs-${}^{129}\mathrm{Xe}$ enhancement factor of $(1.60\pm 0.06)\times {10}^4$.

Figure 1

Diagram of the experimental setup for measuring the enhancement factor. HP, half-wave plate; QP, quarter-wave plate; GP, Glan-Taylor prism; WP, Wollaston prism; CS, current source; LIA, lock-in amplifier; LO, local oscillator.

Figure 2

The dependence of the linewidth of the magnetometer response curve on the longitudinal magnetic field $B_z$. The red line is the linear fitting. The inset shows the Cs magnetometer response curves under various $B_z$. The cell temperature is set at 76 ${}^{\circ }\mathrm{C}$. When $B_z$ is set at 12 and $-12 \mu \mathrm{T}$, it is not able to directly identify the peaks from our data. Thus, these two curves are not included in the further analysis.

Figure 3

The dependence of the measured optical rotation angle on the pump beam power. The Cs polarization can be estimated by fitting these data according to Eq. (6).

Figure 4

The dependence of the Cs polarization on the pump beam power.

Figure 5

The relation between the full width at half maximum of the quadrature signal and the amplitude of driving field $B_1$. The red line is the linear fitting. The inset shows the row data of the in-phase and the quadrature signals obtained from the lock-in amplifier. The cell temperature is set at $110{}^{\circ }\mathrm{C}$ and $B_z$ is set at 2.5 $\mu \mathrm{T}$.

Figure 6

The ${}^{129}\mathrm{Xe}$ longitudinal relaxation time $T_1$ and the transverse relaxation time $T_2$ under various cell temperatures. When the cell temperature is higher than 96 ${}^{\circ }\mathrm{C}, T_1/T_2$ is about 1.

Figure 7

The dependence of the ${}^{129}\mathrm{Xe}$ longitudinal relaxation rate on the Cs density. The slope of the linear fitting is determined by the binary spin-exchange rate coefficient $\epsilon$.

Figure 8

The dependence of the ${}^{129}\mathrm{Xe}$ longitudinal relaxation rate $1/T_1$ on the Cs number density under various pump beam powers. The colored lines are the linear fittings. When the Cs density is lower than $0.4\times {10}^{19}{\mathrm{m}}^{-3}$, the ${}^{129}\mathrm{Xe}$ longitudinal relaxation rate $1/T_1$ no longer decreases linearly because of the collisions between atoms and the cell wall. The depolarization relaxation rate $1/T_D$ limits the decreasing of the longitudinal relaxation rate $1/T_1$.