Spin-polarization dependence of the Rb-Xe spin-exchange optical pumping process

We experimentally study the Rb-Xe spin-exchange optical pumping process. The dependence of the spin-exchange rate on the intensity of the pumping light is measured at different temperatures under low magnetic fields. We demonstrate that the spin-exchange rate will decrease as the Rb spin polarization increases, which agrees well with the theoretical prediction. In our measurement, three spin exchange and spin relaxation mechanisms, namely, the spin exchange rates between Rb and Xe atoms caused by van der Waals molecule (${\mathrm{\Gamma }}_{\mathrm{vdW}}$) and binary collision (${\mathrm{\Gamma }}_{\mathrm{bin}}$) processes, and the spin relaxation rate due to the wall collision of Xe atoms (${\mathrm{\Gamma }}_{\mathrm{w}}$), have comparable magnitudes. These rates are extracted separately from the measured data with different Rb spin polarization at various temperatures. Our work provides a comprehensive confirmation of the physical picture of the spin-exchange optical pumping process.

Figure 1

Schematic illustration of the experiment setup. AOM, acousto-optic modulator; PBS, polarization beam splitter; BPD, balanced photodetector; LIA, lock-in amplifier.

Figure 2

Atomic magnetometer in longitudinal and transverse modes. (a) Amplitude and phase of ${}^{85}\mathrm{Rb}$ magnetic resonance as functions of the bias field. The phase shift near the resonant point, which is linearly proportional to the change of the longitudinal field, is used to measure the Xe field along the $z$ direction. (b) The longitudinal Xe field $b_S^z\left(t\right)$ of the Rabi nutation process (the data in yellow region and the inset) and the spin-exchange pumping process (the blue region). (c) Typical noise spectra of the atomic magnetometer in two modes. [(d), (e)] FID signals measured in the transverse mode with and without the pump beam, respectively.

Figure 3

Schematic of (a) transverse mode magnetometer and (b) longitudinal mode magnetometer. In both cases, $B_0$ is the bias field applied along the $z$ direction, in parallel with the pump beam. The modulation field ${\mathrm{B}}_{\mathrm{ac}}$ is applied along $z$ and $y$ directions for the transverse mode and the longitudinal mode, respectively. The transverse component $\langle S_x\rangle$ of Rb spins is detected by the Faraday rotation effect.

Figure 4

(a) The relative ratios $f_S$ and $f_F$ of the $S$-damping and the $F$-damping processes as functions the buffer gas pressure, respectively. The molecular lifetime is estimated by Eq. (3), and ${}^{85}\mathrm{Rb}$ hyperfine splitting ${\omega }_{\mathrm{hf}}=2\pi \times 6.8\mathrm{GHz}$ is used in the calculation. (b) The behavior of the $\upsilon \left(P\right)$ as a function of the Rb spin polarization $P$ calculated by Eqs. (9), (11), and (12).

Figure 5

[(a)–(c)] The FFT spectra of the FID signal of ${}^{129}\mathrm{Xe}$ under various power of the pump beam. Compared to the signal in the absence of the pump beam (the black curves), the FID spectra in the presence of the pump beam (the red curves) are shifted and broadened. The frequency shift ${\delta }_{\omega L}$ and the peak width are increasing as increasing the power of the pump beam. (d) The frequency shift ${\delta }_{\omega L}$ of ${}^{129}\mathrm{Xe}$ spins as a function of the pump power at different cell temperatures. The horizontal dashed lines indicate the saturated frequency shifts ${\delta }_{\omega L}^{\left(\infty \right)}$ in the case of fully polarized Rb spins at different temperatures (see text).

Figure 6

(a) Two typical spin-exchange pumping processes with high (red curve) and low (black curve) Rb spin polarization respectively. (b) Measured spin-exchange pumping rate ${\mathrm{\Gamma }}_{\mathrm{ex}}^{\prime }$ (symbols) as a function of the calibrated Rb spin polarization. The red curve is the fitted result according to Eq. (17). From the fitting, three contributions ${\mathrm{\Gamma }}_{\mathrm{vdW}}, {\mathrm{\Gamma }}_{\mathrm{bin}}$, and ${\mathrm{\Gamma }}_{\mathrm{w}}$ are extracted.

Figure 7

(a) The measured spin-exchange pumping rates (symbols) at different temperatures and the two-parameter (dashed curves) and three-parameter (solid curves) fitting results according to Eq. (17). (b) The pump-power-independent rate (i.e., ${\mathrm{\Gamma }}_{\mathrm{bin}}+{\mathrm{\Gamma }}_{\mathrm{w}}$) is linearly proportional to the Rb atom density, from which the binary collision cross section and the wall-relaxation rate are determined.