Polarization transfer in a spin-exchange optical-pumping experiment

Spin-exchange optical pumping (SEOP) enables hyperpolarization of magnetic noble gas nuclei and allows enormously enhanced signal in nuclear magnetic resonance studies in materials, biosciences, and medicine. We model the dynamics of the SEOP process taking place in a $\mathrm{Rb}-{}^{129}\mathrm{Xe}$ gas mixture and shed light on how the different microscopic processes influence the macroscopic polarization transfer. For each Rb-Xe collision taking place in simulated molecular dynamics trajectory, we sample a time series of quantum-chemically preparametrized Hamiltonians. Combined electron and nuclear spin dynamics of each event is propagated by solving the corresponding Liouville–von Neumann equation. The rarely occurring, long-lived van der Waals molecules are seen to give the most significant contribution to polarization transfer under the simulated conditions ($T=300$ K, $p=2.4$ bar), in agreement with earlier findings. Besides the lifetime of the collision complex, the average and minimum Rb-Xe interatomic distances characterize the efficiency of the polarization transfer events. We obtain insight into magnetization transfer in both individual binary collisions and van der Waals complexes and demonstrate a stepwise buildup of ${}^{129}\mathrm{Xe}$ spin polarization upon bond-length oscillations in the latter.

Figure 1

Quantum-chemically computed components parallel to the internuclear axis and perpendicular to it of the (a) $g$ tensor and (b) ${}^{129}\mathrm{Xe}$ hyperfine coupling tensor for the interacting Rb-Xe dimer as functions of $R_{\mathrm{RbXe}}$. (c) The Rb-Xe radial distribution function from molecular dynamics simulations.

Figure 2

Simulated distribution of the Rb-Xe interaction events, $N$, as a function of their lifetime.

Figure 3

(a) Distribution of polarization transfer, ${\mathcal{P}}_{z,z}^r$, in different-lifetime Rb-Xe interaction events, at vanishing external magnetic field. Each bar represents a lifetime category $D_1\cdots D_8$ ranging from short, binary collisions to long-lived VDW complexes. For categories with significant statistical uncertainty, the upper half of the error bar is shown in red. (b) The polarization transfer of panel (a) divided by $N_r$, the number of events in $D_r$. $N_r$ is shown for each lifetime category in panel (b).

Figure 4

(a) Simulated polarization transfer in the different event lifetime ranges (see Fig. 3) as a function of the external magnetic field strength. The contributions of the short lifetime ranges $D_1\cdots D_6$, are averaged over. (b) The same divided by the number of events $N_r$ within the individual lifetime categories.

Figure 5

(a) Distribution of polarization transfer in Rb-Xe interaction events with different average Rb-Xe distances, at vanishing external magnetic field. The average is calculated over the lifetime of the event. (b) The same as panel (a), but for different ranges of minimum Rb-Xe distance occurring within the lifetime of the event. The number of events in each distance range is shown. For categories with significant statistical uncertainty, the upper half of the error bar is shown in red.

Figure 6

Simulated polarization transfer between the unpaired Rb electron and ${}^{129}\mathrm{Xe}$ nucleus and the Rb-Xe distance in four binary collisions as a function of time. Events contained in the lifetime categories (a) $D_1$, (b) $D_4$, (c) $D_6$, and (d) $D_1$ (see Fig. 3).

Figure 7

Simulated polarization transfer between the unpaired Rb electron and ${}^{129}\mathrm{Xe}$ nucleus and the Rb-Xe distance, in two VDW complexes as a function of time [panels (a) and (b)]. Both molecules are contained in the $D_8$ lifetime category (see Fig. 3). (c) Simulated polarization decay of the unpaired electron (${\widehat{S}}_z$) in the same VDW molecule as in panel (b). In addition, the Rb-Xe distances of all the collision events with other Xe atoms are plotted with dashed black and red lines.

Figure 8

Additional polarization transfer as a function of time between adjacent local maxima of the Rb-Xe distance in the van der Waals complexes depicted in Fig. 7. The minimum Rb-Xe distance occurring in each oscillation is also illustrated. (a) Unperturbed complex. (b) Longer-lived, perturbed complex.