Introduction

Spin-Exchange Optical Pumping (SEOP) is the process of transferring angular momentum (polarization) from an optically pumped alkali metal vapor to the nuclei in a substance of interest. The most commonly used targets for SEOP are gases like $^3$He or $^{129}$Xe, which both have spin-$\tfrac{1}{2}$ nuclei. These gases, under certain favorable conditions, can maintain their polarization for hundreds of hours (this is the longitudinal relaxation time $T_1$). In a magnetic field, these gases have an equilibrium polarization of about 2 ppm (about 499,999 spins are aligned with the field, and about 500,001 anti-aligned out of each million), but once hyperpolarized using SEOP, they can achieve up to ~50% polarization (about 250,000 aligned and 750,000 anti-aligned out of each million spins). These 'hyperpolarized' gases can then be used in many applications, including magnetic resonance imaging (MRI).

High-Field Optical pumping in $^{133}$Cs

At very high magnetic fields (2.7 Tesla, for instance), the nuclear and electronic spins are almost completely decoupled. Neglecting a few small terms, we can write the hamiltonian of a $^{133}$Cs atom in a given term as $$\mathcal{H}=\mathcal{A} \vec I \cdot \vec J + g_J\mu_B\vec J \cdot \vec B\,,$$
where $\mathcal A$ is the hyperfine coupling constant, $\vec I$ is the nuclear spin operator ($I=7/2$ for $^{133}$Cs), $\vec J$ is the total electronic angular momentum operator. In the $\left|M_I,M_J\right\rangle$ basis (with $\vec B = B \hat z$), we have $$E=\mathcal{A} M_IM_J + g_J\mu_BBM_J\,.$$
The energy levels described have the following structure:

Also shown in the figure are transitions from the ground state manifold excited by lasers—the orange arrow is a strong pump laser used to decrease the number of atoms in the state at the base of the arrow. For now, let's ignore the small red arrows.

If the pump laser power is high enough, it will depopulate the entire hyperfine manifold with $M_S=-1/2$, creating a net electronic polarization in the cesium vapor. As the polarized vapor interacts with the walls of the vapor cell, it becomes depolarized, indicating that angular momentum is transferred to the wall.

NMR Enhancement

It turns out this angular momentum current can be used to polarize $^{133}$Cs nuclei in solid CsH and solid CsCl (this discovery was made by Ishikawa, et al.: reference). They observed this polarization enhancement using NMR at high magnetic fields.

In a solid, the cesium nucleus is effectively decoupled from electrons, and it can be described by the Hamiltonian $$\mathcal H=\frac{g_I}{I} \vec I \cdot \vec B\,,$$ where $g_I$ is the nuclear magnetic moment. This Hamiltonian leads to energy levels split by $\hbar \omega_L$, where the larmor precession frequency is related to the gyromagnetic ratio by $\omega_L/2\pi=\gamma/2\pi~B$. For $^{133}$Cs, $\gamma/2\pi=5.61$ MHz/T. If we excite the nuclei with an rf pulse at the Larmor Precession frequency, we can cause the nuclear spins to precess about an axis perpendicular to the (large) static field. The angle by which the net magnetization (proportional to the ensemble average of the nuclear spin $\vec I$) is rotated is referred to as the "tipping angle". When the magnetization is tipped, a component of it will lie in the plane transverse to the large static field. Using an inductive pickup coil, we can detect this magnetization as it precesses at the Larmor frequency.

Due to relaxation, the amplitude of the in-plane precessing magnetization decays with a characteristic time $T_2^*$, and we observe a signal in the pickup coil like the one pictured below:

This signal, referred to as the FID (for Free Induction Decay) is Fourier transformed to yield the NMR spectrum:

Since the nuclei are at nonzero temperature, they will have a small equilibrium magnetization when immersed in an external field. If we transfer angular momentum to the nuclei, we can increase or decrease their magnetization (measured by the amplitude of the NMR spectrum peak) by over an order of magnitude. For more detail, see Ishikawa, et. al., PRL 98, 183004 (2007).