Optically polarized ${}^3\mathrm{He}$

This article reviews the physics and technology of producing large quantities of highly spin-polarized ${}^3\mathrm{He}$ nuclei using spin-exchange (SEOP) and metastability-exchange (MEOP) optical pumping. Both technical developments and deeper understanding of the physical processes involved have led to substantial improvements in the capabilities of both methods. For SEOP, the use of spectrally narrowed lasers and K-Rb mixtures has substantially increased the achievable polarization and polarizing rate. For MEOP nearly lossless compression allows for rapid production of polarized ${}^3\mathrm{He}$ and operation in high magnetic fields has likewise significantly increased the pressure at which this method can be performed, and revealed new phenomena. Both methods have benefitted from development of storage methods that allow for spin-relaxation times of hundreds of hours, and specialized precision methods for polarimetry. SEOP and MEOP are now widely applied for spin-polarized targets, neutron spin filters, magnetic resonance imaging, and precision measurements.

Figure 1

An example of an apparatus for spin-exchange optical pumping (SEOP). This apparatus has been employed for photon scattering experiments. Whereas SEOP is typically performed in single cells for neutron spin-filter and magnetic resonance imaging applications, both electron and photon scattering applications employ a double cell configuration in which a target cell (TC) is linked to an optical pumping cell (OPC) through a connecting tube. Electron paramagnetic resonance and nuclear magnetic resonance are employed to measure the ${}^3\mathrm{He}$ polarization in the OPC and TC, respectively. Adapted from [529].

Figure 2

An example of an apparatus for metastability-exchange optical pumping. This apparatus has been employed for compressing gas into neutron spin-filter cells. Nine 2 m diameter coils provide the uniform magnetic field for the 2.3 m long OPCs. ${}^3\mathrm{He}$ gas is purified, polarized in the OPCs, compressed in two stages with an intermediate buffer cell, and dispensed into detachable neutron spin-filter cells. The capillary serves to control the flow rate and restrict diffusion for the typical 1 mbar pressure in the OPCs. Adapted from [21].

Figure 3

Development of NSFs and spin-polarized ${}^3\mathrm{He}$ targets, illustrated by representative devices and experiments. In each case, key parameters are listed to show how advances for each method improved performance, e.g., spectrally narrowed lasers and K-Rb mixtures for SEOP, and filling of cells with piston compressors and high-power laser sources for MEOP. See Secs. 6 and 7 for definitions of identifiers. The figure of merit (FOM) is defined to be $P_{\mathrm{He}}^{2}N/\tau$ for SEOP NSFs and targets as well as MEOP cryogenic targets, where $P_{\mathrm{He}}$ is the ${}^3\mathrm{He}$ polarization, $N$ is the total number of atoms in the cell in units of amg-L, and $\tau$ is the time constant for polarizing the cell. (Reminder: to reach 90% of the maximum polarization requires 2.3 time constants.) For compression-based MEOP NSFs and targets, $\tau$ is replaced by $T$, where $T$ is the time to refresh the gas for continuous flow or the time between cell exchange for remotely operated compression. (a) SEOP NSFs: First NSF ([124]), SANS ([179]; [253]), PNR ([103]), TAS ([97]), wide angle ([531]), and VHG narrowed ([98]). (b) SEOP targets for electron-scattering experiments. Here the FOM is equivalent to the potential effective luminosity of [452]. Data provided by J. Singh. E142 ([25]), GDH ([17]), GEN ([413]), duality ([454]), and transversity ([403]). (c) MEOP NSFs and targets: GEn (Bates, cryogenic, Nd:YAP) ([252]), GMn (Bates, cryogenic, Nd:LMA) ([175]), GEn (Toepler pump) ([339]), GEn, GDH (piston) ([281], [282]; [444]), (Toepler pump) ([156]), and piston fill-up mode ([45]).

Figure 4

Calculated spin-independent ($V_0(\xi )$) ([381]) and Fermi-contact [$\alpha (\xi )$] ([482]) potentials for $\mathrm{K}\text{−}{}^3\mathrm{He}$ molecules, as a function of interatomic separation $\xi$ in atomic units.

Figure 5

Spin-exchange efficiency (${\eta }_{\mathrm{S}\mathrm{E}}$) measurement for K and Rb. From [55].

Figure 6

Key elements of the optical pumping cycle for light tuned to the alkali-metal ${\mathrm{S}}_{1/2}\text{−}{\mathrm{P}}_{1/2}$ resonance in the presence of high-pressure He gas. Collisions with the He atoms mix the ${\mathrm{P}}_{1/2}$ and ${\mathrm{P}}_{3/2}$ levels, altering the selection rules for light absorption. Atoms in the $m_S=\pm 1/2$ Zeeman ground-state sublevels absorb photons with relative probabilities $1\mp P_{\infty }$. Once excited, rapid collisional spin-relaxation occurs. Quenching collisions with ${\mathrm{N}}_2$ molecules randomly repopulates the ground-state sublevels. The atoms accumulate in the $m_S=1/2$ sublevel, acquiring a steady-state spin polarization of $P_{\infty }$ in the absence of ground-state spin relaxation.

Figure 7

Energy levels of RbHe molecules in the presence of optical pumping light ([383]; [292]). The green curve, the ground-state potential energy plus one photon, crosses two excited-state potentials at two different interatomic separations. The $5p[M=3/2]$ curve is of purely ${\mathrm{P}}_{3/2}$ nature while the $5p[1/2]$ is of mixed ${\mathrm{P}}_{1/2}\text{−}{\mathrm{P}}_{3/2}$ character. The projection of the electronic angular momentum along the interatomic axis is $M$. For both crossings the colliding atom pair can absorb the circularly polarized optical pumping light even when each is fully spin polarized. From [292].

Figure 8

Circular dichroism of Rb atoms in the presence of He gas. Near the D1 line, the dichroism approaches 1, reaching $-1/2$ for the D2 line. The solid line shows the dichroism neglecting He collisions. The very significant reduction near the D1 line is responsible for excess photon absorption under SEOP conditions. Adapted from [292].

Figure 9

Measured efficiencies at $190°\mathrm{C}$ as a function of density ratio $\mathcal{D}=[\mathrm{K}]/[\mathrm{Rb}]$. The spin-exchange efficiency ${\eta }_{\mathrm{S}\mathrm{E}}$, which is the maximum possible efficiency with which the angular momentum of the pumping light can be transferred to the nuclei, shows the clear increases predicted by Eq. (16), solid line, as the vapor approaches pure K. Measured and modeled photon efficiencies ${\eta }_{\gamma }$ are much smaller, thanks to dichroism effects; see Sec. 2b3. From [38].

Figure 10

Alkali polarization as a function of K-Rb density ratio. The solid line shows the density limit for a narrow-band pumping laser, using the measured K absorption cross section at 795 nm. The dots are experimental measurements using a broad pumping laser whose maximum polarization is limited by the dichroism effect to 0.92. The dashed line shows expected polarization limits predicted from a naive line-broadening model. From [296].

Figure 11

NIST measurements of the $X$ factor, deduced from ${}^3\mathrm{He}$ polarization limits at high temperature, for both blown (solid, red) and flat-windowed (open, blue) neutron spin-filter cells with a range of surface-to-volume ratios $S/V$. Adapted from [34].

Figure 12

Fine and hyperfine structures of the atomic states of He involved in the metastability-exchange optical pumping process, for the ${}^3\mathrm{He}$ (left) and ${}^4\mathrm{He}$ (right) isotopes, in low magnetic field (for negligible magnetic Zeeman energies, i.e., below a few mT). The values of the total angular momenta ($J$ for ${}^4\mathrm{He}$, $F$ for ${}^3\mathrm{He}$) are indicated. Details and names of the magnetic sublevels of the $2{}^3\mathrm{S}$ and $2{}^3{\mathrm{P}}_0$ states are given in blown-up boxes [with notations of 127]. The shifts and splittings are not displayed to scale.

Figure 13

Temperature dependence of calculated and experimentally assessed collision rate coefficients in He. Ab initio calculated rates are plotted for excitation transfer (dashed lines) and total (solid lines) rates of collisions for the $2{}^3\mathrm{S}$ state (red curves, labeled S) and the $2{}^3\mathrm{P}$ state (black curves, labeled P). Experimental $k_{\mathrm{ME}}$ data (symbols, see the legend) are derived from published values of linewidths or ME cross sections in ${}^3\mathrm{He}$ (see text). Three calculated rate coefficients slowly decrease with decreasing temperature and thermal velocities, but the rate coefficients $k_{\mathrm{ME}}$ for ME collisions (the dashed red line and symbols) abruptly decrease below room temperature. This is attributed to a weak repulsive barrier at large distance in the ${\mathrm{He}}^{*}\text{−}\mathrm{He}$ interaction potential. Adapted from [496], Fig. 3 for the calculated curves.

Figure 14

Low-field metastability-exchange optical pumping transitions: (a) computed absorption spectra for the $2{}^3\mathrm{S}\text{−}2{}^3\mathrm{P}$ transition for a low-pressure, optically thin gas at room temperature. The linewidths essentially arise from Doppler broadening. (b) Fine and hyperfine sublevels involved in the transition (see Fig. 12). The three transitions to the $2{}^3{\mathrm{P}}_0$ levels are schematically represented, and the names and positions of the corresponding line components in the spectra are highlighted. (c) The inset displays the optical transitions involved for $C_8$, ${\sigma }_{+}$ pumping (straight arrows, see text). The curved arrow represents population transfer between Zeeman sublevels of the $2{}^3\mathrm{P}$ state. Note that no direct transfer, corresponding to a nuclear spin flip, is expected to occur between these two sublevels.

Figure 15

Results of the MEOP rate equations obtained using the same computer code as in [47] for typical operating conditions: 0.5 mbar ${}^3\mathrm{He}$ gas, $T=293\mathrm{K}$, $B=1\mathrm{mT}$, $n_{\mathrm{m}}=1.2\times {10}^{10}{\mathrm{cm}}^{-3}$, ${\gamma }_{\mathrm{r}}^{\mathrm{S}}={10}^3{\mathrm{s}}^{-1}$, and ${\gamma }_{\mathrm{r}}^{\mathrm{P}}=0.16\times {10}^7{\mathrm{s}}^{-1}$. Atoms of all velocity classes are pumped with the same rates ${\gamma }_{ij}$ (see text). (a) Distributions of the $2{}^3\mathrm{S}$ populations $a_i$ for $C_8$, ${\sigma }_{+}$ optical pumping and ${\gamma }_{ij}=\gamma /10$, $\gamma$, and $10\gamma$ (bars from left to right and from light gray to black in each group). Surrounding red boxes are the spin-temperature populations. (b) Computed absorption coefficients are plotted as functions of reduced pumping rates for $C_8$ and $C_9$ optical pumping and different nuclear polarizations (see the legend). For $C_9$ the two pumping rates for the two pumped sublevels jointly scale with the pumping light intensity, with a fixed ratio $T_{1,18}/T_{2,17}=3$. Introducing $T_{ij}$ in the horizontal scales makes the reduced pumping rates identically proportional to the pump intensity. (c) Differences between nuclear polarizations in the $2{}^3\mathrm{S}$ and ground states are plotted as a functions of $P_{\mathrm{He}}$ for $C_8$ and $C_9$ pumping and different reduced pumping rates (see the legend).

Figure 16

High-field metastability-exchange optical pumping transitions: (a) Computed absorption spectra at $B=1.5\mathrm{T}$ for the $2{}^3\mathrm{S}\text{−}2{}^3\mathrm{P}$ transition (low-pressure, optically thin gas at room temperature) for both circular polarizations. The strong unresolved components in the spectra are labeled $f_n^{\pm }$, where $n=2$ or 4 refers to the number of involved transitions and $\pm$ to the sign of the circular polarization. Doublets of resolved weaker transitions of interest for optical detection purpose are highlighted. (b), (c) Energies of the ${}^3\mathrm{He}$ sublevels at 1.5 T for the $2{}^3\mathrm{S}$ and $2{}^3\mathrm{P}$ states. The transitions induced by the ${\sigma }_{-}$-polarized pumps (thick lines) and the suitable probes (thin lines) are displayed [$f_2^{-}$ pump, ${\sigma }_{+}$ probe in (b); $f_4^{-}$ pump, ${\sigma }_{-}$ probe in (c)].

Figure 17

Optical-pumping-induced additional loss rates vs absorbed pumping power per unit volume for various gas pressures and fields (see the legends) and cell diameters: wide (w: $\ge 5\mathrm{cm}$) and narrow (n: 1.5 cm). Each of the two logarithmic scales spans six decades. The lines are guides for the eye corresponding to linear variations with linear coefficients $200{\mathrm{cm}}^3/\mathrm{J}$ (dashed line, low $B$) and $9{\mathrm{cm}}^3/\mathrm{J}$ (dotted line, 1.5 T). The ordinates of the horizontal lines in the box next to the left axis are the values of the pumping-free decay rates ${\mathrm{\Gamma }}_{\mathrm{D}}$ for the different sets of data. They range from $0.67\times {10}^{-3}{\mathrm{s}}^{-1}$ (solid stars) to $14.5\times {10}^{-3}{\mathrm{s}}^{-1}$ (large open squares). The figure compiles data from Mainz (⋄), Cracow (▾), and Paris (all other symbols; the small and large squares stand for weak and strong discharges in the same cell). Adapted from [46], Fig. 6.62.

Figure 18

Variation with pressure of highest steady-state polarizations achieved by various groups at low fields (open symbols, 1 to 3 mT) and high fields (filled symbols, see the legend). The two lines ($P_{\mathrm{He}}=2.56/p$ and $57/p$) are upper bounds derived from the lines in Fig. 17 (see text). The figure compiles data from Caltech ($⬡$), Mainz (⋄), Cracow (◂, ▸), and Paris (all other symbols). Wide and narrow cells (w, n): see Fig. 17. Adapted from [46], Fig. 6.48, with additional data from [190] and [427].

Figure 19

Diagrams of current electron beam target designs. Top: Jefferson Laboratory. From [144]. Bottom: Mainz. Dimensions are in mm. From [281].

Figure 20

The variation of the neutron polarization $P_{\mathrm{n}}$ and transmission $T_{\mathrm{n}}$ with the opacity factor, where the opacity factor is given by the pressure-length-wavelength product in bar-cm-nm, for ${}^3\mathrm{He}$ polarizations ($P_{\mathrm{He}}$) of 0.5, 0.75, and 1. The neutron transmissions shown do not include the transmission of 0.88 due to neutron scattering from a typical glass NSF cell.

Figure 21

Neutron spin-filter (NSF) cells. Clockwise from top left: MEOP silicon-windowed cells [largest cell is 14 cm diameter by 10 cm long ([314])], MEOP wide-angle cell [6 cm inner diameter, 20 cm outer diameter, 12 cm tall ([23])], cells for neutron interferometry [larger cell is 4 cm diameter by 6 cm long ([230])], horseshoe SEOP cell [9 cm inner diameter, 23 cm outer diameter, 7.5 cm tall ([104])], SEOP wide-angle cell [14 cm inner diameter, 30 cm outer diameter, 8 cm tall ([531])], and typical SEOP NSF cell [12 cm diameter by 7 cm long ([99])].

Figure 22

Coronal (view from the front of the body) ${}^3\mathrm{He}$ magnetic resonance images from a healthy subject (left) and three patients with cystic fibrosis (CF). The number of ventilation defects increases with worsening results of a standard global ventilation test ${\mathrm{FEV}}_1$ (forced expiratory volume in 1 s). ${\mathrm{FEV}}_1$ is shown as a percentage of the predicted value for a healthy subject. From [338].

Figure 23

Axial (perpendicular to the spine) ${}^3\mathrm{He}$ magnetic resonance images of a cross section of the ventilated lung in two emphysema patients, top and bottom. Images on the right are spin-density weighted while those on the left are maps of apparent diffusion coefficient (ADC), where red represents the most restricted air spaces regions and blue the least restricted. The blue regions correspond to the most diseased tissue, where the alveolar walls have been destroyed. These regions do not necessarily correlate with the poorly ventilated regions seen in the spin-density weighted images, which demonstrate the potential for greater specificity with ADC mapping. From [121].

Figure 24

Dual species maser. From [461].

Figure 25

Design of a convection cell for decreased transfer time between the two volumes of a double cell. The flow of gas was monitored using an NMR tagging technique, in which the zapper coil was used to depolarize a slug of gas and NMR signals were then detected at each of four locations along the target chamber (labeled 1, 2, 3, and 4). From [144].