Transfer of spin angular momentum from Cs vapor to nearby Cs salts through laser-induced spin currents

Optical pumping of alkali-metal atoms in vapor cells causes spin currents to flow to the cell walls where excess angular momentum accumulates in the wall nuclei. Experiments reported here indicate that the substantial enhancement of the nuclear-spin polarization of salts at the cell walls is primarily due to the nuclear-spin current, with a lesser contribution from the electron-spin current of the vapor.

Figure 1

Cs NMR spectra of CsH with 11 Torr ${\mathrm{N}}_2$, enhanced by optical pumping of Cs vapor. The positive (red line) and negative (orange line) traces show the enhancement from thermal equilibrium (dotted green line) by ${\sigma }_{+}$ and ${\sigma }_{-}$ light, respectively. The ${\sigma }_{+}$ and ${\sigma }_{-}$ $D_1$ transitions ($6p\hspace{0.5em}{}^2{P}_{1/2}-6s\hspace{0.5em}{}^2{S}_{1/2}$) are 350 GHz detuned from each other due to the Zeeman splitting at 9.4 T. (a) and (d) refer to the $D_1$ pumping transitions shown in Fig. 2. NMR detuning is relative to 52.386 MHz.

Figure 2

Energy levels of Cs atoms at high magnetic field. The electronic angular momentum projection $m_S$ ($m_J$) for the ground (excited) state is indicated by a half-integer. There are eight nuclear-spin levels $|I=7/2\hspace{0.5em}{m}_I\rangle$ in each electronic level. The vertical lines denote groups of high-field, allowed, and forbidden $D_1$ and $D_2$ transitions, labeled from right to left in order of decreasing resonance frequency [$D_2$(a-h), $D_1$(a-d)]. The most effective photon polarization for each transition is indicated by the type of lines: solid red (${\sigma }_{+}$), dotted green ($\pi$), and dashed blue (${\sigma }_{-}$).

Figure 3

Absorption cross section of Cs atoms for ${\sigma }_{+}$ (solid red line), $\pi$ (dotted green line), and ${\sigma }_{-}$ (dashed blue line) light for (a) $D_1$ line and (b) $D_2$ line at 2.7 T and 10 Torr of ${\mathrm{N}}_2$ gas. The horizontal axis is the detuning of single-mode laser from the resonance frequency of hypothetical atoms ($I=0$) with no magnetic field. Lowercase letters denote the transition frequencies noted in Fig. 2. Cross sections on resonance for transitions with $\Delta m_I=\pm 1$ are roughly three orders of magnitude smaller than those for transitions with $\Delta m_I=0$, and smaller by additional orders of magnitude for $\Delta m_I=\pm 2$. Note the logarithmic vertical scale. The absorption length can be calculated from the cross section and the number density [Cs] $=$ $1.5\times {10}^{13}$cm${}^{-3}$ (100 ${}^{°}$C).

Figure 4

Spin sublevel population is represented as orange (gray) beads for ${\sigma }_{+}$ pumping at $D_1$(b). The solid arrows indicate optical excitation and spontaneous decays. The dotted arrows indicate quenching, $S$-damping (SD), and hyperfine-shift (HS) collisions. Since a single-mode laser pumps the adjacent nuclear-spin levels, the electron spin is well polarized by depopulation pumping. The nuclear polarization is due to hyperfine-shift pumping and the $\Delta m_I=1$ transition by ${\sigma }_{+}$ light.

Figure 5

Simulated diffusion spin currents to the side wall of a cylindrical cell (inner diameter 1 cm) at a magnetic field of 2.7 T as a function of laser pumping frequency detuning from the center of the $D_1$ line. Nuclear- and electron-spin currents $J_I$ and $J_S$ are induced by ${\sigma }_{+}$ (solid red line), $\pi$ (dotted green line), and ${\sigma }_{-}$ (dashed blue line) light. All were calculated at 100 ${}^{°}$C with 10 Torr ${\mathrm{N}}_2$ and uniform laser power density of 100 mW/cm${}^2$. The logarithmic scale for both positive and negative spin currents makes the curves discontinuous when the current changes sign. Lowercase letters indicate the transitions noted in Fig. 2. It is important to notice that for each of the transitions a, b, c and d, the nuclear-spin current $J_I$ has the same sign for the same circular polarization and the current reverses sign when the sign of the circular polarization is reversed.

Figure 6

Simulated diffusion spin currents to the side wall of a cylindrical cell as a function of laser frequency across the $D_2$ line at 2.7 T. Nuclear- and electron-spin currents, $J_I$ and $J_S$, are induced by ${\sigma }_{+}$ (solid red line), $\pi$ (dotted green line), and ${\sigma }_{-}$ (dashed blue line) light. All were calculated with the same conditions as in Fig. 5. Note the logarithmic scale for both positive and negative spin currents. Lowercase letters indicate the transitions noted in Fig. 2. Since direct optical pumping and hyperfine-shift pumping have comparable rates but opposite signs at the transitions $D_2$(c–f), $J_I$ changes sign as a function of detuning within each peak.

Figure 7

Simulated diffusion spin currents to the side wall of a cylindrical cell as a function of laser frequency across $D_2$ line at a magnetic field of 0.56 T, about 5 times smaller than the field of Fig. 5. Nuclear- and electron-spin currents $J_I$ and $J_S$ are induced by ${\sigma }_{+}$ (solid red line), $\pi$ (dotted green line), and ${\sigma }_{-}$ (dashed blue line) light. All were calculated by the same parameters as in Fig. 5, and plotted with a linear vertical scale. Many lines at small detuning overlap, so we only assign the labels of Fig. 2 to transitions that remain clearly defined at this lower field.

Figure 8

Experimental setup. Pump light from a cw Ti : sapphire laser was routed through an optical shutter (OS) and a multimode fiber into a superconducting magnet. The light was circularly polarized using a polarizing beamsplitter (PBS) and a quarter-wave ($\lambda /4$) plate, and uniformly illuminated a cylindrical cell. A photodiode (PD) was used to verify optical absorption prior to NMR experiments. A saddle-type coil sensed the free-induction-decay (FID) signals from the alkali-salt on the sidewall of the glass cell. The oven temperature was regulated by a resistive heater (HTR) and a proportional-integral-differential (PID) feedback controller. In the permanent magnet (left), the pump beam was perpendicular to the magnetic field, and linearly polarized with a PBS and a half-wave ($\lambda /2$) plate. The temperature of the magnet was regulated by chilled water to control drifts in the magnetic field. Low-frequency FID signals were picked up with a solenoid coil.

Figure 9

NMR enhancement at 2.7 T with 20 Torr ${\mathrm{N}}_2$. The circle insets show NMR signals for ${\sigma }_{+}$ (red, gray) and ${\sigma }_{-}$ (orange, light gray) pumping. The enhancement calculated from Gaussian fit to the thermal and enhanced NMR signals, depended on the polarization, ${\sigma }_{+}$ (red $▴$) and ${\sigma }_{-}$ (orange $▽$). The pump laser frequency was scanned across the $D_1$ line. The box inset shows the fine structure near the $D_1$(b). Lowercase letters indicate the pump transition named in Fig. 2. The observed enhancement does not match any of the spin currents for pure pump light shown in Fig. 5.

Figure 10

Schematic of a mechanism for polarization mixing in alkali vapors at high magnetic field. For pumping on the transition $D_1$(a) with ${\sigma }_{+}$ light, the unpolarized vapor near the walls absorbs and strongly attenuates the pump light, leading to a strongly fluorescing layer near the cell walls. Fluorescent light with $\pi$ polarization is more likely to be emitted toward the sidewall, where it will be reabsorbed by the vapor.

Figure 11

The nuclear-spin current $J_I$ simulated for partially polarized $D_1$ light. The relative power of each polarization is shown as a percentage. Our simulations ignore the propagation direction of the light; the $\pi$ polarized light is mixed in as a simple model for fluorescence. The parameters for calculation are the same as those in Fig. 5. The solid red curve can be compared to the enhanced signals (red $▴$ in Fig. 9). Note the logarithmic vertical scale.

Figure 12

NMR signals at 2.7 T for the cell with 10 Torr ${\mathrm{N}}_2$, were enhanced at four $D_1$ lines with ${\sigma }_{+}$ (red, gray) and ${\sigma }_{-}$ (orange, light gray) lights. In contrast to the signals with 20 Torr ${\mathrm{N}}_2$ in Fig. 9, the sign was unchanged by switching the pump polarization at $D_1$(b) and $D_1$(c).

Figure 13

Enhancement measured by $D_2$ pumping at 2.7 T with 10 Torr ${\mathrm{N}}_2$. Weak dependence on pump polarization, ${\sigma }_{+}$ (red $△$) or ${\sigma }_{-}$ (orange $▽$), was observed. Lowercase letters denote the transitions named in Fig. 2. The curves are $J_I$ calculated for partially polarized light, again, including $\pi$ polarized light as a simple model for fluorescence. The relative power of each polarization is shown as a percentage. The mixed-polarization spin currents are not linear combinations of the pure-polarization spin currents of Fig. 6.

Figure 14

Cs NMR signals of hydride in the 10 Torr cell at 2.7 T were enhanced by unpolarized light at six $D_2$ lines. The inset shows negative enhancement from polarized light at $D_2$(a) (black curve). The signal amplitude was degraded because these were recorded half a year later after the unpolarized pump measurements.

Figure 15

Cs NMR signals of hydride were enhanced at 0.56 T by linearly polarized $\sigma$ light of $D_2$ line in cells (a) 11 Torr ${\mathrm{N}}_2$ and (b) no buffer gas. The thermal signal was below the noise level (dotted green line). Each spectrum is a Fourier transform after averaging 70 FID’s. RF pulses at a tipping angle of $\pi$/3 were applied at a repetition period of 100 s. Note the spin polarization oppositely enhanced for these cells at respective laser frequencies. The NMR frequency was shifted for these cells because of the difference in cell position and the drift of magnetic field.

Figure 16

$\langle I_z\rangle$ for $\sigma$ pumping and the contribution of (a) quenching (black) and (b) spontaneous decay on ${\sigma }_{+}$ (red), $\pi$ (green), ${\sigma }_{-}$ (blue) transitions. A single laser works as pump and repump due to overlapping of lines and mixing of $\pi$ light. Especially when pumping from $|m_S,m_I\rangle =|-1/2,3/2\rangle$, the repump transitions are very close to the pump transitions at $-5$ GHz. $\langle I_z\rangle$ increases (solid arrow) and decreases (dotted arrow) in each process. Thickness of the arrows indicates the transition strength. Each of the arrows represents transitions for several sublevels with different $m_I$.

Figure 17

NMR area at 0.56 T enhanced by $D_2$ pumping with $\sigma$ light in the hydride cells filled with 11 Torr ${\mathrm{N}}_2$ ($•$), 11 Torr ${\mathrm{H}}_2$ (blue $△$), and no buffer gas (red $▽$). The solid black curve shows the sum of $J_I$ for ${\sigma }_{\pm }$ polarizations in Fig. 7. For the vacuum cell, $\langle I_z\rangle$ is calculated for pure $\sigma$ light (dotted green) and partially polarized light (dashed red).

Figure 18

Single-shot NMR signal of CsCl for accumulation time of 30 min, 10 Torr ${\mathrm{N}}_2$, 2.7 T, and 72 ${}^{°}$C. The difference between the amplitudes for ${\sigma }_{+}$ and ${\sigma }_{-}$ pumping is on the same order as those of CsH signals shown in Fig. 14.

Figure 19

Temperature dependence and time sequence of NMR amplitude for the 11 Torr cell at 9.4 T. The positive signal (red $▴$) was induced by ${\sigma }_{+}$ light at $D_1$(a) and the negative (orange $▾$) by ${\sigma }_{-}$ light at $D_1$(d). The thermal amplitude (green $•$) was almost constant. The temperature was first increased as indicated by the arrows, then decreased because the signal was depleted. After decreasing, the enhancement in this cell never returned to its previous maximum.