Figure 1

Ground-state energy levels of Cs vapor at a magnetic field of $2.7$ T, as used in our experiments. The two manifolds with $m_S=\pm \frac{1}{2}$ are separated by a Zeeman energy of $75.7$ GHz. Each manifold consists of eight sublevels, each separated by a hyperfine energy of $1.149$ GHz. The sublevels are labeled with colored triangles; the direction of the triangle indicates the electronic spin projection $m_S$ and the color indicates the nuclear spin projection $m_I$.Reuse & Permissions

Figure 2

Schematic of our experimental apparatus. Pumping light from a Ti:sapphire laser passed through a single-mode optical fiber (SMF) and was expanded to illuminate the entire vapor cell located in an oven in the bore of a superconducting magnet (not shown). A pellicle reflected part of this beam into an optical power meter (OPM) shielded by a bandpass filter (BPF). The pump beam was linearly polarized using a polaroid sheet (LP). Two diode lasers (DLA, DLB) produced the probe light; we blocked one beam while performing measurements with the other. We controlled the relative intensities using a variable neutral-density filter (VND) and overlapped the two beam paths with a nonpolarizing beam-splitter cube (NBS). We measured the optical frequencies with a wavemeter and scanning Fabry-Pérot étalon (FPE) and modulated the probe intensity with a mechanical chopper. Both pump and probe beams were coupled into single-mode optical fibers (SMF) using fiber couplers (FC). The regions outlined in dashed boxes translated into and out of the page to perform spectroscopic measurements at several positions along a diameter of the cylindrical cell. The probe beam was linearly polarized before passing through the cell; we measured the transmitted intensities of ${\sigma }_{+}$ and ${\sigma }_{-}$ light with a $\lambda /4$-plate (QWP) and polarizing beam splitter (PBS) with outputs monitored by two photodetectors (PD) read with lock-in amplifiers and transmitted to a desktop computer (PC).Reuse & Permissions

Figure 3

Cell geometries used in this work: (a) a cross section of a standard cylindrical cell and (b) a cross section of a dumbbell cell created to minimize refraction in the optical windows. The inner cylinder of the dumbbell cell extends to within 2 mm of the optical window at each end. Photographs of a millimeter-scale grid as seen through (c) the conventional cell and (d) the dumbbell cell demonstrate the difference in distortion near the cell walls.Reuse & Permissions

Figure 4

Energy levels of Cs vapor at high magnetic field. Two probe lasers ($D_1$, $6{}^2{S}_{1/2}\to 6{}^2{P}_{1/2}$, 894 nm) measure the populations of all 16 ground-state sublevels—the manifold $|-\frac{1}{2},m_I\rangle$ with ${\sigma }_{+}$ light (thin solid arrows) and $|+\frac{1}{2},m_I\rangle$ with ${\sigma }_{-}$ light (thin dashed arrows). The sublevels are denoted by triangles, with upward (downward) triangles indicating $m_S=+\frac{1}{2}(-\frac{1}{2})$ and the color indicating $m_I$ from violet ($m_I=-\frac{7}{2}$) to red ($m_I=+\frac{7}{2}$). A pump beam ($D_2$, $6{}^2{S}_{1/2}\to 6{}^2{P}_{3/2}$, 852 nm) can be tuned to depopulate any of the ground-state sublevels via allowed and forbidden transitions. Representative allowed and forbidden transitions are depicted with thick solid and dashed arrows, respectively. At high magnetic fields and low buffer-gas pressures, all transitions can be optically resolved.Reuse & Permissions

Figure 5

Simulated absorption cross section for unpolarized Cs vapor with Maxwellian velocity distribution at $27{}^{\circ }$C and 2.7-T magnetic field in 10 Torr N${}_2$ buffer gas for ${\sigma }_{-}$ [solid (red)], $\pi$ [dot-dashed (green)], and ${\sigma }_{+}$ [dashed (blue)] polarizations—note the logarithmic scale on the vertical axis. In (a), the probe beam frequency sweep ranges are indicated by the gray regions. The representative allowed and forbidden pumping transitions of Fig. 4 are indicated by the thick gray solid and dashed lines in (b), respectively. We label multiplets of transitions with letters according to the convention of Ref. [15].Reuse & Permissions

Figure 6

Absorption spectra of Cs vapor in 10 Torr N${}_2$ buffer gas at $27{}^{\circ }$C. The probe beam passed through the center of a cylindrical Pyrex cell with $R=1.1$ cm and $\ell =5.7$ cm. (a) and (b) show absorption of ${\sigma }_{-}$ and ${\sigma }_{+}$ probe light, respectively, for pumping on the allowed transition $D_2$(g) depicted in Fig. 4; (c) and (d) show absorption of ${\sigma }_{-}$ and ${\sigma }_{+}$ probe light, respectively, for pumping on the forbidden transition $D_2$(h). The dashed (black) traces show absorption with the pump light off and the solid (red) traces with the pump light on. The triangles identify the ground-state sublevels (see Fig. 4).Reuse & Permissions

Figure 7

Dependence of the sublevel populations and spin projections $\langle I_z\rangle$ and $\langle S_z\rangle$ on position along a diameter of the cylindrical vapor cell (see Fig. 4 for symbol definitions). The walls of the cell are approximately at the edges of the plots, at 0 and 21 mm. The individual sublevel populations and spin projections are consistent with a simple diffusion model for an infinitely long cylinder where the vapor is completely depolarized ($g_0\langle {\rho }_{\mu \mu }\rangle =1$) at the cell wall. (a) and (d) show the normalized sublevel populations with $m_S=+\frac{1}{2}$ for allowed and forbidden pumping, respectively. (b) and (e) similarly show the sublevel populations with $m_S=-\frac{1}{2}$ and (c) and (f) show the nuclear- and electron-spin projections, respectively. Fit parameters $\Gamma$ are shown for some representative traces in (a)–(c).Reuse & Permissions

Figure 8

Dependence of the sublevel populations and spin projections $\langle I_z\rangle$ and $\langle S_z\rangle$ on incident pump intensity. (a) and (d) show the normalized sublevel populations with $m_S=+\frac{1}{2}$ for allowed and forbidden pumping, respectively. (b) and (e) similarly show the sublevel populations with $m_S=-\frac{1}{2}$ and (c) and (f) show the spin projections for allowed and forbidden pumping, respectively.Reuse & Permissions

Figure 9

Measured pump frequency dependence of the spin projections $\langle S_z\rangle$ [open (blue) circles] and $\langle I_z\rangle$ [solid (red) circles] near the center of the cell. For the singly forbidden transitions $D_2\left(\mathrm{a}\right)$ and $D_2\left(\mathrm{h}\right)$, the nuclear and electronic polarizations had opposite sign, while for the allowed transitions, they had the same sign. As the hyperfine-shift damping rate ${\Gamma }_{\mathrm{hfs}}$ increased, the electron-spin projection $\langle S_z\rangle$ increased by about 50%, but the nuclear-spin projection $\langle I_z\rangle$ increased by more than an order of magnitude.Reuse & Permissions

Figure 10

Simulated absorption spectra of Cs vapor in 10 Torr N${}_2$ buffer gas at $27{}^{\circ }$C (compare to experimental data in Fig. 6). The probe beam passed through the center of a cylindrical cell with $R=1.1$ cm and $\ell =5.7$ cm. (a) and (b) show absorption of ${\sigma }_{-}$ and ${\sigma }_{+}$ probe light, respectively, for pumping on the allowed transition $D_2\left(\mathrm{g}\right)$ depicted in Fig. 4; (c) and (d) show absorption of ${\sigma }_{-}$ and ${\sigma }_{+}$ probe light, respectively, for pumping on the forbidden transition $D_2\left(\mathrm{h}\right)$. The dashed (black) traces show absorption with the pump light off and the solid (red) traces show absorption with the pump light on. See Fig. 4 for symbol definitions.Reuse & Permissions

Figure 11

Simulated dependence of the sublevel populations $\langle {\rho }_{\mu \mu }\rangle$ and spin projections $\langle I_z\rangle$ and $\langle S_z\rangle$ along a diameter of the cylindrical vapor cell (compare to experimental data in Fig. 7). The walls of the cell are at the edges of the plots. (a) and (d) show the normalized sublevel populations with $m_S=+\frac{1}{2}$ for allowed and forbidden pumping, respectively. (b) and (e) similarly show the sublevel populations with $m_S=-\frac{1}{2}$ and (c) and (f) show the spin projections for allowed and forbidden pumping, respectively.Reuse & Permissions

Figure 12

Simulated dependence of the sublevel populations $\langle {\rho }_{\mu \mu }\rangle$ and spin projections $\langle I_z\rangle$ and $\langle S_z\rangle$ on incident pump intensity (compare the gray regions to experimental data in Fig. 8). (a) and (d) show the normalized sublevel populations with $m_S=+\frac{1}{2}$ for allowed and forbidden pumping, respectively. (b) and (e) similarly show the sublevel populations with $m_S=-\frac{1}{2}$ and (c) and (f) show the spin projections for allowed and forbidden pumping, respectively.Reuse & Permissions

Figure 13

Simulated dependence of the spin projections $\langle S_z\rangle$ and $\langle I_z\rangle$ on the frequency of the pump laser (compare to experimental data in Fig. 9). For the singly forbidden transitions $D_2\left(\mathrm{a}\right)$ and $D_2\left(\mathrm{h}\right)$, the nuclear (light red) and electronic (dark blue) polarizations had opposite sign, while for the allowed transitions, they had the same sign. As the hyperfine-shift damping rate ${\Gamma }_{\mathrm{hfs}}$ increased, the electron-spin projection $\langle S_z\rangle$ increased by about 50%, but the nuclear-spin projection $\langle I_z\rangle$ increased by more than an order of magnitude.Reuse & Permissions

Figure 14

Experimentally observed and simulated pump frequency dependence of the spin projections $\langle S_z\rangle$ (dark blue) and $\langle I_z\rangle$ (light red) for a cell with 10 Torr N${}_2$ buffer gas. The dashed curves are results from the simulation neglecting fluorescence and the solid curves are simulations with an artificial component of $\pi$-polarized light introduced. The simulation with this simple treatment of fluorescence agrees qualitatively with the experimental data, while the simulation without fluorescence predicts the wrong sign for $\langle I_z\rangle$.Reuse & Permissions