Nonlinear effects in optical pumping of a cold and slow atomic beam

By photoionizing hyperfine (HF) levels of the Cs state $6{}^2{P}_{3/2}$ in a slow and cold atom beam, we find how their population depends on the excitation laser power. The long time (around $180\mu \mathrm{s})$ spent by the slow atoms inside the resonant laser beam is large enough to enable exploration of a unique atom-light interaction regime heavily affected by time-dependent optical pumping. We demonstrate that, under such conditions, the onset of nonlinear effects in the population dynamics and optical pumping occurs at excitation laser intensities much smaller than the conventional respective saturation values. The evolution of population within the HF structure is calculated by numerical integration of the multilevel optical Bloch equations. The agreement between numerical results and experiment outcomes is excellent. All main features in the experimental findings are explained by the occurrence of “dark” and “bright” resonances leading to power-dependent branching coefficients.

Figure 1

Excitation and photoionization scheme for cesium $D_2$ line with hyperfine structure and magnetic Zeeman sublevels. Laser excitation occurs from $F_g=4$. Magnetic Zeeman sublevels are numbered according to Eqs. (13).

Figure 2

Zeeman structure for the (a) T44 and (b) T43 transitions upon $\pi$ polarized excitation. The solid arrows show the absorption and stimulated emission transitions, while the dashed ones depict the spontaneous emission paths. The thick levels denote the population accumulation due to optical pumping.

Figure 3

Schematic diagram of the experimental setup: (a) side and (b) top views are reported. The electric field guiding the ions towards the detector is depicted in (a), whereas the spatial distributions of the superposed excitation (pump) and ionization (probe) laser beams are drawn at the bottom of (b). Drawing not to scale.

Figure 4

Ion count rates for (a) T45, (b) T44, and (c) T43 transitions as a function of excitation power. For reference, the top axis reports the excitation intensity determined in the actual experimental conditions.

Figure 5

Branching ratios ${\mathrm{\Pi }}_{F_a,F_b}$ (arrows with rounded frames) for $6^2{S}_{1/2}\to 6^2{P}_{3/2}$ HF transitions and relative line strengths ${\tilde{S}}_{F_a{F}_b}$ (thick lines with rectangular frames). HF frequency splittings are also shown [31].

Figure 6

Ratio (a) of the T45 and T44 ion signals and (b) of the T44 and T43 ion signals derived from data from Fig. 4 as a function of the excitation power. The dots represent the experimental data, while the lines are obtained from the simulation discussed in the text (solid line) and in the limit of weak excitation, i.e., from the ${\tilde{S}}_{F^{\prime \prime }{F}^{\prime }}$ values (dashed lines). For reference, the top axis reports the excitation intensity determined in the actual experimental conditions.

Figure 7

Evolution of the populations in the hyperfine sublevels (a1), (a2) $F_e=5$, (b1), (b2) $F_e=3,4$, and (c1), (c2) $F_g=3,4$ during the atom propagation across the excitation laser beam resonant with the T45 transition. Laser power is $W_{exc}=3\mu \mathrm{W}$ (corresponding to $I_{exc}=58\mu \mathrm{W}/{\mathrm{cm}}^2)$ in (a1), (b1), and (c1) and $W_{exc}=10$ mW (corresponding to $I_{exc}=190\mathrm{mW}/{\mathrm{cm}}^2)$ in (a2), (b2), and (c2).

Figure 8

Schematic illustration of bright-resonance formation within the Zeeman multilevel system involved in the T45 transition, showing partial spontaneous decay rates ${\mathrm{\Gamma }}_m^p$ (circular frames), in units of ${\mathrm{\Gamma }}_e$, and absorption rates ${\mathrm{\Lambda }}_m$ (square frames), in arbitrary units. The thick line denotes the ground state contributing to the bright resonance. For the sake of clarity, details of transitions and relevant rates are reported only for a selected choice of states $(m=0,\pm 1$ for both excited and ground states).

Figure 9

Evolution of the populations in the hyperfine sublevels (a1), (a2) $F_e=3,5$, (b1), (b2) $F_e=4$, and (c1), (c2) $F_g=3$ during the atom propagation across the excitation laser beam resonant with the T44 transition. Laser power is $W_{exc}=3\mu \mathrm{W}$ (corresponding to $I_{exc}=58\mu \mathrm{W}/{\mathrm{cm}}^2)$ for (a1), (b1), and (c1) and $W_{exc}=10$ mW (corresponding to $I_{exc}=190\mathrm{mW}/{\mathrm{cm}}^2)$ for (a2), (b2), and (c2).

Figure 10

Evolution of the $|F_g=4,m=0\rangle$ state population during the atom propagation across the excitation laser beam resonant with the T44 transition. The quite different behaviors for low and high radiation powers, expected to correspond to regimes (ii) and (iii), are shown with solid and dashed lines, respectively.