Atomic orientation driven by broadly-frequency-modulated radiation: Theory and experiment

We investigate magnetic resonances driven in thermal vapor of alkali-metal atoms by laser radiation broadly modulated at a frequency resonant with the Zeeman splitting. A model accounting for both hyperfine and Zeeman pumping is developed, and its results are compared with experimental measurements performed at relatively weak pump irradiance. The interplay between the two pumping processes generates intriguing interaction conditions, often overlooked by simplified models.

Figure 1

Schematics of the setup. WFG, waveform generator; ${\mathrm{D}}_1\mathrm{L}$, pumping laser (MB) at 894 nm; ${\mathrm{D}}_2\mathrm{L}$ (DB), detection laser at 852 nm; A, attenuator; C, single mode, polarization maintaining $2\times 2$ fiber coupler; L, lens, BS, beam splitter, Pol, polarizer; WP, multiorder wave plate acting as quarter-$\lambda$ plate for 894 nm and as a full-$\lambda$ plate for 852 nm; NF, neutral filter; Cs-Ne, cesium cell with buffer gas; IF, interference filter stopping 894 nm; W, Wollaston analyzer; BP, balanced polarimeter for polarization rotation detection, which includes photo diodes and a differential transimpedance amplifier; LIA, lock-in amplifier. In the monitor (MNT) channel, Cs (the cesium vacuum cell) and FP (the Fabry-Pérot interferometer) are used to monitor the radiation parameters.

Figure 2

Simplified level scheme of the Cs $D_1$ line. The frequency of the $F_g=3\to F_e=4$ transition is labeled ${\omega }_0$. The instantaneous detuning $\delta \left(t\right)$ of the MB is outlined. Notice that $\delta$ is varied by a large amount so that the MB radiation can become resonant with each transition. The DB radiation monitors the $F_g=4$ magnetization; it is resonant with the $D_2$ line and is not shown.

Figure 3

Comparison of theoretical and experimental signals as a function of ${\delta }_0/{\mathrm{\Delta }}_g$ in a regime of small modulation. For both plots the following values have been used in the model: $2\mathrm{\Delta }=0.5$ GHz, $r=0.5, \alpha =0.25, {\mathrm{\Delta }}_e=1.1$ GHz, and ${\mathrm{\Delta }}_g=9.2$ GHz. The plots show magnetic resonance amplitudes as obtained with (a) low buffer-gas pressure (2 Torr Ar) and (b) high buffer-gas pressure (90 Torr Ne). Correspondingly, $G=200$ MHz and $G=500$ MHz are used in the simulations. In (b) we also report for comparison the model output obtained with $\alpha =0$.

Figure 4

Comparison of theoretical and experimental signals as a function of ${\delta }_0$ in the intermediate regime. The following values have been used: $G=0.5$ GHz, $2\mathrm{\Delta }=5.6$ GHz, ${\mathrm{\Gamma }}_c^{\prime }/\mathrm{\Gamma }=0.5, \alpha =0.25, {\mathrm{\Delta }}_e=1.1$ GHz, and ${\mathrm{\Delta }}_g=9.2$ GHz.

Figure 5

Comparison between theoretical and experimental signals as a function of ${\delta }_0$ in the regime with $2\mathrm{\Delta }\gg {\mathrm{\Delta }}_g$. The following values have been used: $G=0.5$ GHz, $2\mathrm{\Delta }=20.0$ GHz, ${\mathrm{\Gamma }}_c^{\prime }/\mathrm{\Gamma }=0.5, \alpha =0.20, {\mathrm{\Delta }}_e=1.1$ GHz, and ${\mathrm{\Delta }}_g=9.2$ GHz.

Figure 6

Typical profile obtained from the excitation of a single transition. The peaks are located in correspondence with ${\delta }_0\approx \pm \mathrm{\Delta }$ for $G/\mathrm{\Delta }\lesssim 1$. At larger values of $G$ the peaks broaden and start shifting in opposite directions.