Backward-emitted sub-Doppler fluorescence from an optically thick atomic vapor

Literature mentions only incidentally a sub-Doppler contribution in the excitation spectrum of the backward fluorescence of a dense vapor. This contribution is here investigated on Cs vapor, both on the first resonance line (894 nm) and on the weaker second resonance line (459 nm). We show that in a strongly absorbing medium, the quenching of excited atoms moving towards a window irradiated under near normal incidence reduces the fluorescence on the red side of the excitation spectrum. Atoms moving slowly towards the window produce a sub-Doppler velocity-selective contribution, whose visibility is here improved by applying a frequency-modulation technique. This sub-Doppler feature, induced by a surface quenching combined with a short absorption length for the incident irradiation, exhibits close analogies with the narrow spectra appearing with thin vapor cells. We also show that a normal incidence irradiation is essential for the sub-Doppler feature to be observed, while it should be independent of the detection geometry.

Figure 1

Scheme of relevant Cs levels, showing the first and second resonance lines (894 and 459 nm, respectively) with the most relevant transitions for fluorescence. The $7P$ level decays to $7S$ (with further cascades in the IR to $6P$, detectable in our setup) or to $5D$ (detectable IR fluorescence), or along the second resonance itself at 459 nm, with respective branching ratios of $\sim 50\%,\sim 20\%$, and $\sim 30\%$.

Figure 2

Schematic of the experimental setup. The nearly resonant laser is sent onto the vapor cell close to the normal incidence, here shown as a dashed line, and is rapidly absorbed by the dense vapor. The emitted fluorescence is focused onto the photodetector (solid angle $\sim {10}^{-2}\mathrm{sr}$) and possibly filtered in wavelength. The signal from the photodetector can be processed with a lock-in amplifier (for “FM fluorescence”).

Figure 3

Excitation frequency spectrum of the backward-emitted fluorescence on the $\mathrm{Cs}{D}_1$ line (894 nm) around the $F=4\to F^{\prime }=\{3,4\}$ hyperfine components (splitting 1.17 GHz). On top is the direct fluorescence for the Cs reservoir at $130{}^{\circ }\mathrm{C}(\sim 8\times {10}^{13}\mathrm{at}\mathrm{c}{\mathrm{m}}^{-3})$; the middle is the corresponding simultaneous recording of the FM signal; and the bottom is the zoomed FM signal, with the two additional Cs temperatures $120{}^{\circ }\mathrm{C}(\sim 5\times {10}^{13}\mathrm{at}\mathrm{c}{\mathrm{m}}^{-3})$ and $150{}^{\circ }\mathrm{C}(\sim 2\times {10}^{14}\mathrm{at}\mathrm{c}{\mathrm{m}}^{-3})$. The experiment is performed on a Cs cell made of glass, the temperature of the window is $\sim 200{}^{\circ }\mathrm{C}$, and the frequency markers are provided by the corresponding auxiliary SA reference.

Figure 4

Excitation frequency spectrum of the backward-emitted fluorescence (filtered between 1.1 and 1.7 μm) on the Cs 459 nm around the $F=4\to F^{\prime }=\{3,4\}$ hyperfine components (splitting 377 MHz). On top is the direct fluorescence for the Cs reservoir at $170{}^{\circ }\mathrm{C}$, the middle is the corresponding simultaneous recording of the FM signal, and the bottom is a zoomed FM signal with the two additional Cs temperatures $180{}^{\circ }\mathrm{C}$ and $190{}^{\circ }\mathrm{C}$. The experiment is performed in a Cs cell ended by a sapphire window, whose temperature is $\sim 300{}^{\circ }\mathrm{C}$ (see [1]), and the frequency markers are provided by the corresponding auxiliary SA reference.

Figure 5

Predictions for $I_{\mathrm{fluo}}$ from Eq. (1) for various values of $\mathrm{\Lambda }/\tau$ as indicated. The light dotted (red) line assumes no quenching at all (or $\mathrm{\Lambda }/\tau \to \infty$), which is the standard situation for a (Doppler-broadened) Gaussian excitation line shape, while the light (black) dashed line is for a quenching affecting symmetrically $v$ and $-v$ atoms, in analogy with a thin cell, (see text), except in this last case the excitation line shape is unaffected on the blue side by the Λ/τ value. The numerical calculation assumes $\lambda =1\mu \mathrm{m},u=200\mathrm{m}/\mathrm{s},\tau =100\mathrm{ns}$, and $\gamma =10\mathrm{MHz}$ (i.e., $\gamma \ll \mathrm{ku}$), yielding 50 μm (red, dash-dotted), 20 μm (blue, dotted), 5 μm (black, full line), and 2 μm (green, dotted), respectively, for the absorption length Λ.

Figure 6

Predictions for $I_{\mathrm{fluo}}$ assuming in Eq. (1) that the absorption, maximal on-resonance ($\delta =0$), decreases with the frequency detuning δ according to a Voigt profile; see on the right part of the figure the variations of the absorption length Λ with the detuning. The spatial integration in Eq. (1) is limited to a depth of observation of 3 mm. The numerical values are $\lambda =1\mu \mathrm{m},u=200\mathrm{m}/\mathrm{s}$ (leading to $ku=200\mathrm{MHz}$), $\tau =30\mathrm{ns}$, and $\mathrm{\Lambda }(\delta =0)$ as indicated. One has chosen $\gamma =10\mathrm{MHz}$ for all thick lines, while the light (blue) dash-dotted line is for $\gamma =20\mathrm{MHz}$ and $\mathrm{\Lambda }(\delta =0)=20\mu \mathrm{m}$, showing that γ ($\ll ku$) plays a role only when the effective absorption length Λ(δ) becomes comparable to or larger than the observation depth. The optical thicknesses as governed by $\mathrm{\Lambda }(\delta =0)$ values are chosen for resembling the single path absorption on the $D_1$ line of Cs at $120{}^{\circ }\mathrm{C}$, $130{}^{\circ }\mathrm{C}$, and $150{}^{\circ }\mathrm{C}$, respectively (see Fig. 3).

Figure 7

Same as Fig. 6 for $d{I}_{\mathrm{fluo}}/d\delta$, which is the predicted FM signal for the excitation spectrum of fluorescence.