Probe-intensity dependence of velocity-selective polarization spectra at the rubidium $D_2$ manifold and comparison with a rate-equation calculation

We present a detailed study of the effect of a strong and circularly polarized coupling beam on a probe beam locked to a hyperfine transition of the rubidium $D_2$ manifold. Experiments were carried out in the co- and counterpropagating configurations. Counterpropagating beams are used to study the effect of the probe beam intensity on absorption and polarization spectra. These data are compared with results of a rate-equation calculation. The absorption spectra show very clear indication of saturation, with different saturation intensities for each atomic line. The slope of the dispersionlike profile of the polarization signal increases with the intensity of the probe beam. These results are in very good agreement with the calculation. Experimental absorption and polarization spectra in the copropagating configuration are also well reproduced by the rate-equation calculation. The dispersion profiles in the polarization signal can be used to lock the coupling laser frequency at well defined frequencies.

Figure 1

Experimental setup for polarized velocity selective spectroscopy. ECL: extended cavity laser; OI: optical isolator; PBS: polarizing beam splitter; M: mirror, BS: beam splitter; PD: photodiode; $\lambda /2$: half-wave plate; $\lambda /4$: quarter-wave plate. The paths of the probe and pump light beams are respectively represented by the long and short dashed lines.

Figure 2

Comparison between experiment and theory for counterpropagating, polarized velocity selective spectra in ${}^{87}$Rb. (a) Sum and (b) difference spectra obtained in the region of the $F=2\to F^{\prime }$ transitions. (c) Sum and (d) difference spectra obtained in the region of the $F=1\to F^{\prime }$ transitions. The calculated spectra are shown as continuous lines. The transition frequencies obtained from Ref. [9] are indicated by vertical lines.

Figure 3

Sum spectra for ${}^{85}$Rb in the high F region and for eight different values of the probe beam saturation parameter $s_0$. The coupling beam power was fixed to $100\mu$W and the probe beam power was set to $\{30.0,49.9,70.3,90.5,101.0,110.0,130.0,149.0\}\mu \mathrm{W}$. Left panel: experimental spectra. Right panel: calculated spectra obtained using a 25 MHz linewidth and an effective saturation intensity of $I_s^{\prime }=234.6\mathrm{W}/{\mathrm{m}}^2$. For details about the saturation parameter determination, see text.

Figure 4

On-resonance height of the three atomic transitions in Fig. 3 as a function of the probe saturation parameter $s_0=I/I_s$. For comparison purposes, the effective saturation intensity $I_s^{\prime }=234.6\mathrm{W}/{\mathrm{m}}^2$ was used in the bottom axis and the cycling transition saturation intensity $I_s=16.69\mathrm{W}/{\mathrm{m}}^2$ in the top axis. The dots are the experimental data, and lines are the results of the calculation. The error bars associated to the experimental data are in all cases within the size of the symbols.

Figure 5

Dependence on the probe intensity of the difference spectra for ${}^{85}$Rb. Top: experimental data. Bottom: calculated spectra.

Figure 6

Relation between velocity and frequency for the copropagating sum and difference (panels c and d respectively) VSOP spectra in ${}^{87}$Rb. While the probe beam represented by the solid line in panel (b) selects three velocities, one for each transition ($F=2\to F^{\prime }$), the coupling beam, shown in panel (b) as a set of dashed lines, scans the three velocity groups given by the positions of spectra lines on the frequency axis. The relative weights of the contributions of each velocity group is depicted in panel (a). The straight lines in panel (b) are labeled in accordance with the notation used in Table 2.

Figure 7

Velocity selective spectra for copropagating beams in ${}^{85}$Rb. Left panels: spectra obtained in the region of the $F=3\to F^{\prime }$ transitions. Right panels: spectra obtained in the region of the $F=2\to F^{\prime }$ transitions. Lower panels: sum of the photodiode signals. Top panels: difference of the photodiode signals. The positions of the atomic transitions and crossover lines are indicated by vertical lines. The labels of Table 1 are used to identify the transitions.

Figure 8

Velocity selective spectroscopy for copropagating in ${}^{87}$Rb. Left panels: results in the region of the $F=2\to F^{\prime }$ transitions. Right panels: results in the region of the $F=1\to F^{\prime }$ transitions. Laser 1 was locked to the $2\to 3$ cyclic transition. Bottom: sum of signals detected at both photodiodes. Top: difference of signals detected with the photodiodes. The position of the atomic transitions and crossover lines is indicated by vertical lines. The labels of Table 2 are used to identify the transitions.