Nonlinear magneto-optical rotation in rubidium vapor excited with blue light

We present experimental and numerical studies of nonlinear magneto-optical rotation (NMOR) in rubidium vapor excited with resonant light tuned to the $5{}^2{S}_{1/2}\to 6{}^2{P}_{1/2}$ absorption line (421 nm). Contrary to the experiments performed to date on the strong $D_1$ or $D_2$ lines, in this case, the spontaneous decay of the excited state $6{}^2{P}_{1/2}$ may occur via multiple intermediate states, affecting the dynamics, magnitude, and other characteristics of NMOR. Comparing the experimental results with the results of modeling based on Auzinsh et al. [Phys. Rev. A 80, 053406 (2009)], we demonstrate that despite the complexity of the structure, NMOR can be adequately described with a model, where only a single excited-state relaxation rate is used.

Figure 1

Relevant energy states and transitions of Rb atoms excited by resonant radiation at 421.6 nm. The solid line indicates the excitation light, while the dashed lines indicate channels of spontaneous emission.

Figure 2

Experimental apparatus. P is the polarizer, WP denotes the Wollastone prism, $\lambda$/2 is the half-wave plate, L is the lens, DM denotes the dichroic mirror, I is the iris, FC stands for the fiber coupler, PD is the photodiode, and PM and MM stand for polarization-maintaining and multimode fiber, respectively.

Figure 3

Energy-level diagrams of the $5{}^2{S}_{1/2}\to 6{}^2{P}_{1/2}$ absorption line in ${}^{87}\mathrm{Rb}$ and ${}^{85}\mathrm{Rb}$.

Figure 4

Rotation of linearly polarized blue (a) and IR (b) light tuned to the ${}^{85}\mathrm{Rb}{F}_g=3\to F_e$ transition of the $5{}^2{S}_{1/2}\to 6{}^2{P}_{1/2}$ line and the ${}^{85}\mathrm{Rb}{F}_g=3\to F_e$ transition of the $5{}^2{S}_{1/2}\to 5{}^2{P}_{1/2}$ line, respectively. In both measurements, light intensities and beam diameters were the same $(1.9\mathrm{mW}/{\mathrm{cm}}^2$ and 1 mm, respectively), while temperature of the cell was $85{}^{\circ }\mathrm{C}$ for blue-light measurements and $23{}^{\circ }\mathrm{C}$ for IR measurements. The solid red curve superimposed on the data shown in (a) is the theoretical curve calculated using parameters extracted from the experiment (see text).

Figure 5

Widths of blue NMOR resonances measured as a function of average light intensity for two transitions $\mathrm{[}{F}_g=3\to F_e$ (black circles) and $F_g=2\to F_e$ (red triangle)] of the $5{}^2{S}_{1/2}\to 6{}^2{P}_{1/2}$ line. The error bars of the $F_g=2\to F_e$ points are much larger than those in the $F_g=3\to F_e$ case, as the former signals are much smaller, i.e., with worse signal-to-noise ratio. The solid black line is the constant value determined based on a weighted average of the individual results and its uncertainties marked with the shaded area are determined based on the propagation of uncertainties in such an approach (uncertainty in the determination of the parameter $k_{\gamma })$. Absence of the power broadening of the both resonances proves the weakly perturbing character of the interaction. The signals were measured at $85{}^{\circ }\mathrm{C}$ with beam diameter of 6 mm.

Figure 6

Amplitudes of NMOR signals measured versus the average intensity of light tuned to different hyperfine ground states of ${}^{85}\mathrm{Rb}$. The experimental data are in agreement with theory (solid lines). The signals were measured at $85{}^{\circ }\mathrm{C}$ with 6-mm beam diameter. The shaded areas mark the uncertainty due to the limited precision of ${\kappa }_{\mathrm{\Omega }}$-parameter determination.

Figure 7

Amplitude (a) and width (b) of blue NMOR signal measured versus average light intensity for three iris apertures (i.e., for different beam diameters and profiles). All three experimental data sets reveal good agreement (all $R^2>0.95)$ with the theory (solid lines). The signals were measured for the laser tuned to the $F_g=3\to F_e$ transition of ${}^{85}\mathrm{Rb}$.

Figure 8

(a) Measured and simulated NMOR spectra recorded for a magnetic field of about 8 mG and light intensity of $0.1\mathrm{mW}/{\mathrm{cm}}^2$ and (b) rotation spectra measured for different magnetic fields and same light intensity (0.1 mW/${\mathrm{cm}}^2)$. The signals were obtained for light frequency scanned across all transitions of the $5{}^2{S}_{1/2}\to 6{}^2{P}_{1/2}$ line.

Figure 9

Schematic depicting the effect of an iris on the light-intensity profile of light used in the experiment. For the iris openings significantly larger than the beam diameter (half-width at half maximum), the real profile strongly deviates from the top-hat function. At the same time, the small openings result in a profile close to the top-hat profile.