Microwave transitions and nonlinear magneto-optical rotation in anti-relaxation-coated cells

Using laser optical pumping, widths and frequency shifts are determined for microwave transitions between ground-state hyperfine components of ${}^{85}\mathrm{Rb}$ and ${}^{87}\mathrm{Rb}$ atoms contained in vapor cells with alkane antirelaxation coatings. The results are compared with data on Zeeman relaxation obtained in nonlinear magneto-optical rotation experiments, a comparison important for quantitative understanding of spin-relaxation mechanisms in coated cells. By comparing cells manufactured over a $40\text{‐}\text{year}$ period we demonstrate the long-term stability of coated cells, an important property for atomic clocks and magnetometers.

Figure 1

Experimental setup for measuring microwave transitions.

Figure 2

Examples of the microwave spectra recorded with the Ale-10 ${}^{85}\mathrm{Rb}$ cell (see Table ). The signal corresponds to the intensity of the laser light transmitted through the cell. The common parameters for the three scans are dc magnetic $\text{field}=29\mathrm{mG}$, linear light polarization, laser tuned to the center of the $F=3\to F^{\prime }$ transition, total scan rate (sawtooth sweep) $=0.02\mathrm{Hz}$. Each plot represents an average of approximately five scans. Upper and middle plots: input light power $0.25\mu \mathrm{W}$. Lower plot: input light power $13\mu \mathrm{W}$, microwave power reduced by a factor $\approx 63$. The lower plot also shows a fit by a Lorentzian superimposed on a linear background. The fit Lorentzian linewidth [full width at half maximum (FWHM)] is $10.9\left(3\right)\mathrm{Hz}$, slightly larger than the “intrinsic” width of about $8.7\mathrm{Hz}$ (Table ) due to residual light broadening (see text).

Figure 3

An example of a microwave spectrum recorded with the TT11 ${}^{87}\mathrm{Rb}$ cell (see Table ). The parameters for the scan are dc magnetic $\text{field}=2.7\mathrm{mG}$, linear light polarization, laser tuned to the center of the $F=2\to F^{\prime }$ transition, total scan rate $\left(\text{saw}\text{‐}\text{tooth}\text{sweep}\right)=0.2\mathrm{Hz}$. The plot represents a single scan. Input light $\text{power}=6\mu \mathrm{W}$. The comparison of this plot with the middle plot in Fig. 2 illustrates the advantages of using a ${\mathrm{TE}}_{011}$ microwave cavity as opposed to a current loop: almost complete suppression of the broad pedestal and the $\Delta M_F\ne 0$ microwave transitions.

Figure 4

Simplified schematic of the experimental setup for measuring Zeeman relaxation rate with the FM NMOR technique [23, 24, 25].

Figure 5

An example of the FM NMOR data (the lock-in detector output; see Fig. 4) taken with the Ale-10 cell. The central frequency of the laser is tuned $\approx 400\mathrm{MHz}$ lower than the center of the $F=3\to F^{\prime }$ absorption peak of the $D1$ line (this point corresponds to a maximum of the FM NMOR signal). The laser frequency is modulated with an amplitude of $290\mathrm{MHz}$. A bias magnetic field of $156\mu \mathrm{G}$ is applied along the light-propagation direction. The data are shown along with a fit by a dispersive Lorentzian (see Ref. 25). The width of the resonance corresponds to ${\gamma }_{\mathit{expt}}^{\mathit{NMOR}}=2\pi \times 0.7\mathrm{Hz}$, the narrowest magneto-optical resonance width observed with alkali-metal atoms to date.