Nonlinear magneto-optical rotation and Zeeman and hyperfine relaxation of potassium atoms in a paraffin-coated cell

Nonlinear magneto-optical Faraday rotation (NMOR) on the potassium D1 and D2 lines was used to study Zeeman relaxation rates in an antirelaxation paraffin-coated $3\text{−}\mathrm{cm}$-diameter potassium vapor cell. Intrinsic Zeeman relaxation rates of ${\gamma }^{NMOR}∕2\pi =2.0\left(6\right)\mathrm{Hz}$ were observed. The relatively small hyperfine intervals in potassium lead to significant differences in NMOR in potassium compared to rubidium and cesium. Using laser optical pumping, widths and frequency shifts were also determined for transitions between ground-state hyperfine sublevels of ${}^{39}\mathrm{K}$ atoms contained in the same paraffin-coated cell. The intrinsic hyperfine relaxation rate of ${\gamma }_{\mathit{expt}}^{\mathit{hf}}∕2\pi =10.6\left(7\right)\mathrm{Hz}$ and a shift of $-9.1\left(2\right)\mathrm{Hz}$ were observed. These results show that adiabatic relaxation gives only a small contribution to the overall hyperfine relaxation in the case of potassium, and the relaxation is dominated by other mechanisms similar to those observed in previous studies with rubidium.

Figure 1

Hyperfine splitting of low-lying levels of ${}^{39}\mathrm{K}$.

Figure 2

Schematic diagram of experimental setup for measurement of nonlinear magneto-optical rotation. For the measurement of the transitions between hyperfine levels, the balanced polarimeter was replaced with a single photodiode. An rf loop was introduced next to the vapor cell through one of the ports in the magnetic shield.

Figure 3

(Color online) Faraday rotation for the D1 transition. The data were fit to a dispersive function. The width of the fit is $12.6\mu \mathrm{G}$; the laser light power was $10.7\mu \mathrm{W}$.

Figure 4

Extrapolated NMOR widths for D1 transition. The intercept $B=2.9\left(9\right)\mu \mathrm{G}$ of the fit gives the intrinsic relaxation rate. The error bars were increased to obtain ${\chi }_{\text{reduced}}^2=1$.

Figure 5

(Color online) Nested Faraday rotation feature for D1 signal at a light power of $115\mu \mathrm{W}$. The origin of the narrow central feature is interaction of the light with the hyperfine transitions that are further away in frequency from where the laser is tuned than the transitions contributing to the larger and broader feature. These further-away transitions experience less power broadening. The sign of an FM NMOR feature is determined by several factors, including laser tuning with respect to a resonance, hyperfine structure of the transitions, and the sign of the ground-state $g$ factor (opposite for the two ground-state hyperfine components).

Figure 6

An example of the rf-spectrum recording showing resolved Zeeman components of the hyperfine-structure transition in a mG-sized field. The central peak corresponds to the 0-0 clock transition. Light power: $30\mu \mathrm{W}$; rf power: $500\text{units}$ used in Fig. 10, and the resonances are strongly power broadened.

Figure 7

Example of a measured spectrum of the isolated 0-0 transition. Light power: $12\mu \mathrm{W}$; rf power: $35\text{units}$ used in Fig. 10. The plot represents an average of approximately 50 scans. The fit Lorentzian linewidth is $47.2\mathrm{Hz}$ (full width of half maximum), larger than the “intrinsic” width of $10.6\mathrm{Hz}$ due to residual light- and rf-power broadening.

Figure 8

Experimental results for the shift of the frequency of the 0-0 clock transition from its free-space value. The plot shows all the results obtained with different light and rf powers; no systematic dependence on these parameters was observed. Negative shift means that, in the paraffin-coated cell, the hyperfine transition frequency is lower than that for an atom in free space. Error bars represent the uncertainty obtained from an individual fit. The spread of the points exceeds what would be expected from the size of these error bars, presumably due to slow drifts of experimental parameters (such as cell temperature) that may result in apparent shift of the line.

Figure 9

Linewidths measured for different laser and rf powers. The fit lines correspond to performed extrapolation of the linewidth to zero in the light power. The zero-power widths were used to perform extrapolation in rf power, see Fig. 10.

Figure 10

Extrapolation to zero rf power of the zero-light-power values of the rf-transition width (see Fig. 9).