Measurement of hyperfine coupling constants in the 3dt2 Dj levels of K39 , K40 , and K41 by polarization quantum-beat spectroscopy

Abstract

Hyperfine quantum-beat spectroscopy has been utilized in a pump-probe configuration to measure magnetic dipole (A) and electric quadrupole (B) coupling constants in the 3d${\mathrm{}}^{2}$${\mathrm{D}}_{3\mathrm{/}2}$ and 3d${\mathrm{}}^{2}$${\mathrm{D}}_{5\mathrm{/}2}$ levels of three isotopes of potassium. For many of these levels, the largest hyperfine splitting is smaller than the natural width, and so a subnatural linewidth technique is required. In the experiments, the 3d levels are excited on the 4d${\mathrm{}}^{2}$${\mathrm{S}}_{1\mathrm{/}2}$\ensuremath{\rightarrow}3d${\mathrm{}}^{2}$${\mathrm{D}}_{\mathrm{j}}$ quadrupole transition with linearly polarized light. Time evolution of the alignment components in the d levels is probed by time-delayed resonant radiation on the 3d${\mathrm{}}^{2}$${\mathrm{D}}_{\mathrm{j}}$\ensuremath{\rightarrow}9p${\mathrm{}}^{2}$${\mathrm{P}}_{\mathrm{j}}$ transitions. Comparison of the excitation rate for two orthogonal relative polarization directions of the pump and probe laser at each delay time permits derivation of a linear polarization degree. This quantity contains beats at the various hyperfine frequencies in the d levels. Fitting the experimentally obtained time dependence to theoretical expressions allows extraction of the hyperfine coupling constants. For the 3d${\mathrm{}}^{2}$${\mathrm{D}}_{3\mathrm{/}2}$ level of $^{40}\mathrm{K}$ we obtain A=0.96(4) MHz and B=0.37(8) MHz, indicating a typical precision also obtained for the other levels and isotopes.