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arXiv:1907.02776 · Physical Review A

Precision measurement of the ionization energy and quantum defects of K39 i

Michael Peper, Felix Helmrich, Jonas Butscher, Josef A. Agner, Hansjürg Schmutz, Frédéric Merkt, Johannes Deiglmayr

Published Jul 2, 2019• 27 citations
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Abstract

We present absolute-frequency measurements in ultracold $^{39}\mathrm{K}$ samples of the transitions from the $4{s}_{1/2}$ ground state to $n{p}_{1/2}$ and $n{p}_{3/2}$ Rydberg states. A global nonlinear regression of the $n{p}_{1/2}$ and $n{p}_{3/2}$ term values yields an improved wave number of 35009.8139710(22)${}_{\mathrm{sys}}{(3)}_{\mathrm{stat}}\phantom{\rule{4pt}{0ex}}{\mathrm{cm}}^{\ensuremath{-}1}$ for the first ionization threshold of $^{39}\mathrm{K}$ and the quantum defects of the $n{p}_{1/2}$ and $n{p}_{3/2}$ series. In addition, we report the frequencies of selected one-photon transitions ${n}^{\ensuremath{'}}{s}_{1/2}\ensuremath{\leftarrow}n{p}_{3/2}, {n}^{\ensuremath{'}}{d}_{j}\ensuremath{\leftarrow}n{p}_{3/2}, {n}^{\ensuremath{'}}{f}_{{j}^{\ensuremath{'}}}\ensuremath{\leftarrow}n{d}_{j}$, and ${n}^{\ensuremath{'}}{g}_{{j}^{\ensuremath{'}}}\ensuremath{\leftarrow}n{f}_{j}$ and two-photon transitions $n{f}_{{j}^{\ensuremath{'}}}\ensuremath{\leftarrow}n{p}_{j}$ determined by millimeter-wave spectroscopy, where $j$ is the total angular-momentum quantum number. By combining the results from the laser and millimeter-wave spectroscopic experiments, we obtain improved values for the quantum defects of the ${s}_{1/2}, {d}_{3/2}, {d}_{5/2}, {f}_{j}$, and ${g}_{j}$ states. For the ${d}_{j}$ series, the inverted fine structure was confirmed for $n\ensuremath{\ge}32$. The fine-structure splitting of the $f$ series is less than 100 kHz at $n=31$, significantly smaller than the hydrogenic splitting, and the fine structure of the $g$ series is regular for $n\ensuremath{\ge}30$, with a fine-structure splitting compatible with the hydrogenic prediction. From the measured quantum defects of the $f$ and $g$ series we derive an estimate for the static dipole ${\ensuremath{\alpha}}_{\mathrm{d}}$ and quadrupole ${\ensuremath{\alpha}}_{\mathrm{q}}$ polarizabilities of the ${\mathrm{K}}^{+}$ ion core. Additionally, the hyperfine splitting of the $4{s}_{1/2}$ ground state of $^{39}\mathrm{K}$ was determined to be 461.719700(5) MHz using radio-frequency spectroscopy and Ramsey-type interferometry.

DOI
10.1103/physreva.100.012501

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