Using a laser-excitation, optical-detection scheme, we have observed microwave transitions from the
nd to the
nf and
ng orbital levels in lithium states with principal quantum number
n from 7 to 11. These measurements yield precise values for the
d,
f, and
g state fine-structure intervals as well as $d\ensuremath{-}f$ and $d\ensuremath{-}g$ energy separations. Within the accuracy of these measurements, the fine structures are found to be hydrogenic. The dipole polarizability of the
Li+ core is determined from the $d\ensuremath{-}f$ and $d\ensuremath{-}g$ energy splittings. The $d\ensuremath{-}f$ intervals are compared to pseudopotential calculations.
The spectra of Rydberg atoms are of great significance for studying the energy levels of Rydberg atoms and the interaction between neutral atoms, especially, the high-precision spectra of Rydberg atoms can be used to measure the energy level shifts of Rydberg atoms resulting from the dipole-dipole interactions in room-temperature vapor cells. In this paper we report the preparation of cesium Rydberg states based on the cascaded two-photon excitation of 509 nm laser and 852 nm laser in opposite, and the measurements of the fine structure of cesium Rydberg states. In this experiment, the 509 nm laser is generated by the cavity-enhanced second-harmonic generation from 1018 nm laser with a periodically-poled KTP crystal and has a maximum power of about 1 W, and the 852 nm probe laser is provided by an external-cavity diode laser with a maximum output power of 5 mW and a typical linewidth of 1 MHz. By scanning the frequency of 509 nm coupling laser, it is presented that the Doppler-free spectra based on electromagnetically-induced transparency (EIT) of 509 nm coupling laser and 852 nm probe laser. The velocity-selective EIT spectra are used to study the spectral splitting of 6S1/26P3/257S(D) ladder-type system of cesium Rydberg atoms in a room-temperature vapor cell. The powers of 852 nm probe laser and 509 nm coupling laser are 0.3 upW and 200 mW, respectively. Their waist radii are both approximately 50 m. The intervals of hyperfine splitting of the intermediate state 6P3/2(F'=3, 4, 5) and fine splitting of 57D3/2 and 57D5/2 Rydberg states are measured by a frequency calibrating. Concretely, the velocity-selective spectrum with a radio frequency (RF) modulation of 30 MHz is used as a reference to calibrate the Rydberg fine-structure states in the hot vapor cell, where the RF frequency precision is smaller than a hertz on long time scales and the EIT linewidth is smaller than 13 MHz. The experimental value of the fine structure splitting of 57D3/2 and 57D5/2 Rydberg states is (354.72.5) MHz, that is in consistence with the value of 346.8 MHz calculated by Rydberg-Ritz equation and quantum defects of 57D3/2 and 57D5/2 Rydberg states. The experimental values of hyperfine splitting of intermediate state 6P3/2(F'=3, 4, 5) are also coincident with the theoretical calculated values. The dominant discrepancy existing between the experimental and calculated results may arise from the nonlinear correspondence of the PZT while the 509 nm wavelength cavity is scanned, and the measurement accuracy influenced by the spectral linewidth. The velocity-selective spectroscopy technique can also be used to measure the energy level shifts caused by the interactions of Rydberg atoms.
We present calculations of high Rydberg states for the lithium atom by two different theoretical methods. The first method is based on the
R-matrix theory to obtain the energy levels and the quantum defects for the
1s2nd2D and
1s2nf2F states and their adjacent continuum states. Then the quantum defect functions of the two channels are obtained which vary smoothly with energy based on quantum defect theory. The second method is based on the full core plus correlation method. Our results are compared with data in the literatures; especially the results of the
R-matrix method are in excellent agreement with microwave measurements for the lithium atom.
We present absolute-frequency measurements in ultracold
39K samples of the transitions from the
4s1/2 ground state to
np1/2 and
np3/2 Rydberg states. A global nonlinear regression of the
np1/2 and
np3/2 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
39K and the quantum defects of the
np1/2 and
np3/2 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
s1/2,d3/2,d5/2,fj, and
gj states. For the
dj 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
K+ ion core. Additionally, the hyperfine splitting of the
4s1/2 ground state of
39K was determined to be 461.719700(5) MHz using radio-frequency spectroscopy and Ramsey-type interferometry.
The technique of level-crossing spectroscopy has been used to measure the fine-structure intervals in the
33P state of
4He through the observation of the level crossings at 2277 and 3700 G. The magnetic fields at the crossing points were used in conjunction with calculated
g values to obtain for the $3^{3}P_{0}\ensuremath{-}3^{3}P_{2}$ fine-structure interval the value 8772.552 \ifmmode\pm\else\textpm\fi{} 0.040 MHz (4.5 ppm). These same data yielded for the lifetime of the
33P state the value 97.6 \ifmmode\pm\else\textpm\fi{} 4.5 nsec and for the cross section for coherence-destroying collisions the value $(718\ifmmode\pm\else\textpm\fi{}78)\ensuremath{\pi}{a}_{0}^{2}$.