Millimeter-wave resonance spectroscopy has been used to measure the
(n+2)d5∕2 to
nf5∕2,7∕2 transition frequencies of cold
85Rb atoms in a magneto-optical trap. From these intervals we extract substantially improved Rb
nf quantum defects, fine structure intervals, and limits for the dipole and quadrupole polarizabilities of
Rb+.
We carry out a systematic study of the static and dynamic polarizabilities of the potassium atom using a first-principles high-precision relativistic all-order method in which all single, double, and partial triple excitations of the Dirac-Fock wave functions are included to all orders of perturbation theory. Recommended values are provided for a large number of electric-dipole matrix elements. Static polarizabilities of the 4s, 4p_j, 5s, 5p_j, and 3d_j states are compared with other theory and experiment where available. We use the results of the polarizability calculations to identify magic wavelengths for the 4s-np transitions for
n=4,5, i.e. those wavelengths for which the two levels have the same ac Stark shifts. These facilitate state-insensitive optical cooling and trapping. The magic wavelengths for the
4s−5p transitions are of particular interest for attaining a quantum gas of potassium at high phase-space density. We find 20 such wavelengths in the technically interest region of 1050-1130 nm. Uncertainties of all recommended values are estimated.
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.
Transitions between high Rydberg states of
133Cs atoms have been studied by high-resolution millimeter-wave spectroscopy of an ultracold sample. The spectroscopic measurements were performed after releasing the atoms from a magneto-optical trap. Switching off all trapping fields and compensating the stray electric and magnetic fields to below 1 mV/cm and 2 mG, respectively, prior to the spectroscopic measurement enabled the recording of millimeter-wave spectra of Rydberg states with principal quantum number beyond
n=100 under conditions where the inhomogeneous broadening by stray fields is minimal and no dephasing of the Rydberg-atom sample can be detected over measurement times up to 60 $\ensuremath{\mu}$s. The Fourier-transform-limited line widths of better than 20 kHz enabled the observation of the hyperfine structure of
nS and
nP Rydberg states of Cs beyond
n=90. The analysis of the line shapes of transitions to Rydberg states with $n\ensuremath{\approx}230$ indicated that field inhomogeneities across the atomic sample represent the dominant cause of spectral broadening at high
n values. The analysis also revealed that the initial polarization of the atomic sample (
F=4,
MF=4) is preserved for several tens of microseconds, the depolarization being caused by slow precession along the magnetic stray fields.
We demonstrate resonant detection of rf electric fields from 240 to 900 MHz (very high frequency to ultrahigh frequency) using electromagnetically induced transparency to measure orbital angular momentum $L=3\ensuremath{\rightarrow}{L}^{\ensuremath{'}}=4$ Rydberg transitions. These Rydberg states are accessible with three-photon infrared optical excitation. By resonantly detecting rf in the electrically small regime, these states enable a new class of atomic receivers. We find good agreement between measured spectra and predictions of quantum defect theory for principal quantum numbers
n=45 to 70. Using a superhetrodyne detection setup, we measure the noise floor at
n=50 to be $13\phantom{\rule{0.16em}{0ex}}\textmu{}\mathrm{V}/(\mathrm{m}\sqrt{\mathrm{Hz}})$. Additionally, we utilize data and a numerical model incorporating a five-level master equation solution to estimate the fundamental sensitivity limits of our system.
Millimeter resonances corresponding to single- and double-photon transitions have been observed between Rydberg levels of sodium with principal quantum number
n ranging from 23 to 41. The levels are prepared by laser excitation; transitions are induced by microwaves produced by a backwave oscillator working around 300 GHz; detection is performed through the selective field-ionization technique. Experimental values for quantum defects, fine-structure intervals, and polarizabilities are reported.