Abstract We present an experimental investigation of the Rydberg 23P 1/2 state of single, laser-cooled 40 Ca + ions in a radiofrequency ion trap. Using micromotion sideband spectroscopy on a narrow quadrupole transition, the oscillating electric field at the ion position was precisely characterised, and the modulation of the Rydberg transition due to this field was minimised. From a correlated fit to this P line and previously measured P and F level energies of Ca II, we have determined the ionization energy of 95 751.916(32) cm −1 , in agreement with the accepted value, and the quantum defect for the n P 1/2 states.
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.
Highly excited Rydberg states of lanthanides are a promising, yet largely unexplored, playground for quantum studies. Here, we report on the first high-resolution spectroscopy of 162Dy obtained by two-color trap depletion spectroscopy in a magneto-optical trap. The absolute excitation frequency of over 700 states with effective principal quantum number n between 21 and 130 is measured with an accuracy of 20 MHz. Most states are assigned to the 8 different series converging to the first 4f10(5I8)6s(2S1/2) J = 17/2 ionization potential. This energy is measured at EIP = 47901.8265 +/- 0.0008 cm-1, improving the precision of the literature value by over an order of magnitude. A multichannel quantum defect theory approach is used to benchmark and refine the assignments and to characterize six observed perturbing states belonging to higher ionization limits. These results pave the way for using dysprosium in Rydberg-based quantum architectures, leveraging the unique properties arising from its complex electronic structure. They also represent a compelling benchmark for ab-initio calculations of open-shell atomic systems.
We present a method for measuring the polarizability of Rydberg ions confined in the harmonic potential of a Paul trap. For a highly excited electronic state, the coupling between the electronic wave function and the trapping field modifies the excitation probability depending on the motional state of the ion. This interaction strongly depends on the polarizability of the excited state and manifests itself in the state-dependent secular frequencies of the ion. We initialize a single trapped
40Ca
+ ion from the motional ground state into coherent states with
∣α∣ up to 12 using electric voltages on the trap segments. The internal state, firstly initialised in the long-lived 3D
5/2 state, is excited to a Rydberg S
1/2-state via the 5P
3/2 state in a two-photon process. We probe the depletion of the 3D
5/2 state owing to the Rydberg excitation followed by a decay into the internal ground 4S
1/2 state. By analysing the obtained spectra we extract the polarizability of Rydberg states which agree with numerical calculations. The method is easy-to-implement and applicable to different Rydberg states regardless of their principal or angular quantum numbers. An accurate value of the state polarizability is needed for quantum gate operations with Rydberg ion crystals.
We compute the Rydberg spectrum of a single
Ca+ ion in a Paul trap by incorporating various internal and external coupling terms of the ion to the trap in the Hamiltonian. The coupling terms include spin-orbit coupling in
Ca+, charge (electron and ionic core) coupling to the radio frequency and static fields, ion-electron coupling in the Paul trap, and ion center-of-mass coupling. The electronic Rydberg states are precisely described by a one-electron model potential for ${e}^{\ensuremath{-}}+{\mathrm{Ca}}^{2+}$, and accurate eigenenergies, quantum defect parameters, and static and tensor polarizabilities for a number of excited Rydberg states are obtained. The time-periodic rf Hamiltonian is expanded in the Floquet basis, and the trapping-field-broadened Rydberg lines are compared with recent observations of
Ca+(23P) and
Ca+(52F) Rydberg lines.
Abstract We present a method for measuring the polarizability of Rydberg ions confined in the harmonic potential of a Paul trap. For a highly excited electronic state, the coupling between the electronic wave function and the trapping field modifies the excitation spectra depending on the motional state of the ion. This interaction strongly depends on the polarizability of the excited state and manifests itself in the state-dependent secular frequencies of the ion. We initialize a single trapped 40 Ca + ion from the motional ground state into coherent states with | α | up to 12 using electric voltages on the trap segments. The internal state, firstly initialised in the long-lived 3D 5 / 2 state, is excited to a Rydberg S 1 / 2 -state via the 5P 3 / 2 state in a two-photon process. We probe the depletion of the 3D 5 / 2 state owing to the Rydberg excitation followed by a decay into the internal ground 4S 1 / 2 state. By analysing the obtained spectra we extract the polarizability of Rydberg states which agree with numerical calculations. The method is applicable to different Rydberg states regardless of their principal or angular quantum numbers. An accurate value of the state polarizability is needed for quantum gate operations with Rydberg ion crystals.