Piet O. Schmidt

Single-ion optical clocks have shown systematic frequency uncertainties below 10 − 18 , but typically require more than one week of averaging to achieve a corresponding statistical uncertainty. This time can be reduced with longer probe times, but comes at the cost of a higher time-dilation shift due to motional heating of the ions in the trap. We show that sympathetic ground-state cooling using electromagnetically induced transparency of an Al + clock ion via a cotrapped Ca + ion during clock interrogation suppresses the heating of the ions. Al + can be kept close to the motional ground state, independent from the chosen interrogation time, at a relative time-dilation shift of ( − 1.69 ± 0.20 ) × 10 − 18 . The Ca + cooling light introduces an additional light shift on the Al + clock transition of ( − 9.3 ± 1.1 ) × 10 − 18 . We project that the uncertainty of this light shift can be further reduced by nearly an order of magnitude. This sympathetic cooling enables seconds of interrogation time with 10 − 19 motional and cooling laser-induced uncertainties for Al + and can be employed in other ion clocks as well.

We report the sympathetic cooling and Coulomb crystallization of xenon highly charged ions (HCIs) with laser-cooled Ca + ions. The HCIs are produced in a compact electron beam ion trap, then charge selected, decelerated, and finally injected into a cryogenic linear Paul trap. There, they are captured into Ca + 40 Coulomb crystals, and cocrystallized within them, causing dark voids in their fluorescence images. Fine control over the number of trapped ions and HCIs allows us to realize mixed-species crystals with arbitrary ordering patterns. By investigating Xe q + − Ca + strings, we confirm the HCI charge states, measure their lifetime, and characterize the mixed-species motional modes. Our system effectively combines the established quantum control toolbox for Ca + with the rich set of atomic properties of Xe highly charged ions, providing a resourceful platform for optical frequency metrology, searches for signatures of new physics, and quantum information science.

In quantum logic spectroscopy, internal transitions of trapped ions and molecules can be probed by measuring the motional displacement caused by an applied light field of variable frequency. This provides a solution to “needle-in-a-haystack” problems, such as the search for narrow clock transitions in highly charged ions, recently discussed by Chen []. The main bottleneck is the search speed over a frequency bandwidth, which can be increased by enhancing the sensitivity of displacement detection. In this work, we explore two complementary improvements: the use of squeezed motional states, explained using an analytical phase-space model, and optimal statistical postprocessing of data using a hypothesis-testing framework. We demonstrate that each method independently provides a substantial boost to search speed. Their combination effectively mitigates state preparation and measurement errors, improving the search speed by an order of magnitude and fully leveraging the quantum enhancement offered by squeezing.

We present a quantum logic scheme mitigating systematic effects in the measurement of magnetic properties of ions caused by temporal magnetic field fluctuations through comagnetometry. This is achieved through simultaneous interrogation of a spectroscopy ion and a cotrapped reference ion with a precisely known g factor confined in a Paul trap. This allows measurement of the ground state g factors of a single Ti + 48 ion with uncertainties at the 10 − 6 level in the weak B -field regime. The experimental scheme can be applied to many ions, including those that cannot be directly laser cooled. We compare the experimentally determined g factors of Ti + 48 with new theoretical predictions using a combination of configuration interaction and second-order many-body perturbation theory. Theory and experiment agree within the expected level of accuracy.

Entangled states hold the promise of improving the precision and accuracy of quantum sensors. We experimentally demonstrate that spectroscopy of an optical clock transition using entangled states can outperform its classical counterpart. Two Ca 40 + ions are entangled in a quantum state with vanishing first-order magnetic field sensitivity, extending the coherence time of the atoms and enabling near-lifetime-limited probe times of up to 550 ms. In our protocol, entangled ions reach the same instability as uncorrelated ions, but at half the probe time, enabling faster cycle times of the clock. We run two entangled Ca 40 + ions as an optical clock and compare its frequency instability with a Sr 87 lattice clock. The instability of the entangled ion clock is below a clock operated with classically correlated states for all probe times. We observe instabilities below the theoretically expected quantum projection noise limit of two uncorrelated ions for interrogation times below 100 ms. The lowest fractional frequency instability of 7 × 10 − 16 / τ / 1 s is reached for 250 ms probe time, limited by residual phase noise of the probe laser. This represents the lowest instability reported to date for a Ca 40 + ion clock.

The Ni^{12+} ion features an electronic transition with a natural width of only 8 mHz, allowing for a highly stable optical clock. We predict that the energy of this strongly forbidden 3s^{2}3p^{4} ^{3}P_{2}→3s^{2}3p^{4} ^{3}P_{0} electric quadrupole transition is 20 081(10) cm^{-1}. For this, we use both a hybrid approach combining configuration interaction with a coupled-cluster method and a pure configuration interaction calculation for the complete 16-electron system, ensuring convergence. The resulting very small theoretical uncertainty of only 0.05% allowed us to find the transition experimentally in a few hours, yielding an energy of 20 078.984(10) cm^{-1}. This level of agreement for a 16-electron system is unprecedented and qualifies our method for future calculations of many other complex atomic systems. While paving the way for a high-precision optical clock based on Ni^{12+}, our theory and code development will also enable better predictions for other highly charged ions and other complex atomic systems.

We measured the g -factor of the excited-state P 1 3 in Ca 14 + ion to be g = 1.499032 ( 6 ) with a relative uncertainty of 4 × 10 − 6 . The magnetic field magnitude is derived from the Zeeman splitting of a Be + ion, cotrapped in the same linear Paul trap as the highly charged Ca 14 + ion. Furthermore, we experimentally determined the second-order Zeeman coefficient C 2 of the P 0 3 − P 1 3 clock transition. For the m J = 0 → m J ′ = 0 transition, we obtained C 2 = 0.39 ± 0.04 Hz mT − 2 , which is to our knowledge the smallest reported for any atomic transition to date. This confirms the predicted low sensitivity of highly charged ions to higher-order Zeeman effects, making them ideal candidates for high-precision optical clocks. Comparison of the experimental results with our state-of-the art electronic structure calculations shows good agreement and demonstrates the significance of the frequency-dependent Breit contribution, negative energy states, and QED effects on magnetic moments.

Nonlinearities in King plots (KP) of isotope shifts (IS) can reveal the existence of beyond-standard-model (BSM) interactions that couple electrons and neutrons. However, it is crucial to distinguish higher-order standard model (SM) effects from BSM physics. We measure the IS of the transitions P 3 0 → P 3 1 in Ca 14 + and S 2 1 / 2 → D 5 / 2 2 in Ca + with sub-Hz precision as well as the nuclear mass ratios with relative uncertainties below 4 × 10 − 11 for the five stable, even isotopes of calcium ( Ca 40 , 42 , 44 , 46 , 48 ). Combined, these measurements yield a calcium KP nonlinearity with a significance of ∼ 10 3 σ . Precision calculations show that the nonlinearity cannot be fully accounted for by the expected largest higher-order SM effect, the second-order mass shift, and identify the little-studied nuclear polarization as the only remaining SM contribution that may be large enough to explain it. Despite the observed nonlinearity, we improve existing KP-based constraints on a hypothetical Yukawa interaction for most of the new boson masses between 10 eV / c 2 and 10 7 eV / c 2 .

Extending quantum control to increasingly complex systems is crucial for both advancing quantum technologies and fundamental physics. In trapped ion systems, quantum logic techniques that combine a well-controlled logic species with a more complex spectroscopy species have proven to be a powerful tool for extending the range of accessible species. Here, we demonstrate that a quantum system as complex as Ti + 48 with its many metastable states can be controlled employing a combination of intrinsic thermalization due to collisions with background gas and quantum-logic techniques using a far-detuned Raman laser. The preparation of pure quantum states allows coherent manipulation and high resolution measurements of the Zeeman structure in Ti + 48 . The presented techniques are applicable to a wide range of ionic species giving access to a larger variety of systems for fundamental physics and constitute the first step for quantum-controlled spectroscopy of transition metals, relevant, e.g., for the interpretation of astrophysical spectra.