Coherent laser spectroscopy of highly charged ions using quantum logic

Collinear Laser Spectroscopy of 2 ^{3}S_{1}→2 ^{3}P_{J} Transitions in Helium-like ^{12}C^{4+}

Transition frequencies and fine-structure splittings of the 2 ^{3}S_{1}→2 ^{3}P_{J} transitions in helium-like ^{12}C^{4+} were measured by collinear laser spectroscopy on a 1-ppb level. Accuracy is increased by more than 3 orders of magnitude with respect to previous measurements, enabling tests of recent nonrelativistic (NR) QED calculations including terms up to mα^{7}. Deviations between the theoretical and experimental values are within theoretical uncertainties and are ascribed to mα^{8} and higher-order contributions in the series expansion of the NR QED calculations. Finally, prospects for an all-optical charge radius determination of light isotopes are evaluated.

Observation of a Low-Lying Metastable Electronic State in Highly Charged Lead by Penning-Trap Mass Spectrometry

Highly charged ions (HCIs) offer many opportunities for next-generation clock research due to the vast landscape of available electronic transitions in different charge states. The development of extreme ultraviolet frequency combs has enabled the search for clock transitions based on shorter wavelengths in HCIs. However, without initial knowledge of the energy of the clock states, these narrow transitions are difficult to be probed by lasers. In this Letter, we provide experimental observation and theoretical calculation of a long-lived electronic state in Nb-like Pb^{41+} that could be used as a clock state. With the mass spectrometer PENTATRAP, the excitation energy of this metastable state is directly determined as a mass difference at an energy of 31.2(8) eV, corresponding to one of the most precise relative mass determinations to date with a fractional uncertainty of 4×10^{-12}. This experimental result agrees within 1σ with two partially different ab initio multiconfiguration Dirac-Hartree-Fock calculations of 31.68(13) eV and 31.76(35) eV, respectively. With a calculated lifetime of 26.5(5.3) days, the transition from this metastable state to the ground state bears a quality factor of 1.1×10^{23} and allows for the construction of a HCI clock with a fractional frequency instability of <10^{-19}/sqrt[τ].

Trap-integrated fluorescence detection with silicon photomultipliers for sympathetic laser cooling in a cryogenic Penning trap

We present a fluorescence-detection system for laser-cooled 9Be+ ions based on silicon photomultipliers (SiPMs) operated at 4 K and integrated into our cryogenic 1.9 T multi-Penning-trap system. Our approach enables fluorescence detection in a hermetically sealed cryogenic Penning-trap chamber with limited optical access, where state-of-the-art detection using a telescope and photomultipliers at room temperature would be extremely difficult. We characterize the properties of the SiPM in a cryocooler at 4 K, where we measure a dark count rate below 1 s-1 and a detection efficiency of 2.5(3)%. We further discuss the design of our cryogenic fluorescence-detection trap and analyze the performance of our detection system by fluorescence spectroscopy of 9Be+ ion clouds during several runs of our sympathetic laser-cooling experiment.

Cryogenic vacuum valve with actuation times down to 50 ms

We have conceived, built, and operated a cryogenic vacuum valve with opening and closing times as short as 50 ms that can be used in strong magnetic fields and across a broad range of duty cycles. It is used to seal a cryogenic Penning trap at liquid-helium temperature for long-term storage of highly charged ions in a vacuum better than 10-15 hPa from a room-temperature ion beamline at vacuum conditions around 10-9 hPa. It will significantly improve any experiment where a volume at the most extreme vacuum conditions must be temporarily connected to a less demanding vacuum during repeated experimental cycles. We describe the design of this valve and show measurements that characterize its main features.

Narrow and Ultranarrow Transitions in Highly Charged Xe Ions as Probes of Fifth Forces

Optical frequency metrology in atoms and ions can probe hypothetical fifth forces between electrons and neutrons by sensing minute perturbations of the electronic wave function induced by them. A generalized King plot has been proposed to distinguish them from possible standard model effects arising from, e.g., finite nuclear size and electronic correlations. Additional isotopes and transitions are required for this approach. Xenon is an excellent candidate, with seven stable isotopes with zero nuclear spin, however it has no known visible ground-state transitions for high resolution spectroscopy. To address this, we have found and measured twelve magnetic-dipole lines in its highly charged ions and theoretically studied their sensitivity to fifth forces as well as the suppression of spurious higher-order standard model effects. Moreover, we identified at 764.8753(16) nm a E2-type ground-state transition with 500 s excited state lifetime as a potential clock candidate further enhancing our proposed scheme.

Trapping and Ground-State Cooling of a Single H_{2}^{+}

We demonstrate co-trapping and sideband cooling of a H_{2}^{+}-^{9}Be^{+} ion pair in a cryogenic Paul trap. We study the chemical lifetime of H_{2}^{+} and its dependence on the apparatus temperature, achieving lifetimes of up to 11_{-3}^{+6}  h at 10 K. We demonstrate cooling of two of the modes of translational motion to an average phonon number of 0.07(1) and 0.05(1), corresponding to a temperature of 22(1) and 55(3)  μK, respectively. Our results provide a basis for quantum logic spectroscopy experiments of H_{2}^{+}, as well as other light ions such as HD^{+}, H_{3}^{+}, and He^{+}.

Coherent Control of Trapped-Ion Qubits with Localized Electric Fields

We present a new method for coherent control of trapped ion qubits in separate interaction regions of a multizone trap by simultaneously applying an electric field and a spin-dependent gradient. Both the phase and amplitude of the effective single-qubit rotation depend on the electric field, which can be localized to each zone. We demonstrate this interaction on a single ion using both laser-based and magnetic-field gradients in a surface-electrode ion trap, and measure the localization of the electric field.

Effects of an Oscillating Electric Field on and Dipole Moment Measurement of a Single Molecular Ion

We characterize and model the Stark effect due to the radio-frequency (rf) electric field experienced by a molecular ion in an rf Paul trap, a leading systematic in the uncertainty of the field-free rotational transition. The ion is deliberately displaced to sample different known rf electric fields and measure the resultant shifts in transition frequencies. With this method, we determine the permanent electric dipole moment of CaH^{+}, and find close agreement with theory. The characterization is performed by using a frequency comb which probes rotational transitions in the molecular ion. With improved coherence of the comb laser, a fractional statistical uncertainty for a transition line center of as low as 4.6×10^{-13} was achieved.

Commissioning of the HITRAP Cooling Trap with Offline Ions

Highly charged heavy ions at rest offer a wide spectrum of precision measurements. The GSI Helmholtzzentrum für Schwerionenforschung GmbH is able to deliver ions up to U92+. As the production of these heavy, highly charged ions requires high kinetic energies, it is necessary to decelerate these ions for ultimate precision. The broad energy distribution, which results from the deceleration in the HITRAP linear decelerator, needs to be reduced to allow for further transportation and experiments. The HITRAP cooling trap is designed to cool, i.e., reduce, this energy spread by utilizing electron cooling. The commissioning of this trap is done with Ar16+-ions from a local EBIT ion source. By analyzing the signal of stored ions after ejection, properties such as ion lifetime, charge exchange, and ion motions can be observed. Here, we provide an overview of the recent results of the commissioning process and discuss future experiments.

Scalable Quantum Logic Spectroscopy

In quantum logic spectroscopy (QLS), one species of trapped ion is used as a sensor to detect the state of an otherwise inaccessible ion species. This extends precision measurements to a broader class of atomic and molecular systems for applications like atomic clocks and tests of fundamental physics. Here, we develop a new technique based on a Schrödinger cat interferometer to address the problem of scaling QLS to larger ion numbers. We demonstrate the basic features of this method using various combinations of ^{25}Mg^{+} logic ions and ^{27}Al^{+} spectroscopy ions. We observe higher detection efficiency by increasing the number of ^{25}Mg^{+} ions. Applied to multiple ^{27}Al^{+}, this method will improve the stability of high-accuracy optical clocks and could enable Heisenberg-limited QLS.

Fast silicon carbide MOSFET based high-voltage push-pull switch for charge state separation of highly charged ions with a Bradbury-Nielsen gate

In this paper, we report on the development of a fast high-voltage switch, which is based on two enhancement mode N-channel silicon carbide metal-oxide-semiconductor field-effect transistors in push-pull configuration. The switch is capable of switching high voltages up to 600 V on capacitive loads with rise and fall times on the order of 10 ns and pulse widths ≥20 ns. Using this switch, it was demonstrated that, from the charge state distribution of bunches of highly charged ions ejected from an electron beam ion trap with a specific kinetic energy, single charge states can be separated by fast switching of the high voltage applied to a Bradbury-Nielsen Gate with a resolving power of about 100.

A frequency comb stabilized Ti:Sa laser as a self-reference for ion-trap experiments with a 40Ca+ ion

In this study, we report on the stabilization of a continuous-wave Ti:Sa laser to an optical frequency comb. The laser is emitting at 866 nm to address one of the transitions required for Doppler cooling of a single ⁴⁰Ca⁺ ion in a linear Paul trap (²D_3/2 ↔P1/22). The stabilized Ti:Sa laser is utilized to calibrate an ultra-accurate wavelength meter. We certify this self-reference laser source by comparing the results from monitoring the laser-cooled ⁴⁰Ca⁺ ion in the linear Paul trap, with those obtained when a HeNe laser is used for calibration. The use of this self-reference is compatible with the simultaneous use of the comb for precision spectroscopy in the same ion-trap experiment.

Observation of Feshbach resonances between a single ion and ultracold atoms

The control of physical systems and their dynamics on the level of individual quanta underpins both fundamental science and quantum technologies. Trapped atomic and molecular systems, neutral¹ and charged², are at the forefront of quantum science. Their extraordinary level of control is evidenced by numerous applications in quantum information processing^3,4 and quantum metrology^5,6. Studies of the long-range interactions between these systems when combined in a hybrid atom-ion trap^7,8 have led to landmark results^9-19. However, reaching the ultracold regime-where quantum mechanics dominates the interaction, for example, giving access to controllable scattering resonances^20,21-has so far been elusive. Here we demonstrate Feshbach resonances between ions and atoms, using magnetically tunable interactions between ¹³⁸Ba⁺ ions and ⁶Li atoms. We tune the experimental parameters to probe different interaction processes-first, enhancing three-body reactions^22,23 and the related losses to identify the resonances and then making two-body interactions dominant to investigate the ion's sympathetic cooling¹⁹ in the ultracold atomic bath. Our results provide deeper insights into atom-ion interactions, giving access to complex many-body systems^24-27 and applications in experimental quantum simulation^28-30.

Simultaneous bicolor interrogation in thulium optical clock providing very low systematic frequency shifts

Optical atomic clocks have already overcome the eighteenth decimal digit of instability and uncertainty, demonstrating incredible control over external perturbations of the clock transition frequency. At the same time, there is an increasing demand for atomic (ionic) transitions and new interrogation and readout protocols providing minimal sensitivity to external fields and possessing practical operational wavelengths. One of the goals is to simplify the clock operation while maintaining the relative uncertainty at a low 10⁻¹⁸ level achieved at the shortest averaging time. This is especially important for transportable and envisioned space-based optical clocks. Here, we demonstrate implementation of a synthetic frequency approach for a thulium optical clock with simultaneous optical interrogation of two clock transitions. Our experiment shows suppression of the quadratic Zeeman shift by at least three orders of magnitude. The effect of the tensor lattice Stark shift in thulium can also be reduced to below 10⁻¹⁸ in fractional frequency units. This makes the thulium optical clock almost free from hard-to-control systematic shifts. The “simultaneous” protocol demonstrates very low sensitivity to the cross-talks between individual clock transitions during interrogation and readout.

There are continuous efforts in improving the stability and systematic shifts of optical clocks. Here the authors demonstrate thulium optical clock utilizing bicolor scheme involving interrogation of both hyperfine levels and they are able to cancel the quadratic Zeeman shift.

An ultralow-noise superconducting radio-frequency ion trap for frequency metrology with highly charged ions

We present a novel ultrastable superconducting radio-frequency (RF) ion trap realized as a combination of an RF cavity and a linear Paul trap. Its RF quadrupole mode at 34.52 MHz reaches a quality factor of Q ≈ 2.3 × 10⁵ at a temperature of 4.1 K and is used to radially confine ions in an ultralow-noise pseudopotential. This concept is expected to strongly suppress motional heating rates and related frequency shifts that limit the ultimate accuracy achieved in advanced ion traps for frequency metrology. Running with its low-vibration cryogenic cooling system, electron-beam ion trap, and deceleration beamline supplying highly charged ions (HCIs), the superconducting trap offers ideal conditions for optical frequency metrology with ionic species. We report its proof-of-principle operation as a quadrupole-mass filter with HCIs and trapping of Doppler-cooled ⁹Be⁺ Coulomb crystals.

Sympathetic cooling of a trapped proton mediated by an LC circuit

Efficient cooling of trapped charged particles is essential to many fundamental physics experiments1,2, to high-precision metrology3,4 and to quantum technology5,6. Until now, sympathetic cooling has required close-range Coulomb interactions7,8, but there has been a sustained desire to bring laser-cooling techniques to particles in macroscopically separated traps5,9,10, extending quantum control techniques to previously inaccessible particles such as highly charged ions, molecular ions and antimatter. Here we demonstrate sympathetic cooling of a single proton using laser-cooled Be+ ions in spatially separated Penning traps. The traps are connected by a superconducting LC circuit that enables energy exchange over a distance of 9 cm. We also demonstrate the cooling of a resonant mode of a macroscopic LC circuit with laser-cooled ions and sympathetic cooling of an individually trapped proton, reaching temperatures far below the environmental temperature. Notably, as this technique uses only image-current interactions, it can be easily applied to an experiment with antiprotons1, facilitating improved precision in matter-antimatter comparisons11 and dark matter searches12,13.

A simple, powerful diode laser system for atomic physics

External-cavity diode lasers are ubiquitous in atomic physics and a wide variety of other scientific disciplines, due to their excellent affordability, coherence length, and versatility. However, for higher-power applications, the combination of seed lasers, injection-locking and amplifiers can rapidly become expensive and complex. Here we present a high-power, single-diode laser design with specifications: >210mW, 100 ms-linewidth (427±7)kHz, >99% mode purity, 10 GHz mode-hop-free tuning range, and 12 nm coarse tuning. Simple methods are outlined to determine the spectral purity and linewidth with minimal additional infrastructure. The laser has sufficient power to collect 10¹⁰⁸⁷Rb atoms in a single-chamber vapor-loaded magneto-optical trap. With appropriate diodes and feedback, the system could be easily adapted to other atomic species and diode laser architectures.

Adaptively controlled fast production of defect-free beryllium ion crystals using pulsed laser ablation

Trapped atomic ions find wide applications ranging from precision measurement to quantum information science and quantum computing. Beryllium ions are widely used due to the light mass and convenient atomic structure of beryllium; however, conventional ion loading from thermal ovens exerts undesirable gas loads for a prolonged duration. Here, we demonstrate a method to rapidly produce pure linear chains of beryllium ions with pulsed laser ablation, serving as a starting point for large-scale quantum information processing. Our method is fast compared to thermal ovens, reduces the gas load to only 10^-12 Torr (10^-10 Pa) level, yields a short recovery time of a few seconds, and also eliminates the need for a deep ultraviolet laser for photoionization. We also study the loading dynamics, which show non-Poissonian statistics in the presence of sympathetic cooling. In addition, we apply feedback control to obtain defect-free ion chains with desirable lengths.

XUV frequency comb production with an astigmatism-compensated enhancement cavity

We have developed an extreme ultraviolet (XUV) frequency comb for performing ultra-high precision spectroscopy on the many XUV transitions found in highly charged ions (HCI). Femtosecond pulses from a 100 MHz phase-stabilized near-infrared frequency comb are amplified and then fed into a femtosecond enhancement cavity (fsEC) inside an ultra-high vacuum chamber. The low-dispersion fsEC coherently superposes several hundred incident pulses and, with a single cylindrical optical element, fully compensates astigmatism at the w₀ = 15 µm waist cavity focus. With a gas jet installed there, intensities reaching ∼ 10¹⁴ W/cm² generate coherent high harmonics with a comb spectrum at 100 MHz rate. We couple out of the fsEC harmonics from the 7th up to the 35th (42 eV; 30 nm) to be used in upcoming experiments on HCI frequency metrology.

Optical Mass Spectrometry of Cold RaOH^{+} and RaOCH_{3}^{+}

We present an all-optical mass spectrometry technique to identify trapped ions. The new method uses laser-cooled ions to determine the mass of a cotrapped dark ion with a sub-dalton resolution within a few seconds. We apply the method to identify the first controlled synthesis of cold, trapped RaOH^{+} and RaOCH_{3}^{+}. These molecules are promising for their sensitivity to time and parity violations that could constrain sources of new physics beyond the standard model. The nondestructive nature of the mass spectrometry technique may help identify molecular ions or highly charged ions prior to optical spectroscopy. Unlike previous mass spectrometry techniques for small ion crystals that rely on scanning, the method uses a Fourier transform that is inherently broadband and comparatively fast. The technique's speed provides new opportunities for studying state-resolved chemical reactions in ion traps.

Sub-kelvin temperature management in ion traps for optical clocks

The uncertainty of the ac Stark shift due to thermal radiation represents a major contribution to the systematic uncertainty budget of state-of-the-art optical atomic clocks. In the case of optical clocks based on trapped ions, the thermal behavior of the rf-driven ion trap must be precisely known. This determination is even more difficult when scalable linear ion traps are used. Such traps enable a more advanced control of multiple ions and have become a platform for new applications in quantum metrology, simulation, and computation. Nevertheless, their complex structure makes it more difficult to precisely determine its temperature in operation and thus the related systematic uncertainty. We present here scalable linear ion traps for optical clocks, which exhibit very low temperature rise under operation. We use a finite-element model refined with experimental measurements to determine the thermal distribution in the ion trap and the temperature at the position of the ions. The trap temperature is investigated at different rf-drive frequencies and amplitudes with an infrared camera and integrated temperature sensors. We show that for typical trapping parameters for In+, Al+, Lu+, Ca+, Sr+, or Yb+ ions, the temperature rise at the position of the ions resulting from rf heating of the trap stays below 700 mK and can be controlled with an uncertainty on the order of a few 100 mK maximum. The corresponding uncertainty of the trap-related blackbody radiation shift is in the low 10-19 and even 10-20 regime for 171Yb+(E3) and 115In+, respectively.

Quadruply Ionized Barium as a Candidate for a High-Accuracy Optical Clock

We identify Ba^{4+} (Te-like) as a promising candidate for a high-accuracy optical clock. The lowest-lying electronic states are part of a ^{3}P_{J} fine structure manifold with anomalous energy ordering, being nonmonotonic in J. We propose a clock based on the 338.8 THz electric quadrupole transition between the ground (^{3}P_{2}) and first-excited (^{3}P_{0}) electronic states. We perform relativistic many-body calculations to determine relevant properties of this ion. The lifetime of the excited clock state is found to be several seconds, accommodating low statistical uncertainty with a single ion for practical averaging times. The differential static scalar polarizability is found to be small and negative, providing suppressed sensitivity to blackbody radiation while simultaneously allowing cancellation of Stark and excess micromotion shifts. With the exception of Hg^{+} and Yb^{+}, sensitivity to variation of the fine structure constant is greater than other optical clocks thus far demonstrated.

Evidence for Nonlinear Isotope Shift in Yb^{+} Search for New Boson

We measure isotope shifts for five Yb^{+} isotopes with zero nuclear spin on two narrow optical quadrupole transitions ^{2}S_{1/2}→^{2}D_{3/2}, ^{2}S_{1/2}→^{2}D_{5/2} with an accuracy of ∼300  Hz. The corresponding King plot shows a 3×10^{-7} deviation from linearity at the 3σ uncertainty level. Such a nonlinearity can indicate physics beyond the Standard Model (SM) in the form of a new bosonic force carrier, or arise from higher-order nuclear effects within the SM. We identify the quadratic field shift as a possible nuclear contributor to the nonlinearity at the observed scale, and show how the nonlinearity pattern can be used in future, more accurate measurements to separate a new-boson signal from nuclear effects.

Interrogating the Temporal Coherence of EUV Frequency Combs with Highly Charged Ions

A scheme to infer the temporal coherence of EUV frequency combs generated from intracavity high-order harmonic generation is put forward. The excitation dynamics of highly charged Mg-like ions, which interact with EUV pulse trains featuring different carrier-envelope-phase fluctuations, are simulated. While demonstrating the microscopic origin of the macroscopic equivalence between excitations induced by pulse trains and continuous-wave lasers, we show that the coherence time of the pulse train can be determined from the spectrum of the excitations. The scheme will provide a verification of the comb temporal coherence at timescales several orders of magnitude longer than current state of the art, and at the same time will enable high-precision spectroscopy of EUV transitions with a relative accuracy up to δω/ω∼10^{-17}.

Accurate Prediction of Clock Transitions in a Highly Charged Ion with Complex Electronic Structure

We develop a broadly applicable approach that drastically increases the ability to predict the properties of complex atoms accurately. We apply it to the case of Ir^{17+}, which is of particular interest for the development of novel atomic clocks with a high sensitivity to the variation of the fine-structure constant and to dark matter searches. In general, clock transitions are weak and very difficult to identify without accurate theoretical predictions. In the case of Ir^{17+}, even stronger electric-dipole (E1) transitions have eluded observation despite years of effort, raising the possibility that the theoretical predictions are grossly wrong. In this work, we provide accurate predictions of the transition wavelengths and E1 transition rates for Ir^{17+}. Our results explain the lack of observations of the E1 transitions and provide a pathway toward the detection of clock transitions. The computational advances we demonstrate in this work are widely applicable to most elements in the periodic table and will allow us to solve numerous problems in atomic physics, astrophysics, and plasma physics.