Sympathetic cooling of molecular ions through the Coulomb interaction with laser-cooled atomic ions is an efficient tool to prepare translationally cold molecules without, ideally, affecting the internal state of the molecular ions. However, the electric field due to the Coulomb interaction may induce rotational transitions that change the purity of initially quantum state prepared molecules. Here, we use estimates of rotational state changes in single collisions of diatomic ions with atomic ions [arXiv:1905.02130] to determine the overall rotational excitation accumulated over the sympathetic cooling. Considering two different experimental scenarios, that of a molecular ion co-trapped with a single atomic ion and a molecular ion immersed in a Coulomb crystal of atomic ions, we also estimate the cooling time.

We investigate rotational state changes in a single collision of diatomic molecular ions, polar or apolar, with an atomic ion. Rotational state changes may occur since the angular degree of freedom of the molecular ions interacts with the electric field due to the atomic ion. Thanks to the very different time and energy scales of translational and rotational motion, we may treat the collision classically and describe only the rotations quantum mechanically. We first investigate a number of example systems numerically and then derive closed-form approximations for the rotational excitation per collision, depending on the scattering energy and the molecular parameters. These findings provide the basis for estimating the accumulated rotational excitation in sympathetic cooling of molecular ions by laser-cooled atomic ions [J. M. Berglund et al., Phys. Rev. A 113, 042817 (2026)] which involves many single collisions.

In the study of ion-atom interactions, the ion often remains trapped during experiments; however, the effects of the trapping potential on ion-neutral dynamics remain largely unexplored. Previous work has modeled trap-assisted ion-neutral complex formation using semiclassical theories, treating the ion as a point charge. Here, we extend this by substituting the point charge with a delocalized charged distribution according to its motional ground state in the trap. We find that the trapping frequency, which determines the spatial extent of the ion’s wavefunction, significantly alters elastic and transport cross sections in interactions with neutral atoms. Based on these findings, we propose experimental procedures to verify the effects of the delocalized charge distribution in ion-atom interactions by measuring the heating rate of the ion resulting from energy transfer in atomic collisions. This framework offers opportunities to study ion-neutral systems, providing insight into ionic polarons and trap-induced losses in hybrid experiments. The study of ion-atom interactions often requires the ion to be trapped, however the effects of the trapping potential have been elusive. The authors find that if the trapped ion is described as a delocalized charged distribution according to its motional ground state in the trap, the trap frequency modifies the scattering and transport properties of the ion in a neutral bath.

Wigner crystals formed by laser-cooled ions in traps are unconventional condensed-matter systems, characterized by interparticle distances of several micrometers and energy scales on the order of μeV. Their crystalline structure emerges from the interplay between Coulomb repulsion and the external confining potential, which can be readily tuned. Moreover, individual ions can be precisely manipulated with lasers and imaged via resonance fluorescence. These unusual and unique properties make ion crystals a powerful platform for studying phases of matter and their dynamics in the strongly correlated quantum regime. This review examines the theoretical framework and experimental characterization of ion Coulomb crystals from a condensed-matter perspective. We highlight their dynamical and thermodynamic properties in one, two, and three dimensions, along with recent investigations into their out-of-equilibrium behavior. We provide outlooks on future directions for exploring novel condensed matter phenomena with trapped ion crystals, as well as their many scientific and technical applications, which have driven advances in controlling and measuring ion crystals in the lab.

In the last decade, a growing interest has been devoted to models of spontaneous collapse of the wavefunction, known also as collapse models. They coherently solve the well-known quantum measurement problem by suitably modifying the Schrödinger evolution. Quantum experiments are now finally within the reach of testing such models (and thus testing the limits of quantum theory). Here, we propose a method based on a two-ions confined in a linear Paul trap to possibly enhance the testing capabilities of such experiments. The combination of an atomic and a macromolecular ion provide a good match for the cooling of the motional degrees of freedom and a non-negligible insight in the collapse mechanism, respectively.

By combining high-resolution spectroscopy of the 3d 2D3/2 − 3d 2D5/2 interval with an accuracy of ∼20 Hz using direct frequency-comb Raman spectroscopy with isotope shift measurements of the 4s 2S1/2 ↔ 3d 2D5/2 transition in all stable even isotopes of ACa+ (A = 40, 42, 44, 46, and 48) at the accuracy of ∼1 kHz, we have been able to carry out a King plot analysis with unprecedented sensitivity to coupling between electrons and neutrons by bosons beyond the Standard Model. Furthermore, we estimate that by improved spectroscopic techniques available, King plots based on data from spectroscopy on either Ca+, Ba+ and Yb+ ions should be able to produce sensitivity to such potentially new bosons, which surpass other current methods in a broad mass range of 10 to 108 eV/c2.

We explore the interaction between two trapped ions mediated by a surrounding quantum degenerate Bose or Fermi gas. Using perturbation theory valid for weak atom-ion interaction, we show analytically that the interaction mediated by a Bose gas has a power-law behavior for large distances whereas it has a Yukawa form for intermediate distances. For a Fermi gas, the mediated interaction is given by a power law for large density and by a Ruderman-Kittel-Kasuya-Yosida form for low density. For strong atom-ion interaction, we use a diagrammatic theory to demonstrate that the mediated interaction can be a significant addition to the bare Coulomb interaction between the ions, when an atom-ion bound state is close to threshold. Finally, we show that the induced interaction leads to substantial and observable shifts in the ion phonon frequencies.

We reflect on the prospect of exploiting the recoil associated with absorption and emission of photons to perform spectroscopy of a single molecular ion. For this recoil to be detectable, the molecular ion is sympathetically cooled by a laser-cooled atomic ion to near their common quantum-mechanical ground state within a trapping potential. More specifically, we present a general framework for simulating the expected photon recoil spectra in regimes where either the natural transition linewidth ???t of the molecular ion or the spectral width ???L of the exciting light source exceeds the motional frequencies of the two-ion system. To exemplify the framework, we present two complementary cases: spectroscopy of the broad 3s 2S1/2 ???3p 2P3/2 electronic transition (???t/2?? = 41.8 MHz) of a single 24Mg+ ion at ?? = 279.6 nm by a narrow laser source (???L/2?? 1 MHz) and mid-infrared vibrational spectroscopy of the very narrow |v = 0, J = 1) ??? |v' = 1,J' = 0) transition (???t/2?? = 2.50 Hz) at ?? = 6.17??m in the 1???+ electronic ground state of 24MgH+ by a broadband laser source (???L/2?? 50 MHz). The atomic ion 24Mg+ has been picked to introduce a simple system to make comparisons with experimental results while still capturing most of the physics involved in electronic excitations of molecular ions.

This corrects the article DOI: 10.1103/PhysRevLett.125.123003.

We perform high-resolution spectroscopy of the 3d ^{2}D_{3/2}-3d ^{2}D_{5/2} interval in all stable even isotopes of ^{A}Ca^{+} (A=40, 42, 44, 46, and 48) with an accuracy of ∼20  Hz using direct frequency-comb Raman spectroscopy. Combining these data with isotope shift measurements of the 4s ^{2}S_{1/2}↔3d ^{2}D_{5/2} transition, we carry out a King plot analysis with unprecedented sensitivity to coupling between electrons and neutrons by bosons beyond the standard model. Furthermore, we estimate the sensitivity to such bosons from equivalent spectroscopy in Ba^{+} and Yb^{+}. Finally, the data yield isotope shifts of the 4s ^{2}S_{1/2}↔3d ^{2}D_{3/2} transition at 10 parts per billion through combination with recent data of Knollmann, Patel, and Doret [Phys. Rev. A 100, 022514 (2019)PLRAAN2469-992610.1103/PhysRevA.100.022514].

We present two methods for efficient detection of chiral molecules based on sequences of single pulses and Raman pulse pairs. The chiral molecules are modelled by a closed-loop three-state system with different signs in one of the couplings for the two enantiomers. One method uses a sequence of three interaction steps: a single pulse, a Raman pulse, and another single pulse. The other method uses a sequence of only two interaction steps: a Raman pulse, and a single pulse. The second method is simpler and faster but requires a more sophisticated Raman pulse than the first one. Both techniques allow for straightforward generalizations by replacing the single and Raman pulses with composite pulse sequences. The latter achieve very high signal contrast and far greater robustness to experimental errors than by using single pulses. We demonstrate that both constant-rotation (i.e., with phase compensation) and variable-rotation (i.e., with phase distortion) composite pulses can be used, the former being more accurate and the latter being simpler and faster.

We introduce a method for detection of chiral molecules using sequences of three pulses driving a closed-loop three-state quantum system. The left- and right-handed enantiomers have identical optical properties (transition frequencies and transition dipole moments) with the only difference being the sign of one of the couplings. We identify twelve different sequences of resonant pulses for which chiral resolution with perfect contrast occurs. In all of them the first and third pulses are $\pi/2$-pulses and the middle pulse is a $\pi$-pulse. In addition, one of the three pulses must have a phase shift of $\pi/2$ with respect to the other two. The simplicity of the proposed chiral resolution technique allows for straightforward extensions to more efficient and more robust implementations by replacing the single $\pi/2$ and $\pi$-pulses by composite pulses. We present specific examples of chiral resolution by composite pulses which compensate errors in the pulse areas and the detuning of the driving fields.

Optical frequency combs have in the recent past revolutionized the field of high-resolution spectroscopy by being applied both as frequency references and light sources for direct comb spectroscopy. With respect to the latter application, we have demonstrated the use of an optical frequency comb to coherently drive stimulated Raman transitions between terahertz-spaced atomic energy levels. Specifically, we have measured the 3d 2D3/2 - 3d 2D5/2 fine structure splitting of a single trapped 40Ca+ ion to be 1,819,599,021,534±8Hz, which is five times more accurate than previous measurements, and currently only limited by the stability of our atomic clock reference. Furthermore, Rabi oscillations with a contrast of 99.3(6)% and millisecond coherence time have been realized experimentally, indicating great potentials for future qubit applications. Importantly, the technique should generally be applicable to drive Raman transitions spanning the level spacings ranging from sub-kHz to tens of THz range, including hyperfine transitions in highly charged ions and spin-resolved rovibrational transitions in molecular ions. High-resolution spectroscopy of such systems may find applications in the search for new physics beyond the Standard Model.

measurements of the D3/2−D5/2 interval in Ca Cyrille Solaro, ∗ Steffen Meyer, † Karin Fisher, Julian C. Berengut, ‡ Elina Fuchs, 4, § and Michael Drewsen Department of Physics and Astronomy, Aarhus University, DK-8000 Aarhus C, Denmark School of Physics, University of New South Wales, Sydney NSW 2052, Australia Fermilab, Theory Department, Batavia, IL 60510, USA University of Chicago, Department of Physics, Chicago, IL 60637, USA (Dated: May 4, 2020)

We perform high-resolution spectroscopy of the 3d D23/2−3d D25/2 interval in all stable even isotopes of CaA+ (A=40, 42, 44, 46, and 48) with an accuracy of ∼20 Hz using direct frequency-comb Raman spectroscopy. Combining these data with isotope shift measurements of the 4s S21/2↔3d D25/2 transition, we carry out a King plot analysis with unprecedented sensitivity to coupling between electrons and neutrons by bosons beyond the standard model. Furthermore, we estimate the sensitivity to such bosons from equivalent spectroscopy in Ba+ and Yb+. Finally, the data yield isotope shifts of the 4s S21/2↔3d D23/2 transition at 10 parts per billion through combination with recent data of Knollmann, Patel, and Doret [Phys. Rev. A 100, 022514 (2019)].Received 1 May 2020Accepted 20 August 2020DOI:https://doi.org/10.1103/PhysRevLett.125.123003© 2020 American Physical SocietyPhysics Subject Headings (PhySH)Research AreasElectronic transitionsExtensions of Higgs sectorExtensions of gauge sectorLong-range interactionsPhysical SystemsTrapped ionsTechniquesFemtosecond laser spectroscopySpectroscopyAtomic, Molecular & OpticalParticles & Fields

I will present high-resolution isotope shift spectroscopy of five calcium isotopes using direct frequency-comb-driven Raman transitions between the terahertz-spaced 3d 2 D 3/2 and 3d 2 D 5/2 levels. Fig.1.c) shows absolute frequency measurements on a single 40 Ca + [1]. The achieved relative accuracy of 5.5 × 10 -12 is nearly a factor of five better than the previous best Raman spectroscopy [2], and is currently limited by the inaccuracy of our atomic clock reference. By performing similar measurements on 42,44,46,48 Ca + ions, we determined the isotope shift of this transition with an accuracy of about 25 Hz. These measurements in combination with precise measurements of the 4s 2 S 1/2 - 3d 2 D 5/2 transition are today's best isotope shift measurements to our knowledge and allow for improved bounds on new physics beyond the standard model [3].

We study the dynamic properties of a thermal autonomous machine made up of two quantum Brownian particles, each of which is in contact with an environment at different temperature and moves on a periodic sinusoidal track. When such tracks are shifted, the center of mass of the system exhibits a nonvanishing velocity, for which we provide an exact expression in the limit of small track undulations. We discuss the role of the broken spatial symmetry in the emergence of directed motion in thermal machines. We then consider the case in which external deterministic forces are applied to the system, and we characterize its steady-state velocity. If the applied external force opposes the system motion, work can be extracted from such a steady-state thermal machine, without any external cyclic protocol. When the two particles are not interacting, our results reduce to those of Fisher and Zwerger [Phys. Rev. B 32, 6190 (1985)PRBMDO0163-182910.1103/PhysRevB.32.6190] and Aslangul, Pottier, and Saint-James [J. Phys. France 48, 1093 (1987)JOPQAG0302-073810.1051/jphys:019870048070109300] for a single particle moving in a periodic tilted potential. We finally use our results for the motor velocity to check the validity of the quantum molecular dynamics algorithm in the nonlinear, nonequilibrium regime.

I will present high-resolution isotope shift spectroscopy of five calcium isotopes using direct frequency-comb-driven Raman transitions between the terahertz-spaced 3d <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> D <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3/2</sub> and 3d <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> D <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">5/2</sub> levels. Fig.1.c) shows absolute frequency measurements on a single <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">40</sup> Ca <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">+</sup> [1]. The achieved relative accuracy of 5.5 × 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-12</sup> is nearly a factor of five better than the previous best Raman spectroscopy [2], and is currently limited by the inaccuracy of our atomic clock reference. By performing similar measurements on <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">42,44,46,48</sup> Ca <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">+</sup> ions, we determined the isotope shift of this transition with an accuracy of about 25 Hz. These measurements in combination with precise measurements of the 4s <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> S <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1/2</sub> - 3d <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> D <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">5/2</sub> transition are today's best isotope shift measurements to our knowledge and allow for improved bounds on new physics beyond the standard model [3].

Light-induced control of ions within small Coulomb crystals is investigated. By intense intracavity optical standing-wave fields, subwavelength localization of individual ions is achieved for one-, two-, and three-dimensional crystals. Based on these findings, we illustrate numerically how the application of such optical potentials can be used to tailor the normal-mode spectra and patterns of multidimensional Coulomb crystals. The results represent, among others, important steps towards controlling the crystalline structure of Coulomb crystals, investigating heat-transfer processes at the quantum limit, and quantum simulations of many-body systems.