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Quantum Logic Techniques for Transition Metal and Molecular Ions

Till Rehmert

Published Jan 1, 2026• 0 citations
Publisher

Abstract

High-precision spectroscopy of atomic and molecular ions is an established platform for investigating fundamental aspects of physics. An important step in this direction was the development of quantum logic techniques that enable the spectroscopy of ions whose electronic structure does not allow direct laser cooling. Particularly challenging in this context is the investigation of atomic and molecular systems with many long-lived metastable states. The preparation of a pure quantum state for spectroscopy purposes often requires the prior detection of these long-lived states. For molecular ions, schemes for the detection of their rotational degree of freedom have already been developed in the past. However, quantum logic control of transition metals, in which the many metastable states result from several valence electrons, remained elusive. In this cumulative thesis, the first experimental implementation of a quantum logic assisted scheme for internal state detection of atomic systems as complex as a titanium ion is presented. Furthermore, a scheme based on simultaneous co-magnetometry for measuring the Landé g factor was developed and demonstrated for different fine structure states in 48Ti+. The presented method allows the suppression of systematic uncertainties arising from varying magnetic fields at the position of the ion and can be transferred to a variety of other species. Crucial for quantum logic based applications is the reliable preparation of a two-ion crystal consisting of one spectroscopy ion and one logic ion. A third aspect of this work is the deterministic preparation of such a two-ion crystal. The method based on fluorescence imaging is associated with a significantly reduced calibration effort compared to other schemes and can be easily transferred to other combinations of spectroscopy and logic ions. The quantum logic control capabilities demonstrated in this work are applicable to a wide range of other atoms with complex electronic structures as well as to molecular ions. The investigation of transition metals can provide important reference data for the calibration of absorption spectra from astrophysical objects. Molecular ions have applications in the search for a possible variation of fundamental constants or the measurement of energy shifts caused by an electron electric dipole moment, both representing promising approaches to test the standard model of particle physics.

DOI
10.15488/21256

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High-precision spectroscopy of atomic and molecular ions is an established platform for investigating fundamental aspects of physics. An important step in this direction was the development of quantum logic techniques that enable the spectroscopy of ions whose electronic structure does not allow direct laser cooling. Particularly challenging in this context is the investigation of atomic and molecular systems with many long-lived metastable states. The preparation of a pure quantum state for spectroscopy purposes often requires the prior detection of these long-lived states. For molecular ions, schemes for the detection of their rotational degree of freedom have already been developed in the past. However, quantum logic control of transition metals, in which the many metastable states result from several valence electrons, remained elusive. In this cumulative thesis, the first experimental implementation of a quantum logic assisted scheme for internal state detection of atomic systems as complex as a titanium ion is presented. Furthermore, a scheme based on simultaneous co-magnetometry for measuring the Landé g factor was developed and demonstrated for different fine structure states in 48Ti+. The presented method allows the suppression of systematic uncertainties arising from varying magnetic fields at the position of the ion and can be transferred to a variety of other species. Crucial for quantum logic based applications is the reliable preparation of a two-ion crystal consisting of one spectroscopy ion and one logic ion. A third aspect of this work is the deterministic preparation of such a two-ion crystal. The method based on fluorescence imaging is associated with a significantly reduced calibration effort compared to other schemes and can be easily transferred to other combinations of spectroscopy and logic ions. The quantum logic control capabilities demonstrated in this work are applicable to a wide range of other atoms with complex electronic structures as well as to molecular ions. The investigation of transition metals can provide important reference data for the calibration of absorption spectra from astrophysical objects. Molecular ions have applications in the search for a possible variation of fundamental constants or the measurement of energy shifts caused by an electron electric dipole moment, both representing promising approaches to test the standard model of particle physics.
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 ^{48}Ti^{+} 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 ^{48}Ti^{+}. 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.
Laser spectroscopy is a versatile tool to investigate the internal structure of atoms, molecules and nuclei.High precision spectroscopy requires laser cooling to reduce Doppler broadening and Doppler shifts.Sympathetic cooling extends these advantages to species which do not have an appropriate transition for laser cooling and allows precision spectroscopy of previously inaccessible species using the quantum logic technique.The original implementation of quantum logic spectroscopy relies on the long lifetime of the excited spectroscopy state to realize a transfer sequence.Precision spectroscopy of transitions with a short-lived excited state is typically performed using laser induced uorescence or laser absorption spectroscopy.Neither of these methods has reached the fundamental quantum projection noise limit and are rather limited by photon shot noise.For these situations, we develop the technique of photon recoil spectroscopy as an extension of quantum logic spectroscopy to broad transitions.The common motion of a sideband-cooled two-ion crystal is excited by photon recoil during photon absorption on the spectroscopically investigated ion.This motional excitation is transferred to an internal state excitation on the co-trapped ion of a dierent species and detected with high eciency.We demonstrate the technique on the 2 S 1/2 ↔ 2 P 1/2 transition of the 40 Ca + ion and resolve the line center to 1/300 of its observed linewidth.The simplicity and versatility of the technique promises applications to other previously inaccessible species.A variation of the technique is proposed for rotational state preparation of molecular ions.A moving optical lattice is employed to exert a state-dependent force on the molecule.This would allow the detection of the rotational state of the molecular ion and therefore enable precision spectroscopy of specic rovibrational transitions in the molecule.
Fundamental interactions and symmetries define the structure and properties of all matter, in particular of its small and diverse visible constituents—the atoms. The study of their distinctive spectra through precision spectroscopy is therefore a vital tool to advance our understanding of nature. Highly charged ions (HCIs) constitute the largest fraction of all atoms since every atom has as many charge states as electrons it can bind. Although most of the matter on Earth is neutral, HCIs are ubiquitous in the universe and their systematic study is essential not only for atomic physics but eminently for astrophysics, nuclear physics, and fusion research, among others. Recently, HCIs have been identified as ideal candidates for sensitive tests of physics beyond the Standard Model of particle physics and for use in future high-accuracy optical atomic clocks. However, the realization of such proposals has been hindered by the hitherto constrained laboratory control and limited spectroscopic accuracy of about parts-per-million fractional uncertainty levels. This thesis reports the first coherent laser spectroscopy of HCIs, boosting the achievable spectroscopic precision by eight orders of magnitude compared to traditional spectroscopy methods. The 2P1/2–2P3/2 fine-structure ground-state transition in highly charged 40Ar13+ at an optical wavelength of 441 nm was chosen as a proof-of-principle case. A single ion of this species was isolated from a megakelvin-hot plasma cloud and co-trapped together with a laser-cooled singly charged 9Be+ ion in a two-ion crystal, confined in the harmonic potential of a cryogenic linear Paul trap. This coupled quantum-mechanical system was then cooled to its ground state of axial motion, corresponding to the lowest temperature of a HCI ever achieved. The spectroscopy was realized by implementing quantum logic techniques which allow preparation of the quantum state of the HCI and to map its electronic state after spectroscopy onto the 9Be+ logic ion in order to detect it there with high efficiency through electron shelving. In addition to the increase of spectroscopic precision, the excited-state lifetime and g-factor were measured—the latter one to unprecedented accuracy, resolving effects from special relativity, interelectronic interactions, and quantum electrodynamics. Moreover, it settled a discrepancy between theoretical predictions. The demonstrated techniques are not limited to the specific 40Ar13+ species but universally applicable to other HCIs. Thereby, this work unlocks the potential of HCIs for unrivaled tests of fundamental physics, the search for new physics—such as a 5th force, variations of fundamental constants and dark matter candidates—as well as the use of HCIs in novel optical atomic clocks.
Quantum logic enables state preparation, readout and spectroscopy of otherwise difficult-to-study ions. Using the coupled harmonic motion shared between co-trapped ions, information can be transferred from the "spectroscopy" ion to the easily manipulated "logic" ion. With this technique we perform high-resolution terahertz-scale rotational spectroscopy of a single CaH+ molecular ion in pure states by leveraging a Ca+ ion as our logic ion. Entangled states between a CaH+ and a Ca+ have also been demonstrated, making molecular ions possible components of hybrid systems for quantum information processing. Because all our laser operations on the molecule are driving stimulated Raman transitions with high detuning, the technique promises to be generalizable to a wide variety of molecular ion species. Additionally, we study the systematic effects of the trap RF electric field on molecular levels and use it to obtain a measurement of the dipole moment of the charged molecule.
Abstract Precision spectroscopy has been the driving force for progress of our physical understanding and still is a promising tool for the investigation of new physics. Molecules offer transitions which allow tests that are not possible in atomic systems. However, usually precision spectroscopy of molecules is challenging due to the lack of cycling transitions for state preparation and state detection. For molecular ions, this obstacle can be overcome by quantum logic spectroscopy, where dissipation for state preparation and detection is provided by a co-trapped atomic ion exploiting the shared eigenstates of motion. Here, we propose a full quantum logic spectroscopy scheme for molecular oxygen ions and theoretically investigate the feasibility of quantum logic-assisted state detection and preparation. Furthermore, we provide coupling rates for a direct single-photon quadrupole excitation of a vibrational overtone transition that can serve as a sensitive reference for tests of a possible variation of the proton-to-electron mass ratio.
This paper presents an experimental platform designed to facilitate quantum logic control of polar molecular ions in a segmented ring ion trap, paving the way for precision measurements. This approach focuses on achieving near-unity state preparation and detection, as well as long spin-precession coherence. A distinctive aspect lies in separating state preparation and detection conducted in a static frame from parity-selective spin precession in a rotating frame. Moreover, the method is designed to support spatially and temporally coincident measurements on multiple ions prepared in states with different sensitivity to the new physics of interest. This provides powerful techniques to probe and minimize potential sources of systematic error. While the primary focus of this paper is on detecting the electron's electric dipole moment (eEDM) using 232ThF+^{232}\mathrm{ThF}^{+}232ThF+ ions, the proposed methodology holds promise for broader applications, particularly with ion species that exhibit enhanced sensitivity to the nuclear magnetic quadruple moment (nMQM).