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Quantum Control of a Single H2+ Molecular Ion

David Holzapfel

Published Jan 1, 2025• 0 citations
Publisher

Abstract

In this thesis I describe how we achieve control over the quantum state of a single H2+ hydrogen molecular ion. Scientific progress is based on the comparison of theories with experimental measurements. For the simplest molecular quantum systems, such as the hydrogen molecular ions H2+ or HD+, the theoretical predictions of quantum electrodynamics are very accurate. In order to test the theory or to extract fundamental constants from the combination of theory and experiments, the experiments must also achieve high precision. In the recent past, hydrogen molecular ions were mainly measured in ensembles. For example, measurements exist both on molecular beams and with dissociative detection in ion traps. However, the spectroscopy of single ions is one of the most precise measurement methods in physics, which was demonstrated by the spectroscopy of a single ytterbium ion in an ion trap. To perform spectroscopy of a single ion in this way, it must have a suitable energy structure for laser cooling, state preparation and fluorescence detection. This is not the case for many ions, including H2+. Quantum logic spectroscopy (QLS) is a technique that makes it possible to perform measurements on an ion without such an energy structure. The ion to be measured (spectroscopy ion) is trapped in an ion trap with a second ion (helper ion), which has the properties described in the previous paragraph. The shared modes of motion between the two ions allow cooling, preparation and detection of the spectroscopy ion via the helper ion. This was demonstrated with an aluminum spectroscopy ion co-trapped with a magnesium helper ion. QLS can also be used for molecules. This has been shown with MgH+, CaH+ and N2+. We implement QLS to enable spectroscopy of a single H2+ ion. For this we trap H2+ together with a 9Be+ ion. We cool the joint motion of the ions to their ground state. We combine buffer gas cooling with a laser and microwave pulse based state preparation sequence to prepare the H2+ molecule in a pure quantum state. This allows us to perform high contrast QLS on a single H2+ ion. Furthermore, we can change and control the quantum state in the hyperfine structure using microwave pulses. We demonstrate the power of our technique by performing microwave spectroscopy on a magnetic field insensitive hyperfine transition. We use QLS to read out the result of the measurement. Within half an hour, we can achieve a statistical uncertainty of 2 Hz. This paves the way for future high-precision measurements on H2+. The techniques described here could potentially be applied to other light molecular ions.

DOI
10.3929/ethz-c-000793369

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In this thesis I describe how we achieve control over the quantum state of a single H2+ hydrogen molecular ion. Scientific progress is based on the comparison of theories with experimental measurements. For the simplest molecular quantum systems, such as the hydrogen molecular ions H2+ or HD+, the theoretical predictions of quantum electrodynamics are very accurate. In order to test the theory or to extract fundamental constants from the combination of theory and experiments, the experiments must also achieve high precision. In the recent past, hydrogen molecular ions were mainly measured in ensembles. For example, measurements exist both on molecular beams and with dissociative detection in ion traps. However, the spectroscopy of single ions is one of the most precise measurement methods in physics, which was demonstrated by the spectroscopy of a single ytterbium ion in an ion trap. To perform spectroscopy of a single ion in this way, it must have a suitable energy structure for laser cooling, state preparation and fluorescence detection. This is not the case for many ions, including H2+. Quantum logic spectroscopy (QLS) is a technique that makes it possible to perform measurements on an ion without such an energy structure. The ion to be measured (spectroscopy ion) is trapped in an ion trap with a second ion (helper ion), which has the properties described in the previous paragraph. The shared modes of motion between the two ions allow cooling, preparation and detection of the spectroscopy ion via the helper ion. This was demonstrated with an aluminum spectroscopy ion co-trapped with a magnesium helper ion. QLS can also be used for molecules. This has been shown with MgH+, CaH+ and N2+. We implement QLS to enable spectroscopy of a single H2+ ion. For this we trap H2+ together with a 9Be+ ion. We cool the joint motion of the ions to their ground state. We combine buffer gas cooling with a laser and microwave pulse based state preparation sequence to prepare the H2+ molecule in a pure quantum state. This allows us to perform high contrast QLS on a single H2+ ion. Furthermore, we can change and control the quantum state in the hyperfine structure using microwave pulses. We demonstrate the power of our technique by performing microwave spectroscopy on a magnetic field insensitive hyperfine transition. We use QLS to read out the result of the measurement. Within half an hour, we can achieve a statistical uncertainty of 2 Hz. This paves the way for future high-precision measurements on H2+. The techniques described here could potentially be applied to other light molecular ions.
Science is founded on the benchmarking of theoretical models against experimental measurements, with the challenge that, for all but the simplest systems, the calculations required for high precision become extremely challenging. H 2 + is the simplest stable molecule, and its structure is calculable to high precision. However, studying H 2 + experimentally presents significant challenges: Standard control methods such as laser cooling are not applicable due to the long lifetimes of its rotational and vibrational states. Here, we solve this issue by combining buffer gas cooling to quench the H 2 + rovibrational excitation with quantum logic operations between H 2 + and a cotrapped “helper” ion to control the molecule’s hyperfine structure. This enables us to perform pure quantum state preparation, coherent control, and nondestructive readout, which we use to demonstrate high-resolution microwave spectroscopy in the hyperfine structure of H 2 + with a precision of 2 Hz. Our results pave the way for high-precision spectroscopy of H 2 + in both the microwave and optical domains. Because of the wide applicability of buffer gas cooling, our method provides a general tool for molecular ion species that are hard to control with quantum logic tools alone.
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.
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.
Precision vibrational spectroscopy of the molecular hydrogen ions is of significant interest for determining fundamental constants, for searching for new forces, and for testing quantum electrodynamics calculations. Future experiments can profit from the ability of preparing molecular hydrogen ions at ultralow kinetic energy and in preselected internal states, with respect to vibration, rotation, and spin degrees of freedom. For the homonuclear ions (H2+,D2+{\mathrm{H}}_{2}{}^{+}, {\mathrm{D}}_{2}{}^{+}H2​+,D2​+), direct laser cooling of the rotational degree of freedom is not feasible. We show by quantum calculations that rotational cooling by cold He buffer gas is an effective approach. For this purpose we have computed the energy-dependent cross sections for rotationally elastic and inelastic collisions, ${\mathrm{h}}_{2}{}^{+}(v=0,\phantom{\rule{0.16em}{0ex}}N)+\mathrm{He}\phantom{\rule{0.16em}{0ex}}\ensuremath{\rightarrow} {\mathrm{h}}_{2}{}^{+}(v=0,\phantom{\rule{0.16em}{0ex}}{N}^{\ensuremath{'}})+\mathrm{He}$ (where h=H,D)\mathrm{h}=\mathrm{H},\phantom{\rule{0.16em}{0ex}}\mathrm{D})h=H,D), using ab initio coupled-channel calculations. We find that rotational cooling to the lowest rotational state is possible within tens of seconds under experimentally realistic conditions. We furthermore describe possible protocols for the preparation of a single quantum state, where also the spin state is well defined.
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.
We present theoretical and experimental progress towards a new approach for the precision spectroscopy, coherent manipulation and state-to-state chemistry of single isolated molecular ions in the gas phase. Our method uses a molecular beam for creating packets of rotationally cold neutrals from which a single molecule is state-selectively ionized and trapped inside a radiofrequency ion trap. In addition to the molecular ion, a single co-trapped atomic ion is used to cool the molecular external degrees of freedom to the ground state of the trap and to detect the molecular state using state-selective coherent motional excitation from a modulated optical-dipole force acting on the molecule. We present a detailed discussion and theoretical characterization of the present approach. We simulate the molecular signal experimentally using a single atomic ion, indicating that different rovibronic molecular states can be resolved and individually detected with our method. The present approach for the coherent control and non-destructive detection of the quantum state of a single molecular ion opens up new perspectives for precision spectroscopies relevant for, e.g., tests of fundamental physical theories and the development of new types of clocks based on molecular vibrational transitions. It will also enable the observation and control of chemical reactions of single particles on the quantum level. While focusing on N2+ as a prototypical example in the present work, our method is applicable to a wide range of diatomic and polyatomic molecules.