Stefan Willitsch

Modern experiments with cold molecular ions have reached a high degree of complexity requiring frequent sample preparation, state initialization and protocol execution while demanding precise control over multiple devices and laser sources. To maintain a high experimental duty cycle and robust measurement conditions, automation becomes essential. We present a fully automated control system for the preparation of trapped state-selected molecular ions and subsequent quantum logic-based experiments. Adaptive feedback routines based on real-time image analysis introduce and identify single molecular ions in atomic-ion Coulomb crystals. By appropriate manipulation of the trapping potentials, excess atomic ions are released from the trap to produce dual-species two-ion strings, here Ca$^+-$N$_2^+$. After mass and state identification of the molecular ion, nanosecond-level synchronization of laser pulses employing the Sinara/ARTIQ framework and real-time data analysis enable quantum-logic-spectroscopic measurements. The present automated control system enables robust, unsupervised operation over extended periods resulting in an increase of the number of experimentation cycles by about a factor of ten compared to manual operation and a factor of about eight in loaded molecules in typical practical situations. The modular, distributed design of the system provides a scalable blueprint for similar molecular-ion experiments.

Over the past years, radiofrequency ion traps have become an attractive platform for studying chemical reactions as they enable a high degree of control over ion-molecule dynamics. In this review, we summarize techniques for the trapping and cooling of atomic and molecular ions in radiofrequency traps including Doppler and resolved-sideband laser cooling, sympathetic cooling, and cryogenic buffer-gas methods. We discuss strategies for controlling key reaction parameters: the preparation of specific internal quantum states by internal cooling, optical pumping, state-selective photoionization and quantum-logic spectroscopy; the manipulation of collision energies through micromotion control, dynamic trapping and combination with molecular beams; and the selection of molecular structure via isotopic substitution, conformational separation and isomer-specific ion generation. We illustrate applications of these approaches by discussing studies on quantum-state-dependent kinetics, quantum-resonance effects and structure-sensitive reactivity in ion-neutral collisions. We conclude by outlining future challenges, including full state-to-state reaction mapping, reaching the ultracold quantum regime free of micromotion, and the exploration of complex and chiral systems.

Quantum-logic spectroscopy has become an increasingly important tool for the state detection and readout of trapped atomic and molecular ions which do not possess easily accessible closed-cycling optical transitions. In this approach, the internal state of the target ion is mapped onto a co-trapped auxiliary ion. This mapping is typically mediated by normal modes of motion of the two-ion Coulomb crystal in the trap. The present study investigates the role of spectator modes not directly involved in a measurement protocol relying on a state-dependent optical-dipole force. We identify a Debye-Waller-type effect that modifies the response of the two-ion string to the force. We show that cooling the spectator modes of the string allows for the detection of the rovibrational ground state of an N$_2^+$ molecular ion with a computed statistical fidelity exceeding 99.99%, improving on previous experiments by more than an order of magnitude while also halving the experimental time. This enhanced sensitivity enables the simultaneous identification of multiple rotational states with markedly weaker signals.

Coulomb crystals -- ordered structures of cold ions confined in ion traps -- find applications in a variety of research fields. The number and temperature of the ions forming the Coulomb crystals are two key attributes of interest in many trapped-ion experiments. Here, we present a fast and accurate approach to determining these attributes from fluorescence images of the ions based on convolutional neural networks (CNNs). In this approach, we first generate a large number of images of Coulomb crystals with different ion numbers and temperatures using molecular-dynamics simulations and then train CNN models on these images to classify the desired attributes. The classification performance of several common pretrained CNN models was compared in example tasks. We find that for crystals with ion numbers in the range 100--299 and secular temperatures of 5--15 mK, the best-performing model can discern number variations on the level of one ion with an accuracy of 93% and temperature variations by 1 mK with an accuracy of 92%. Since the trained model can be directly integrated into experiments, in-situ determination of these attributes can be realized in a non-invasive fashion, which has the potential to greatly facilitate the analysis and control of trapped ions in real time.

Cold ions in traps are well-established, highly controllable quantum systems with a wide variety of applications in quantum information, precision spectroscopy, clocks and chemistry. Nanomechanical oscillators are used in advanced sensing applications and for exploring the border between classical and quantum physics. Here, we report on the implementation of a hybrid system combining a metallic nanowire with laser-cooled ions in a miniaturised ion trap. We demonstrate resonant and off-resonant coupling of the two systems and the coherent motional excitation of the ion by the mechanical drive of the nanowire. The present results open up avenues for mechanically manipulating the quantum motion of trapped ions, for the development of ion-mechanical hybrid quantum systems and for the sympathetic cooling of mechanical systems by trapped ions and vice versa.

We review recent progress in the field of cold trapped molecular ions. A new generation of collision and cold chemistry experiments between atoms and ions has emerged, where cold atoms and ions are brought into contact in a controlled way in novel hybrid atom-ion platforms. Furthermore, new possibilities for the preparation and detection of molecular quantum states with high sensitivity and precision have been demonstrated based on quantum-logic schemes. These advances represent important stepping stones for new directions in fundamental research and technological applications across various domains including precision measurements, quantum technologies and chemical dynamics.

We demonstrate the Doppler laser cooling of $^{40}$Ca$^+$ ions confined in a segmented linear Paul trap in the presence of a strong quadrupolar magnetic field generated by two permanent ring magnets. Magnetic field gradients of 800 to 1600 G/mm give rise to a highly position-dependent Zeeman shift on the energy levels of the trapped ions. Efficient laser cooling is demonstrated using two 397 nm cooling laser beams with appropriate wavelengths and polarizations and one 866 nm repumper laser beam. Coulomb crystals of ions are found to exhibit similar secular temperatures to those trapped in absence of the magnetic field. In addition, the position dependency of the Zeeman effect is used to generate a map of the field strength. This work forms the basis for developing hybrid trapping experiments for cold ions and neutral molecules that consist of an ion and a magnetic trap to study cold interactions between these species, and opens up new possibilities for quantum-science experiments that employ trapped ions in inhomogeneous magnetic fields.

This work examines optimized strategies for the preparation of single molecular ions in well-defined rotational quantum states in an ion trap with the example of the molecular nitrogen ion N2+. It advances a two-step approach consisting of an initial threshold-photoionization stage which produces molecular ions with a high probability in the target state, followed by a measurement-based state purification of the sample. For this purpose, a resonance-enhanced threshold photoionization scheme for producing N2+ in its rovibrational ground state proposed by Gardner et al. [Sci. Rep. 9, 506 (2019)] was characterized. The molecular state was measured using a recently developed quantum-non-demolition state-detection method finding a total fidelity of 38(7)% for producing ground-state N2+ under the present experimental conditions. By discarding ions from the trap not found to be in the target state, essentially state-pure samples of single N2+ ions can be generated for subsequent state-specific experiments.

We report the generation, trapping and sympathetic cooling of individual conformers of molecular ions with the example of cis- and trans-meta-aminostyrene. Following conformationally selective photoionization, the incorporation of the conformers into a Coulomb crystal of laser-cooled calcium ions was confirmed by fluorescence imaging, mass spectrometry and molecular dynamics simulations. We deduce the molecules to be stable in the trap environment for more than ten minutes. The present results pave the way for the spectroscopy and controlled chemistry of distinct ionic conformers in traps.

Rate constants for the charge transfer reaction between N${}_{2}$H${}^{+}$ and Rb in the mK regime are measured in an ion-atom hybrid trap and are found to be lower than the Langevin capture limit. Multireference ab initio computation of the potential energy surfaces involved in the reaction reveals that the low-temperature charge transfer is hindered by short-range features highly dependent on the collision angle and is promoted by a deformation of the molecular frame. The present study highlights the importance of polyatomic effects and of stereodynamics in cold molecular ion-neutral collisions.

Recent advances in experimental methodology enabled studies of the quantum-state and conformational dependence of chemical reactions under precisely controlled conditions in the gas phase. Here, we generated samples of selected gauche and s-trans 2,3-dibromobutadiene (DBB) by electrostatic deflection in a molecular beam and studied their reaction with Coulomb crystals of laser-cooled $\mathrm{Ca^{+}}$ ions in an ion trap. The rate coefficients for the total reaction were found to strongly depend on both the conformation of DBB and the electronic state of $\mathrm{Ca^{+}}$. In the $\mathrm{(4p)~^{2}P_{1/2}}$ and $\mathrm{(3d)~^{2}D_{3/2}}$ excited states of $\mathrm{Ca^{+}}$, the reaction is capture-limited and faster for the gauche conformer due to long-range ion-dipole interactions. In the $\mathrm{(4s)~^{2}S_{1/2}}$ ground state of $\mathrm{Ca^{+}}$, the reaction rate for s-trans DBB still conforms with the capture limit, while that for gauche DBB is strongly suppressed. The experimental observations were analysed with the help of adiabatic capture theory, ab-initio calculations and reactive molecular dynamics simulations on a machine-learned full-dimensional potential energy surface of the system. The theory yields near-quantitative agreement for s-trans-DBB, but overestimates the reactivity of the gauche-conformer compared to the experiment. The present study points to the important role of molecular geometry even in strongly reactive exothermic systems and illustrates striking differences in the reactivity of individual conformers in gas-phase ion-molecule reactions.

Hybrid traps for the simultaneous confinement of neutrals and ions have recently emerged as versatile tools for studying interactions between these species at very low temperatures. Such traps rely on the combination of different types of external fields for the confinement of either species raising the question of interactions between the individual traps. Here, the influence of a strongly inhomogeneous magnetic field used for trapping neutrals on the trapping and laser cooling of a single Ca$^+$ ion in a radiofrequency ion trap is studied theoretically using molecular-dynamics simulations based on multilevel rate equations. The inhomogeneous magnetic field couples the different components of the ion motion and introduces position-dependent Zeeman splittings. Nonetheless, laser cooling is still found to work efficiently as the ion samples different magnetic field strengths and directions along its trajectory. Offsetting the centres of the two traps generates a linear magnetic-field gradient so that multiple lasers are required to address the resulting range of Zeeman splittings in order to ensure efficient cooling. The present study yields detailed insights into the ion cooling dynamics in combined magnetic and radiofrequency electric fields relevant for the characterisation and optimisation of hybrid trapping experiments.

We theoretically investigate the collisional dynamics of laser-cooled $^{87}$Rb ground-state atoms and $^{40}$Ca$^+$ ground-state ions in the context of the hybrid trap experiment of Ref. [Phys. Rev. Lett. 107, 243202 (2011)], leading to ion losses. Cold $^{87}$Rb$^{40}$Ca$^+$ ground-state molecular ions are created by radiative association, and we demonstrate that they are protected against photodissociation by black-body radiation and by the $^{40}$Ca$^+$ cooling laser at 397~nm. This study yields an interpretation of the direct observation of $^{87}$Rb$^{40}$Ca$^+$ ions in the experiment, in contrast to other hybrid trap experiments using other species. Based on novel molecular data for the spin-orbit interaction, we also confirm that the non-radiative charge-exchange is the dominant loss process for Ca$^+$ and obtain rates in agreement with experimental observations and a previous calculation.

Quantum-logic techniques for state preparation, manipulation, and non-destructive interrogation are increasingly being adopted for experiments on single molecular ions confined in traps. The ability to control molecular ions on the quantum level via a co-trapped atomic ion offers intriguing possibilities for new experiments in the realms of precision spectroscopy, quantum information processing, cold chemistry, and quantum technologies with molecules. The present article gives an overview of the basic experimental methods, recent developments and prospects in this field.

Diels-Alder cycloadditions are efficient routes for the synthesis of cyclic organic compounds. There has been a long-standing discussion whether these reactions proceed via stepwise or concerted mechanisms. Here, we adopt a new experimental approach to explore the mechanistic details of the model polar cycloaddition of 2,3-dibromo-1,3-butadiene with propene ions by probing its conformational specificities in the entrance channel under single-collision conditions in the gas phase. Combining a conformationally controlled molecular beam with trapped ions, we find that both conformers of the diene, gauche and s-trans, are reactive with capture-limited reaction rates. Aided by quantum-chemical and quantum-capture calculations, this finding is rationalised by a simultaneous competition of concerted and stepwise reaction pathways, revealing an interesting mechanistic borderline case.

Recent advances in quantum technologies have enabled the precise control of single trapped molecules on the quantum level. Exploring the scope of these new technologies, we studied theoretically the implementation of qubits and clock transitions in the spin, rotational, and vibrational degrees of freedom of molecular nitrogen ions including the effects of magnetic fields. The relevant spectroscopic transitions span six orders of magnitude in frequency illustrating the versatility of the molecular spectrum for encoding quantum information. We identified two types of magnetically insensitive qubits with very low ("stretched"-state qubits) or even zero ("magic" magnetic-field qubits) linear Zeeman shifts. The corresponding spectroscopic transitions are predicted to shift by as little as a few mHz for an amplitude of magnetic-field fluctuations on the order of a few mG translating into Zeeman-limited coherence times of tens of minutes encoded in the rotations and vibrations of the molecule. We also found that the Q(0) line of the fundamental vibrational transition is magnetic-dipole allowed by interaction with the first excited electronic state of the molecule. The Q(0) transitions, which benefit from small systematic shifts for clock operation and high sensitivity to a possible variation in the proton-to-electron mass ratio, were so far not considered in single-photon spectra. Finally, we explored possibilities to coherently control the nuclear-spin configuration of N$_2^+$ through the magnetically enhanced mixing of nuclear-spin states.

Trapped atoms and ions are among the best controlled quantum systems which find widespread applications in quantum information, sensing and metrology. For molecules, however, a similar degree of control is currently lacking owing to their complex energy-level structure. Quantum-logic protocols in which atomic ions serve as probes for molecular ions are a promising route for achieving this level of control, especially with homonuclear molecules that decouple from black-body radiation. Here, a quantum-non-demolition protocol on single trapped N$_2^+$ molecules is demonstrated. The spin-rovibronic state of the molecule is detected with more than 99% fidelity and the position and strength of a spectroscopic transition in the molecule are determined, both without destroying the molecular quantum state. The present method lays the foundations for new approaches to molecular precision spectroscopy, for state-to-state chemistry on the single-molecule level and for the implementation of molecular qubits.

We report a precise determination of the lifetime of the (4p)$^2$P$_{3/2}$ state of $^{40}$Ca$^+$, $τ_{\textrm{P}_{3/2}}=6.639(42)$ ns, using a combination of measurements of the induced light shift and scattering rate on a single trapped ion. Good agreement with the result of a recent high-level theoretical calculation, $6.69(6)$ ns [Safronova et al., PRA 83, 012503 (2011)], but a 6-$σ$ discrepancy with the most precise previous experimental value, $6.924(19)$ ns [Jin et al., PRL 70, 3213 (1993)] is found. To corroborate the consistency and accuracy of the new measurements, relativistically corrected ratios of reduced-dipole-matrix elements are used to directly compare our result with a recent result for the P$_{1/2}$ state, yielding a good agreement. The application of the present method to precise determinations of radiative quantities of molecular systems is discussed.

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 consists of 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 N$_2^+$ as a prototypical example in the present work, our method is applicable to a wide range of diatomic and polyatomic molecules.

We report a study of cold charge-transfer (CT) collisions of Rb atoms with N$_2^+$ and O$_2^+$ ions in the mK regime using a dynamic ion-neutral hybrid trapping experiment. State- and collision-energy- dependent reaction rate coefficients have been measured for both systems. We observe markedly different charge-transfer kinetics and dynamics for the different systems and reaction channels. While the kinetics in some channels are consistent with classical capture theory for the rate coefficient, others show distinct non-universal dynamics. The experimental results are interpreted with the help of classical capture, quasiclassical trajectory and quantum scattering calculations using state-of-the-art ab-initio potentials for the highly excited molecular states involved. The theoretical analysis reveals an intricate interplay between short- and long-range effects in the different reaction channels which ultimately determines the CT dynamics and rates. At short range, CT was found to occur via both single and multiple collision events with the latter typically showing pronounced large-amplitude internal motions of the collision complex. Our results illustrate salient mechanisms that determine the efficiency of cold molecular CT reactions.

We demonstrate the long-term ($<$ 1 minute) trapping of Stark-decelerated OH radicals in their $X~^{2}Π_{3/2}~(ν= 0,~J = 3/2,~M_{J} = 3/2,~f)$ state in a permanent magnetic trap. The trap environment was cryogenically cooled to a temperature of 17 K in order to efficiently suppress black-body-radiation-induced pumping of the molecules out of trappable quantum states and collisions with residual background gas molecules which usually limit the trap lifetimes. The cold molecules were kept confined on timescales approaching minutes, an improvement of up to two orders of magnitude compared to room-temperature experiments, at translational temperatures on the order of 25 mK. The present results pave the way for spectroscopic studies of trapped molecules with long interaction times enabling high precision, for investigations of cold collisions and reactions with very small reaction rates, for new avenues for the production of ultracold molecules via sympathetic cooling and for the realisation of new forms of hybrid matter with co-trapped atoms or ions.

We discuss the design and optimisation of two types of junctions between surface-electrode radiofrequency ion-trap arrays that enable the integration of experiments with sympathetically cooled molecular ions on a monolithic chip device. A detailed description of a multi-objective optimisation procedure applicable to an arbitrary planar junction is presented, and the results for a cross junction between four quadrupoles as well as a quadrupole-to-octupole junction are discussed. Based on these optimised functional elements, we propose a multi-functional ion-trap chip for experiments with translationally cold molecular ions at temperatures in the millikelvin range. This study opens the door to extending complex chip-based trapping techniques to Coulomb-crystallised molecular ions with potential applications in mass spectrometry, spectroscopy, controlled chemistry and quantum technology.

Many molecules exhibit multiple conformers that often easily interconvert under thermal conditions. Therefore, single conformations are difficult to isolate which renders the study of their distinct chemical reactivities challenging. We have recently reported a new experimental method for the characterization of conformer-specific effects in chemical reactions [Y. P. Chang et al., Science 342, 98 (2013)]. Different conformers are spatially separated using inhomogeneous electric fields and reacted with a Coulomb crystal of cold, spatially localized ions in a trap. As a first application, we studied reactions between the two conformers of 3-aminophenol and Ca$^+$. We observed a twofold larger rate constant for the $cis$ compared to the $trans$ conformer which was rationalized in terms of the differences in the long-range ion-molecule interactions. The present article provides a detailed description of the new method and a full account of the experimental results as well as the accompanying theoretical calculations.

The study of interactions between simultaneously trapped cold ions and atoms has emerged as a new research direction in recent years. The development of ion-atom hybrid experiments has paved the way for investigating elastic, inelastic and reactive collisions between these species at very low temperatures, for exploring new cooling mechanisms of ions by atoms and for implementing new hybrid quantum systems. The present lecture reviews experimental methods, recent results and upcoming developments in this emerging field.

Many molecules exhibit multiple rotational isomers (conformers) that interconvert thermally and are difficult to isolate. Consequently, a precise characterization of their role in chemical reactions has proven challenging. We have probed the reactivity of specific conformers using an experimental technique based on their spatial separation in a molecular beam by electrostatic deflection. The separated conformers react with a target of Coulomb-crystallized ions in a trap. In the reaction of Ca$^+$ with 3-aminophenol, we find a twofold larger rate constant for the \textit{cis}- compared to the \textit{trans}-conformer (differentiated by the O-H bond orientation). This result is explained by conformer-specific differences in the long-range ion-molecule interaction potentials. Our approach demonstrates the possibility of controlling reactivity through selection of conformational states.

Cold chemical reactions between laser-cooled Ca^+ ions and Rb atoms were studied in an ion-atom hybrid trap. Reaction rate constants were determined in the range of collision energies <E_{coll}>/k_B = 20 mK-20 K. The lowest energies were achieved in experiments using single localized Ca^+ ions. Product branching ratios were studied using resonant-excitation mass spectrometry. The dynamics of the reactive processes in this system (non-radiative and radiative charge transfer as well as radiative association leading to the formation of CaRb^+ molecular ions) have been analyzed using high-level quantum-chemical calculations of the potential energy curves of CaRb^+ and quantum-scattering calculations for the radiative channels. For the present low-energy scattering experiments, it is shown that the energy dependence of the reaction rate constants is governed by long-range interactions in line with the classical Langevin model, but their magnitude is determined by short-range non-adiabatic and radiative couplings which only weakly depend on the asymptotic energy. The quantum character of the collisions is predicted to manifest itself in the occurrence of narrow shape resonances at well-defined collision energies. The present results highlight both universal and system-specific phenomena in cold ion-neutral reactive collisions.

Light-assisted reactive collisions between laser-cooled Ba+ ions and Rb atoms were studied in an ion-atom hybrid trap. The reaction rate was found to strongly depend on the electronic state of the reaction partners with the largest rate constant (7(2) x 10^-11 cm^3 s^-1) obtained for the excited Ba+(6s)+Rb(5p) reaction channel. Similar to the previously studied Ca+ + Rb system, charge transfer and radiative association were found to be the dominant reactive processes. The generation of molecular ions by radiative association could directly be observed by their sympathetic cooling into a Coulomb crystal. Potential energy curves up to the Ba+(6s)+Rb(5p) asymptote and reactive-scattering cross sections for the radiative processes were calculated. The theoretical rate constant obtained for the lowest reaction channel Ba+(6s)+Rb(5s) is compatible with the experimental estimates obtained thus far.

We report on a study of cold reactive collisions between sympathetically-cooled molecular ions and laser-cooled atoms in an ion-atom hybrid trap. Chemical reactions were studied at average collision energies <Ecoll>/k > 20 mK, about two orders of magnitude lower than has been achieved in previous experiments with molecular ions. Choosing N2+ +Rb as a prototypical system, we find that the reaction rate is independent of the collision energy, but strongly dependent on the internal state of Rb. Highly efficient charge exchange about four times faster than the Langevin rate was observed with Rb in the excited (5p) 2P3/2 state. This observation is rationalized in terms of a capture process dominated by the charge- quadrupole interaction and a near resonance between the entrance and exit channels of the reaction. Our results provide a test of classical models for reactions of molecular ions at the lowest energies reached thus far.

State-selected Coulomb-crystallized molecular ions were employed for the first time in ion-molecule reaction studies using the prototypical charge-transfer process $\mathrm{N_2^++N_2\rightarrow N_2+N_2^+}$ as an example. By preparing the reactant ions in a well-defined rovibrational state and localizing them in space by sympathetic cooling to millikelvin temperatures in an ion trap, state- and energy-controlled reaction experiments with sensitivities on the level of single ions were performed. The experimental results were interpreted with quasi-classical trajectory simulations on a six-dimensional potential-energy surface which provided detailed insight into translation-to-rotation energy transfer occurring during charge transfer between N$_2$ and N$_2^+$.

We present a combined experimental and theoretical study of cold reactive collisions between laser-cooled Ca+ ions and Rb atoms in an ion-atom hybrid trap. We observe rich chemical dynamics which are interpreted in terms of non-adiabatic and radiative charge exchange as well as radiative molecule formation using high-level electronic structure calculations. We study the role of light-assisted processes and show that the efficiency of the dominant chemical pathways is considerably enhanced in excited reaction channels. Our results illustrate the importance of radiative and non-radiative processes for the cold chemistry occurring in ion-atom hybrid traps.

We present a new method for the generation of rotationally and vibrationally state-selected, translationally cold molecular ions in ion traps. Our technique is based on the state-selective threshold photoionization of neutral molecules followed by sympathetic cooling of the resulting ions with laser-cooled calcium ions. Using N$_2^+$ ions as a test system, we achieve > 90 % selectivity in the preparation of the ground rovibrational level and state lifetimes on the order of 15 minutes limited by collisions with background-gas molecules. The technique can be employed to produce a wide range of apolar and polar molecular ions in the ground and excited rovibrational states. Our approach opens up new perspectives for cold quantum-controlled ion-molecule-collision studies, frequency-metrology experiments with state-selected molecular ions and molecular-ion qubits.