Ultracold atom-ion mixtures are gaining increasing interest due to their potential applications in ultracold and state-controlled chemistry, quantum computing, and many-body physics. Here, we studied the dynamics of a single ground-state cooled ion during few, to many, Langevin (spiraling) collisions with ultracold atoms. We measured the ion's energy distribution and observed a clear deviation from the Maxwell-Boltzmann distribution, characterized by an exponential tail, to a power-law distribution best described by a Tsallis function. Unlike previous experiments, the energy scale of atom-ion interactions is not determined by either the atomic cloud temperature or the ion's trap residual excess-micromotion energy. Instead, it is determined by the force the atom exerts on the ion during a collision which is then amplified by the trap dynamics. This effect is intrinsic to ion Paul traps and sets the lower bound of atom-ion steady-state interaction energy in these systems. Despite the fact that our system is eventually driven out of the ultracold regime, we are capable of studying quantum effects by limiting the interaction to the first collision when the ion is initialized in the ground state of the trap.

Whenever several quantum light emitters are brought in proximity with one another, their interaction with common electromagnetic fields couples them, giving rise to cooperative shifts in their resonance frequency. Such collective line shifts are central to modern atomic physics, being closely related to superradiance[1] on one hand and the Lamb shift[2] on the other. Although collective shifts have been theoretically predicted more than fifty years ago [3], the effect has not been observed yet in a controllable system of a few isolated emitters. Here, we report a direct spectroscopic observation of the cooperative shift of an optical electric dipole transition in a system of up to eight Sr + ions suspended in a Paul trap. We study collective resonance shift in the previously unexplored regime of far-field coupling, and provide the first observation of cooperative effects in an array of quantum emitters. These results pave the way towards experimental exploration of cooperative emission phenomena in mesoscopic systems.Soon after the discovery of superradiance by Dicke[1], it was realized [3][4][5] that superradiance phenomena are accompanied by a dispersive counterpart that shifts the resonance energies of the collective excitations relative to those of isolated emitters. The superradiance effects and the resonance shift originate, respectively, from the real and imaginary parts of resonant dipole-dipole interaction between emitters. The collective shifts arise via emission and reabsorption of virtual photons, and are therefore referred to as cooperative Lamb shift [6][7][8][9][10].Although cooperative phenomena have received a great deal of scientific attention, the experimental observations of collective Lamb shift have been relatively few. Cooperative shifts have been detected in a three-photon excitation resonance in Xenon [11] and, recently, in the absorption line of Rubidium vapor confined to an ultrathin cell [7]. In both cases, the cooperative shifts, arising from statistically averaged interaction of a large ensemble of atoms, were proportional to the atomic density.In a different approach, the energy level shifts due to resonant dipole-dipole interaction in the near field were studied in a system of two fluorescent molecules embedded in a dielectric film [12]. Such near-field interactions * These authors contributed equally to this work have also played an essential role in a number of experiments with Rydberg atoms [13][14][15]. In particular, the near-field cooperative shift in a system of two atoms has been utilized to prevent the transition of more than one atom to the Rydberg state, bringing about a phenomenon known as Rydberg blockade [16][17][18].Cooperative phenomena can be amplified by placing the emitters inside a resonator. Cavity-enhanced cooperative frequency shift in a nuclear excitation has been observed in a layer of Fe atoms embedded in a planar waveguide [8]. The coupling between emitters can also be enhanced by interaction with a single mirror. Such arrangement enabled the observation...

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.The impressive advances achieved in the control of ultracold trapped atoms and ions on the quantum level are now increasingly being transferred to molecular systems. Cold, trapped molecules have been created by, e.g., binding ultracold atoms via Feshbach resonances [1] and photoassociation [2, 3], molecular-beam slowing [4], direct laser cooling [5,6] and sympathetic cooling [7,8]. The trapping of the cold molecules enables experiments with long interaction times and thus paves the way for new applications such as studies of ultracold chemistry [9] and precision spectroscopic measurements which aim, e.g., at a precise determination of fundamental physical constants [10] and their possible time variation [11,12] as well as tests of fundamental theories which reach beyond the standard model [13,14].The complex energy level structure and the absence of optical cycling transitions in most molecular systems constitute a major challenge in the state preparation, laser cooling, state detection and coherent manipulation of molecules. Molecular ions trapped in radiofrequency ion traps which are sympathetically cooled by simultaneously trapped atomic ions [7,8] have proven a promising route for overcoming these obstacles. Recently, their rotational cooling and state preparation has been achieved [15][16][17][18], precision measurements of quantum electrodynamics and fundamental constants have been performed [10,19], the first studies of dipole-forbidden spectroscopic transitions in the mid-infrared spectral domain have been reported [20] and state-and energy-controlled collisions with cold atoms have been realized [21,22]. However, in order to reach the same exquisite level of control on the quantum level for a single molecule which can be achieved with trapped atoms [23], new methodological developments are required. In this context, the most promising route for achieving ultimate quantum control of molecular ions in trap experiments is constituted by quantum-logic protocols [24] in which a cotrapped atomic ion acts as a probe for th...

Quantum control of chemical reactions is an important goal in chemistry and physics. Ultracold chemical reactions are often controlled by preparing the reactants in specific quantum states. Here we demonstrate spin-controlled atom–ion inelastic (spin-exchange) processes and chemical (charge-exchange) reactions in an ultracold Rb-Sr+ mixture. The ion’s spin state is controlled by the atomic hyperfine spin state via spin-exchange collisions, which polarize the ion’s spin parallel to the atomic spin. We achieve ~ 90% spin polarization due to the absence of strong spin-relaxation channel. Charge-exchange collisions involving electron transfer are only allowed for (RbSr)+ colliding in the singlet manifold. Initializing the atoms in various spin states affects the overlap of the collision wave function with the singlet molecular manifold and therefore also the reaction rate. Our observations agree with theoretical predictions.

Experimental realizations of charged ions and neutral atoms in overlapping traps are gaining increasing interest due to their wide research application ranging from chemistry at the quantum level to quantum simulations of solid-state systems. Here, we describe a system in which we overlap a single ground-state cooled ion trapped in a linear Paul trap with a cloud of ultracold atoms such that both constituents are in the µK regime. Excess micromotion (EMM) currently limits atom-ion interaction energy to the mK energy scale and above. We demonstrate spectroscopy methods and compensation techniques which characterize and reduce the ion's parasitic EMM energy to the µK regime even for ion crystals of several ions. We give a substantial review on the non-equilibrium dynamics which governs atom-ion systems. The non-equilibrium dynamics is manifested by a powerlaw distribution of the ion's energy. We overview the coherent and non-coherent thermometry tools which we used to characterize the ion's energy distribution after single to many atom-ion collisions.

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 study the time-dependent fluorescence of an initially hot, multi-level, single atomic ion trapped in a radio-frequency Paul trap during Doppler cooling. We have developed an analytical model that describes the fluorescence dynamics during Doppler cooling which is used to extract the initial energy of the ion. While previous models of Doppler cooling thermometry were limited to atoms with a two-level energy structure and neglected the effect of the trap oscillating electric fields, our model applies to atoms with multi-level energy structure and takes into account the influence of micromotion on the cooling dynamics. This thermometry applies to any initial energy distribution. We experimentally test our model with an ion prepared in a coherent, thermal and Tsallis energy distributions. CONTENTS

Sympathetic cooling is the process of energy exchange between a system and a colder bath. We investigate this fundamental process in an atom-ion experiment where the system is composed of a single ion trapped in a radio-frequency Paul trap and prepared in a classical oscillatory motion with total energy of ∼200  K, and the bath is an ultracold cloud of atoms at μK temperature. We directly observe the sympathetic cooling dynamics with single-shot energy measurements during one to several collisions in two distinct regimes. In one, collisions predominantly cool the system with very efficient momentum transfer leading to cooling in only a few collisions. In the other, collisions can both cool and heat the system due to nonequilibrium dynamics in the presence of the ion trap's oscillating electric fields. While the bulk of our observations agree well with a molecular-dynamics simulation of hard-sphere (Langevin) collisions, a measurement of the scattering angle distribution reveals forward-scattering (glancing) collisions which are beyond the Langevin model. This work paves the way for further nonequilibrium and collision dynamics studies using the well-controlled atom-ion system.