Great advances in precision quantum measurement have been achieved with trapped ions and atomic gases at the lowest possible temperatures [1-3]. These successes have inspired ideas to merge the two systems [4]. In this way one can study the unique properties of ionic impurities inside a quantum fluid [5][6][7][8][9][10][11] or explore buffer gas cooling of the trapped ion quantum computer [12]. Remarkably, in spite of its importance, experiments with atom-ion mixtures remained firmly confined to the classical collision regime [13]. We report a collision energy of 1.15(0.23) times the s-wave energy (or 9.9(2.0) µK) for a trapped ytterbium ion in an ultracold lithium gas. We observed a deviation from classical Langevin theory by studying the spin-exchange dynamics, indicating quantum behavior in the atom-ion collisions. Our results open up numerous opportunities, such as the exploration of atom-ion Feshbach resonances [14,15], in analogy to neutral systems [16].

We report on the observation of cold collisions between 6 Li atoms and Yb + ions. This combination of species has recently been proposed as the most suitable for reaching the quantum limit in hybrid atom-ion systems, due to its large mass ratio. For atoms and ions prepared in the 2 S 1/2 ground state, the charge transfer and association rate is found to be at least 10 3 times smaller than the Langevin collision rate. These results confirm the excellent prospects of 6 Li-Yb + for sympathetic cooling and quantum information applications. For ions prepared in the excited electronic states 2 P 1/2 , 2 D 3/2 and 2 F 7/2 , we find that the reaction rate is dominated by charge transfer and does not depend on the ionic isotope nor the collision energy in the range ∼ 1-120 mK. The low charge transfer rate for ground state collisions is corroborated by theory, but the 4f shell in the Yb + ion prevents an accurate prediction for the charge transfer rate of the 2 P 1/2 , 2 D 3/2 and 2 F 7/2 states. Using ab initio methods of quantum chemistry we calculate the atom-ion interaction potentials up to energies of 30×10 3 cm −1 , and use these to give qualitative explanations of the observed rates.

We perform numerical simulations of trapped 171 Yb + ions that are buffer gas cooled by a cold cloud of 6 Li atoms. This species combination has been suggested to be the most promising for reaching the quantum regime of interacting atoms and ions in a Paul trap. Treating the atoms and ions classically, we compute that the collision energy indeed reaches below the quantum limit for a perfect linear Paul trap. We analyze the effect of imperfections in the ion trap that cause excess micromotion. We find that the suppression of excess micromotion required to reach the quantum limit should be within experimental reach. Indeed, although the requirements are strong, they are not excessive and lie within reported values in the literature. We analyze the detection and suppression of excess micromotion in our experimental setup. Using the obtained experimental parameters in our simulation, we calculate collision energies that are a factor 2-11 larger than the quantum limit, indicating that improvements in micromotion detection and compensation are needed there. We also analyze the buffergas cooling of linear and two-dimensional ion crystals. We find that the energy stored in the eigenmodes of ion motion may reach 10-100 µK after buffer-gas cooling under realistic experimental circumstances. Interestingly, not all eigenmodes are buffer-gas cooled to the same energy. Our results show that with modest improvements of our experiment, studying atom-ion mixtures in the quantum regime is in reach, allowing for buffer-gas cooling of the trapped ion quantum platform and to study the occurrence of atom-ion Feshbach resonances.

The accurate transport of an ion over macroscopic distances represents a challenging control problem due to the different length and time scales that enter and the experimental limitations on the controls that need to be accounted for. Here, we investigate the performance of different control techniques for ion transport in state-of-the-art segmented miniaturized ion traps. We employ numerical optimization of classical trajectories and quantum wavepacket propagation as well as analytical solutions derived from invariant based inverse engineering and geometric optimal control. The applicability of each of the control methods depends on the length and time scales of the transport. Our comprehensive set of tools allows us make a number of observations. We find that accurate shuttling can be performed with operation times below the trap oscillation period. The maximum speed is limited by the maximum acceleration that can be exerted on the ion. When using controls obtained from classical dynamics for wavepacket propagation, wavepacket squeezing is the only quantum effect that comes into play for a large range of trapping parameters. We show that this can be corrected by a compensating force derived from invariant based inverse engineering, without a significant increase in the operation time.

We report on observations of spin dynamics in single Yb + ions immersed in a cold cloud of spinpolarized 6 Li atoms. This species combination has been proposed to be the most suitable system to reach the quantum regime in atom-ion experiments. For 174 Yb + , we find that the atomic bath polarizes the spin of the ion by 93(4) % after a few Langevin collisions, pointing to strong spinexchange rates. For the hyperfine ground states of 171 Yb + , we also find strong rates towards spin polarization. However, relaxation towards the F = 0 ground state occurs after 7.7(1.5) Langevin collisions. We investigate spin impurity atoms as possible source of apparent spin-relaxation leading us to interpret the observed spin-relaxation rates as an upper limit. Using ab initio electronic structure and quantum scattering calculations, we explain the observed rates and analyze their implications for the possible observation of Feshbach resonances between atoms and ions once the quantum regime is reached.