Peter Schmelcher

We consider a hybrid atom-ion system consisting of a pair of bosons interacting with a single ion in a quasi-one-dimensional trapping geometry. Building upon a model potential for the atom-ion interaction developed in earlier theoretical works, we investigate the behaviour of the low-energy eigenstates for varying contact interaction strength $g$ among the atoms. In particular, we contrast the two cases of a static and a mobile ion. Our study is carried out by means of the Multi-Layer Multi-Configuration Time-Dependent Hartree method for Bosons, a numerically-exact $\textit{ab initio}$ method for the efficient simulation of entangled mixtures. We find that repulsive atom interactions induce locally-distinct modifications of the atomic probability distribution unique to each eigenstate. Whilst the atoms on average separate from each other with increasing $g$, they do not necessarily separate from the ion. The mobility of the ion leads in general to greater separations among the atoms as well as between the atoms and the ion. Notably, we observe an exchange between the kinetic energy of the atoms and the atom-ion interaction energy for all eigenstates, which is both interaction- and mobility-induced. For the ground state, we provide an intuitive description by constructing an effective Hamiltonian for each species, which aptly captures the response of the atoms to the ion's mobility. Furthermore, the effective picture predicts enhanced localisation of the ion, in agreement with our results from exact numerical simulations.

We consider a degenerate Bose gas confined in a double-well potential in interaction with a trapped ion in one dimension and investigate the impact of two relevant sources of imperfections in experiments on the system dynamics: ion motion and thermal excitations of the bosonic ensemble. Particularly, their influence on the entanglement generation between the spin state of the moving ion and the atomic ensemble is analyzed. We find that the detrimental effects of the ion motion on the entanglement protocol can be mitigated by properly choosing the double-well parameters as well as timings of the protocol. Furthermore, thermal excitations of the bosons affect significantly the system's tunneling and self-trapping dynamics at moderate temperatures; i.e., thermal occupation of a few double-well quanta reduces the protocol performance by about 10%. Hence, we conclude that finite temperature is the main source of decoherence in such junctions and we demonstrate the possibility to entangle the condensate motion with the ion vibrational state.

We investigate the non-equilibrium dynamics of coupled Coulomb crystals of different sizes trapped in a double well potential. The dynamics is induced by an instantaneous quench of the potential barrier separating the two crystals. Due to the intra- and inter-crystal Coulomb interactions and the asymmetric population of the potential wells we observe a complex reordering of ions within the two crystals as well as ion transfer processes from one well to the other. The study and analysis of the latter processes constitutes the main focus of this work. In particular we examine the dependence of the observed ion transfers on the quench amplitude performing an analysis for different crystalline configurations ranging from one-dimensional ion chains via two-dimensional zig-zag chains and ring structures to three-dimensional spherical structures. Such an analysis provides us with the means to extract the general principles governing the ion transfer dynamics and we gain some insight on the structural disorder caused by the quench of the barrier height.

We explore the non-equilibrium dynamics of two coupled zig-zag chains of trapped ions in a double well potential. Following a quench of the potential barrier between both wells, the induced coupling between both chains due to the long-range interaction of the ions leads to their complete melting. The resulting dynamics is however not exclusively irregular but leads to phases of motion during which various ordered structures appear with ions arranged in arcs, lines and crosses. We quantify the emerging order by introducing a suitable measure and complement our analysis of the ion dynamics using a normal mode analysis showing a decisive population transfer between only a few distinguished modes.

We explore the non-equilibrium escape dynamics of long-range interacting ions in one-dimensional traps. The phase space of the few ion setup and its impact on the escape properties are studied. As a main result we show that an instantaneous reduction of the trap's potential depth leads to the synchronized emission of a sequence of ion pairs if the initial configurations are close to the crystalline ionic configuration. The corresponding time-intervals of the consecutive pair emission as well as the number of emitted pairs can be tuned by changing the final trap depth. Correlations between the escape times and kinetic energies of the ions are observed and analyzed.