We theoretically investigate the dynamics of a trapped ion immersed in a spatially localized buffer gas. For a homogeneous buffer gas, the ion's energy distribution reaches a stable equilibrium only if the mass of the buffer gas atoms is below a critical value. This limitation can be overcome by using multipole traps in combination with a spatially confined buffer gas. Using a generalized model for elastic collisions of the ion with the buffer-gas atoms, the ion's energy distribution is numerically determined for arbitrary buffer-gas distributions and trap parameters. Three regimes characterized by the respective analytic form of the ion's equilibrium energy distribution are found. Final ion temperatures down to the millikelvin regime can be achieved by adiabatically decreasing the spatial extension of the buffer gas and the effective ion trap depth (forced sympathetic cooling).

No abstract

We report the trapping of ultracold neutral Rb atoms and Ba + ions in a common optical potential in absence of any radiofrequency (RF) fields. We prepare Ba + at 370 µK and demonstrate efficient sympathetic cooling by 100 µK after one collision. Our approach is currently limited by the Rb density and related three-body losses, but it overcomes the fundamental limitation in RF traps set by RF-driven, micromotion-induced heating. It is applicable to a wide range of ion-atom species, and may enable novel ultracold chemistry experiments and complex many-body dynamics.

The electronic and motional degrees of freedom of trapped ions can be controlled and coherently coupled on the level of individual quanta. Assembling complex quantum systems ion by ion while keeping this unique level of control remains a challenging task. For many applications, linear chains of ions in conventional traps are ideally suited to address this problem. However, driven motion due to the magnetic or radio-frequency electric trapping fields sometimes limits the performance in one dimension and severely affects the extension to higher-dimensional systems. Here, we report on the trapping of multiple barium ions in a single-beam optical dipole trap without radio-frequency or additional magnetic fields. We study the persistence of order in ensembles of up to six ions within the optical trap, measure their temperature, and conclude that the ions form a linear chain, commonly called a one-dimensional Coulomb crystal. As a proof-of-concept demonstration, we access the collective motion and perform spectrometry of the normal modes in the optical trap. Our system provides a platform that is free of driven motion and combines advantages of optical trapping, such as state-dependent confinement and nanoscale potentials, with the desirable properties of crystals of trapped ions, such as long-range interactions featuring collective motion. Starting with small numbers of ions, it has been proposed that these properties would allow the experimental study of many-body physics and the onset of structural quantum phase transitions between one-and two-dimensional crystals.

We provide a comprehensive theoretical framework for describing the dynamics of a single trapped ion interacting with a neutral buffer gas, thus extending our previous studies on buffer-gas cooling of ions beyond the critical mass ratio [B. Höltkemeier et al., Phys. Rev. Lett. 116, 233003 (2016)]. By transforming the collisional processes into a frame, where the ion's micromotion is assigned to the buffer gas atoms, our model allows one to investigate the influence of non-homogeneous buffer gas configurations as well as higher multipole orders of the radio-frequency trap in great detail. Depending on the neutral-to-ion mass ratio, three regimes of sympathetic cooling are identified which are characterized by the form of the ion's energy distribution in equilibrium. We provide analytic expressions and numerical simulations of the ion's energy distribution, spatial profile and cooling rates for these different regimes. Based on these findings, a method for actively decreasing the ion's energy by reducing the spatial expansion of the buffer gas arises (Forced Sympathetic Cooling).