Blue-sky bifurcation of ion energies and the limits of neutral-gas sympathetic cooling of trapped ions

Introduction

The concept of using a background gas to facilitate the loading of metallic particles into early ion traps was first demonstrated in 1959 (ref. 1). Since then, using collisions with cold, chemically inert gases to sympathetically cool trapped ions has become a general technique in many areas of scientific research. Today, the sympathetic cooling of ions with neutral buffer gases is routinely used to control the energy scales of chemical reactions2, to improve the performance of commercial mass spectrometers3, and to prepare short-lived exotic nuclei for tests of the Standard Model4. It has also been proposed as a method to initialize qubits in future quantum computation architecture5.

Despite the widespread use of sympathetic cooling in ion traps, its kinetics have not yet been completely described and, likewise, its limitations are still not fully understood. The complexity of the cooling process derives from the fact that a system of trapped ions immersed in a cold buffer gas is not an isolated system. Instead, due to the presence of the time-dependent trapping potential, energy is injected and removed from the system over a single trapping cycle. Thus, as it is not a true representation of the canonical ensemble, the trapped ions do not tend to thermal equilibrium with the cold buffer gas as one might expect. As a result, collisions in the ion trap lead to fundamentally nonequilibrium processes that have made it difficult to establish a complete kinetic description of the technique and, as later explained, limits its ability to create and maintain translationally cold temperatures.

To probe this nonequilibrium behaviour, we characterize the collisional processes between trapped ions and a buffer gas of laser-cooled atoms in a hybrid atom–ion trap. In our conception of this apparatus (shown inFig. 1a), laser-cooled barium ions confined by a linear quadrupole trap (LQT) are immersed in a 4 mK gas of magneto-optically trapped calcium atoms. Thus far, relatively little work has been done to fully understand the complex statistical mechanics of these hybrid systems6,7,8,9,10,11, despite being critical to current applications such as observing atom–ion collisions and reactions at cold temperatures7,12,13,14,15,16 and producing cold molecular ions17,18. Through a more complete understanding of the collisional processes and nonequilibrium phenomena in these systems, which offer precise experimental control, we can establish the general limits of sympathetic cooling in ion traps.

Figure 1: Emergence of nonequilbrium dynamics in a hybrid atom–ion trap.

(a) A 3D rendering of the hybrid trap used to create an ensemble of trapped ions immersed in a laser-cooled buffer gas, as shown in the inset composite photograph. (b) Analytical heating and cooling rates for ions in a hybrid atom–ion trap. Three characteristic regimes exist for different relative heating and cooling strengths as parameterized by Ni and are characterized by the number and type of fixed points they exhibit. (c) Steady-state evolution of ion temperatures for different Ni and initializations as calculated by the MD simulation and analytical model. The left (right) pairs convey this evolution near the opening (closing) of the bifurcation at Ni=3 (Ni=26), where the number of steady-state temperatures go from one (two) to two (one). (d) Steady-state temperatures for different Ni and initializations as calculated by the MD simulation and analytical model. Error bars represent s.e. Red (blue)-shaded regions represent the ranges of ion temperatures before immersion for the hot (cold) initialization. Regimes I, II, and III are observed and indicated by differently shaded regions. The transitions between these regimes are marked by blue-sky bifurcations.