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

Abstract

Sympathetic cooling of trapped ions through collisions with neutral buffer gases is critical to a variety of modern scientific fields, including fundamental chemistry, mass spectrometry, nuclear and particle physics, and atomic and molecular physics. Despite its widespread use over four decades, there remain open questions regarding its fundamental limitations. To probe these limits, here we examine the steady-state evolution of up to 10 barium ions immersed in a gas of three-million laser-cooled calcium atoms. We observe and explain the emergence of nonequilibrium behaviour as evidenced by bifurcations in the ion steady-state temperature, parameterized by ion number. We show that this behaviour leads to the limitations in creating and maintaining translationally cold samples of trapped ions using neutral-gas sympathetic cooling. These results may provide a route to studying non-equilibrium thermodynamics at the atomic level.

Sympathetic cooling of molecular ions with ultracold atoms

“…This expression for ln , first presented in [29] and shown in Fig. 4 extends the previous determination in [28] to the lower temperatures and trapped ion number of one-dimensional ion chains.…”

“…This model, which has been verified by detailed molecular dynamics simulations [27,28] and experiment when possible [27,29], provides a simple and accurate means to calculate both the relaxation dynamics and the properties of the ion steady-state. Further, this model has been shown to agree with a quantum mechanical calculation of a single ion immersed in a buffer gas over its range of validity [30].…”

“…It was known that this phenomenon is due to the fact that ions are subject to a timedependent confining potential and are therefore not an isolated system. However, despite pioneering work by Dehmelt and others [24,25], an accurate analytical description of the relaxation process was not achieved until very recently [26][27][28][29].…”

“…Building upon the important work of Moriwaki et al [24], we have developed a kinematic model [27][28][29] over the last three years, which accurately describes the ion relaxation process in the presence of a buffer gas, as well as the heating effect that occurs when multiple ions are trapped simultaneously. This model, which has been verified by detailed molecular dynamics simulations [27,28] and experiment when possible [27,29], provides a simple and accurate means to calculate both the relaxation dynamics and the properties of the ion steady-state.…”

“…4 The experimental and MD determinations of ln versus g. Despite large variation in trap parameters the observed values fall along the same curve, indicating a universal form for ln . The dashed black curve represents the analytical form used here and in [29] (modified to agree with low temperature data), while the other curves represent previous forms described elsewhere [27]. The top x-axis denotes the domain of this graph in terms of the plasma coupling parameter, , which is the ratio of potential to kinetic energy This behavior creates very rich dynamics for the cooling of ions, either by a laser or by a buffer gas.…”