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Chinese Physics Letters

Kinetic Energy of Trapped Ions Cooled by Buffer Gas

Chen Liang, Lei She, Jiaomei Li, Kelin Gao

Published Jun 1, 2010• 5 citations
Publisher

Abstract

The average kinetic energy of 40 Ca + ions is measured by the method of evaporating ions in an rf ion trap. The kinetic energy of the ion 40 Ca + varies from 0.5 eV to 0.2eV with changing buffer gas pressure from 10 −7 mbar to 10 −5 mbar. The Brownian motion model is also introduced to calculate the average kinetic energy of the trapped ions.

DOI
10.1088/0256-307x/27/6/063201

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The average kinetic energy of 40 Ca + ions is measured by the method of evaporating ions in an rf ion trap. The kinetic energy of the ion 40 Ca + varies from 0.5 eV to 0.2eV with changing buffer gas pressure from 10 −7 mbar to 10 −5 mbar. The Brownian motion model is also introduced to calculate the average kinetic energy of the trapped ions.
We have investigated the efficiency of ion trapping in a linear Paul trap. First, we measured the dependence of trapping efficiency on dc and rf voltages using a channel electron multiplier for the direct detection of the electric current of the trapped ions. The most efficient dc and rf voltages were 5.0 and 175 V, respectively. Second, we calculated the trapping efficiency using a simulation code and compared it with the experimental results. We determined that the efficiency of ion trapping decreased monotonically with increasing dc voltage and had an optimum rf voltage. From the numerical calculation, the dependences of trapping efficiency on dc and rf voltages and the initial kinetic energy of ions was derived and the optimum dc and rf voltages and the initial kinetic energy of ions were found to be 0, 210 V, and 1 eV, respectively.
The immersion of a single ion confined by a radiofrequency (RF) trap in an ultracold atomic gas extends the concept of buffer gas cooling to a new temperature regime. The steady-state energy distribution of the ion is determined by its kinetics in the RF field rather than the temperature of the buffer gas. Moreover, the finite size of the ultracold gas facilitates the observation of back-action of the ion onto the buffer gas. We numerically investigate the system's properties depending on atom–ion mass ratio, trap geometry, differential cross-section and non-uniform neutral atom density distribution. Experimental results are well reproduced by our model considering only elastic collisions. We identify excess micromotion to set the typical scale for the ion energy statistics and explore the applicability of the mobility collision cross-section to the ultracold regime.
We present an experimental method for the characterization of the kinetic energies of ions confined in a 22-pole radio frequency trap by inducing a small potential barrier using the surrounding ring electrodes, allowing the selective extraction of ions. Energy sampling experiments have been performed on buffer-gas thermalized He + ions at trap temperatures between 10 and 180 K, resulting in distinct extraction curves as a function of the potential barrier, and a differentiated behavior depending on the escape time from the trap. The experiments are complemented by Monte Carlo simulations of the ion trajectories inside the calculated trap potential and allow us to investigate the properties of the sampling method, the role of ion motion coupling, and the impact of residual buffer-gas collisions on the observed results. The technique has also been successfully applied to identify energetic H 3 + ions produced in an exothermic reaction inside the trap. Upon calibration, this method can provide relative kinetic energy distributions or be used to filter the maximum desired kinetic energy of the ions inside the trap.
We identify plain evaporation of ions as the fundamental loss mechanism out of a multipole ion trap. Using thermalized negative Cl- ions we find that the evaporative loss rate is proportional to a Boltzmann factor. This thermodynamic description allows us to extract the effective depth of the ion trap. As a function of the rf amplitude we find two distinct regimes related to the stability of motion of the trapped ions. For low amplitudes the entire trap allows for stable motion and the trap depth increases with the rf field. For larger rf amplitudes rapid energy transfer from the field to the ion motion can occur at large trap radii, which leads to a reduction of the effective trapping volume. In this regime the trap depth decreases again with increasing rf amplitude. We give an analytical parametrization of the trap depth for various multipole traps that allows predictions of the most favorable trapping conditions.
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. H\"oltkemeier 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 us to investigate the influence of nonhomogeneous 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).
Individual Ba ions are trapped in a gas-filled linear ion trap and observed with a high signal-to-noise ratio by resonance fluorescence. Single-ion storage times of $\ensuremath{\sim}5\phantom{\rule{0.3em}{0ex}}\mathrm{min}$ $(\ensuremath{\sim}1\phantom{\rule{0.3em}{0ex}}\mathrm{min})$ are achieved using He (Ar) as a buffer gas at pressures in the range $8\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}5}--4\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}\phantom{\rule{0.3em}{0ex}}\text{torr}$. Trap dynamics in buffer gases are experimentally studied in the simple case of single ions. In particular, the cooling effects of light gases such as He and Ar and the destabilizing properties of heavier gases such as Xe are studied. A simple model is offered to explain the observed phenomenology.