Direct Observation of Atom-Ion Nonequilibrium Sympathetic Cooling

Ziv Meir, Meirav Pinkas, Tomas Sikorsky, Ruti Ben-shlomi, Nitzan Akerman, and Roee Ozeri

Phys. Rev. Lett. 121, 053402 – Published 2 August 2018

Abstract

Sympathetic cooling is the process of energy exchange between a system and a colder bath. We investigate this fundamental process in an atom-ion experiment where the system is composed of a single ion trapped in a radio-frequency Paul trap and prepared in a classical oscillatory motion with total energy of $\sim 200 K$ , and the bath is an ultracold cloud of atoms at $μ K$ temperature. We directly observe the sympathetic cooling dynamics with single-shot energy measurements during one to several collisions in two distinct regimes. In one, collisions predominantly cool the system with very efficient momentum transfer leading to cooling in only a few collisions. In the other, collisions can both cool and heat the system due to nonequilibrium dynamics in the presence of the ion trap’s oscillating electric fields. While the bulk of our observations agree well with a molecular-dynamics simulation of hard-sphere (Langevin) collisions, a measurement of the scattering angle distribution reveals forward-scattering (glancing) collisions which are beyond the Langevin model. This work paves the way for further nonequilibrium and collision dynamics studies using the well-controlled atom-ion system.

Received 6 February 2018

DOI:https://doi.org/10.1103/PhysRevLett.121.053402

Physics Subject Headings (PhySH)

Scattering of atoms, molecules, clusters & ions

Atomic gases Trapped ions Ultracold gases

Atom & ion trapping & guiding Molecular dynamics Time-resolved light scattering spectroscopy

Atomic, Molecular & Optical

Authors & Affiliations

Ziv Meir^*, Meirav Pinkas, Tomas Sikorsky, Ruti Ben-shlomi, Nitzan Akerman, and Roee Ozeri

Department of Physics of Complex Systems, Weizmann Institute of Science, Rehovot 7610001, Israel

^*Present address: Department of Chemistry, University of Basel, Basel 4056, Switzerland. ziv.meir@unibas.ch

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Vol. 121, Iss. 5 — 3 August 2018

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Images

Figure 1
(a) Two experimental configurations. Ellipses indicate the sizes and positions of the atomic cloud with respect to the ion-trap center. Gray is the initial position before interaction; blue (red) is the position in the axial (radial) equilibrium (nonequilibrium) experiment. Dashed arrows indicate the ion’s initial motion amplitude in each of the experiments. Arrows and ellipses are to scale. The ion-trap axial axis (black lines, not to scale) coincides with the atom-trap long axis. (b) Single-shot Doppler-cooling thermometry. Dots are the measured fluorescence signal of an ion prepared solely in the trap’s axial mode. Lines are the results of ion-fluorescence numerical calculations for different initial axial to total energy ratios (legend). Inset is the total ion’s energy for the different numerical calculations. Dashed line indicates the ion’s total energy for cooling time of 200 ms for the different calculations. In all graphs, zero time indicates the onset of reaching the Doppler temperature.
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Figure 2
Sympathetic cooling. (a)–(f) Experimentally measured energy histograms of the ion’s total energy for different interaction times, $t_{int}$ [31]. The color of the bars indicates the axial energy to total energy ratio of the ion according to the LRT analysis (see legend). The color code is the same as in Fig. 1. The dark red bars are cold events with cooling times less than 50 ms for which the LRT cannot determine the mode distribution [31]; however, the SSDCT can determine the energy. We use the steady-state energy distribution ( ${E_{z} / E}_{ion} = 0.15$ ) for these events. The lines are results of MD simulation which takes into account only Langevin collisions which are also presented in the right column. In the left column, the red line separates the simulation events with no collisions (above) and simulation events with one or more collisions (below). (A)–(F) MD-simulation energy histograms. The color of the bars indicates the axial energy to total energy ratio in the simulation binned according to the available numerical simulations. Simulation times $t_{sim}$ are chosen to match the measured mean energy in the experiment.
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Figure 3
Scattering angle distribution. Histograms of the energy difference divided by the radial energy after a collision (a) and the cosine of the scattering angle (b). Red lines are the theoretical prediction of Langevin scattering. Blue x’s are an analysis of MD-simulation results [Figs. 2]. The analysis takes into account experimental limitations which modify the distributions. Gray areas reflect the uncertainty regions of the simulation analysis due to experimental limitations. The simulation treats only Langevin collisions [31]. Blue circles are calculated from the experimental data of Figs. 2.
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Figure 4
Nonequilibrium dynamics. (X) Dots are the measured single-shot fluorescence signal where the ion’s energy is initialized in the trap’s $x$ -radial mode. Lines are numerical calculation results where the ion’s energy is initialized in the $x$ mode (green), $z$ mode (blue), and the steady-state mixture (0.4, $x$ ; 0.45, $y$ ; 0.15, $z$ ) of modes. (a)–(e) Experimentally measured total-energy histograms for increasing interaction time. The color of the bars indicates the result of the LRT, and it is the same as in (X). Dark red bars are low-energy events which are below the LRT sensitivity. The energy value of all events is extracted using the $x$ -mode numerical calculation. Lines are MD-simulation results. The area underneath the red line represents events with at least a single collision while the area above the red line signals events which did not collide according to the simulation. (A)–(E) MD-simulation total-energy histograms. Color code indicates events which are more than 99% $x$ mode (green) or $z$ mode (blue). The rest of the events are colored in red. Probability for collision is given for each graph.
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