Experimental apparatus for overlapping a ground-state cooled ion with ultracold atoms

Abstract

Experimental realizations of charged ions and neutral atoms in overlapping traps are gaining increasing interest due to their wide research application ranging from chemistry at the quantum level to quantum simulations of solid state systems. In this paper, we describe our experimental system in which we overlap a single ground-state cooled ion trapped in a linear Paul trap with a cloud of ultracold atoms such that both constituents are in the $\mathrm{\mu }$K regime. Excess micromotion (EMM) currently limits atom–ion interaction energy to the mK energy scale and above. We demonstrate spectroscopy methods and compensation techniques which characterize and reduce the ion’s parasitic EMM energy to the $\mathrm{\mu }$K regime even for ion crystals of several ions. We further give a substantial review on the non-equilibrium dynamics which governs atom–ion systems. The non-equilibrium dynamics is manifested by a power law distribution of the ion’s energy. We also give an overview on the coherent and non-coherent thermometry tools which can be used to characterize the ion’s energy distribution after single to many atom–ion collisions.

Keywords:

• Atom–ion
• trapped ions
• non-equilibrium
• power law
• micromotion
• ultracold collisions

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Notes

No potential conflict of interest was reported by the authors.

1 Different authors use different notion for the power law of the energy distribution. Here it is defined as $P\left(E\right)\propto E^{2-n}$. In Chen et. al. [39] it is defined as $P\left(E\right)\propto E^{-(\mathit{\nu }+1)}$. In Holtkemeier et. al. [53] it is defined as $P\left(E\right)\propto E^{\mathit{\kappa }}$. In Zipkes et. al. [37] it is defined as $P\left(E\right)\propto E^{\mathit{\alpha }-1}$ (see remark in SM of [53]). Thus, the following relation should hold when comparing between these works: $2-n=-(\mathit{\nu }+1)=\mathit{\kappa }=\mathit{\alpha }-1$.

2 The low energy part of the energy distribution is dominated by the density of states. Since in our simulation, we take into account the total energy (kinetic and potential), the density of states is quadratic $P\left(E\ll E_{}\text{scale}\right)\propto E^2$. In other work, [53] only, the kinetic energy was considered such that the density of states was $P\left(E\ll E_{}\text{scale}\right)\propto E^{3/2}$.

3 The rf frequency that maximize the voltage on the trap electrodes and hence the ion’s radial frequency differs from the rf frequency that minimizes rf reflections from the trap.

Additional information

Funding

This work was supported by the Crown Photonics Center; I-Core-Israeli excellence center circle of light; the Israeli Science Foundation; the U.S.–Israel Binational Science Foundation [2008473]; the European Research Council [consolidator grant 616919-Ionology].