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arXiv:1710.09958 · Physical Review Letters

Cooling Dynamics of a Single Trapped Ion via Elastic Collisions with Small-Mass Atoms

Shinsuke Haze, Mizuki Sasakawa, Ryoichi Saito, Ryosuke Nakai, Takashi Mukaiyama

Published Jan 24, 2018• 32 citations
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Abstract

We demonstrated sympathetic cooling of a single ion in a buffer gas of ultracold atoms with small mass. Efficient collisional cooling was realized by suppressing collision-induced heating. We attempt to explain the experimental results with a simple rate equation model and provide a quantitative discussion of the cooling efficiency per collision. The knowledge we obtained in this work is an important ingredient for advancing the technique of sympathetic cooling of ions with neutral atoms.

DOI
10.1103/physrevlett.120.043401

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We demonstrated sympathetic cooling of a single ion in a buffer gas of ultracold atoms with small mass. Efficient collisional cooling was realized by suppressing collision-induced heating. We attempt to explain the experimental results with a simple rate equation model and provide a quantitative discussion of the cooling efficiency per collision. The knowledge we obtained in this work is an important ingredient for advancing the technique of sympathetic cooling of ions with neutral atoms.
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).
Abstract Sympathetic cooling of a Fermi gas with a buffer gas of bosonic atoms is an efficient way to achieve quantum degeneracy in Fermi systems. However, all attempts to use this method for cooling ions until recently were ineffective because of the unremovable ion “micromotion” in electromagnetic Paul traps, which prevents the realization of a number of hot projects with cold atom-ion systems. In this regard, we propose a new efficient method for sympathetic cooling of ions: the use for this purpose of cold buffer atoms in the region of atom-ion confinement-induced resonances (CIRs) [V.S. Melezhik, Phys. Rev. A103, 53109 (2021)]. We show that the destructive effect of “micromotion” on its sympathetic cooling can, however, be suppressed in the vicinity of the atom-ion CIR. Here, the resonant blocking of a close collision of an atom with an ion also resists its heating due to “micromotion”. We investigate the effect of sympathetic cooling around CIRs in atom-ion, and atom-atom confined collisions within the quantum-quasiclassical approach using the Li–Yb+ and Li–Yb confined systems as an example. In this approach, the Schrödinger equation for a cold light atom is integrated simultaneously with the classical Hamilton equations for a hotter heavy-ion or atom during a collision. We have found the region near the atom-ion CIR where the sympathetic cooling of the ion by cold atoms is possible in a hybrid atom-ion trap. We also show that it is possible to improve the efficiency of sympathetic cooling in atomic traps by using atomic CIRs.
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.
In this thesis the dynamics of a trapped ion immersed in \na spatially localized buffer gas is investigated. For a homogeneous buffer gas, the ion’s energy distribution reaches a stable equilibrium only if the mass of the buffer gas atoms is below a critical value. This limitation can be overcome by using multipole traps in combination and/or a spatially confined buffer gas. Using a generalized model \nfor elastic collisions of the ion with the buffer gas atoms, the ion’s energy distribution is numerically determined for arbitrary buffer gas distributions and trap parameters. Three regimes characterized by the respective analytic form of the ion’s equilibrium energy distribution \nare found. One of these is a novel regime at large atom-to-ion mass ratios where the final ion temperature can tuned by adiabatically decreasing the spatial extension of the buffer gas and the effective ion trap depth (forced sympathetic cooling). The second part of the thesis presents a hybrid atom ion trap designed for sympathetic cooling of hydroxide anions. In this hybrid trap the anions are immersed in a cloud of laser cooled rubidium atoms. The translational and rovibrational temperatures of the anions is probed by photodetachment tomography and spectroscopy which shows the first ever indication of sympathetic cooling of anions by laser cooled atoms.
Abstract We present a series of recent experimental and numerical results which allow us to propose and explain the mechanisms for collisional cooling of a trapped ion by sequential binary collisions with atoms. Our experiments in hybrid atom-ion traps study the cooling of ions when the reservoir of the coolant atoms is spatially localized at the centre of the ion trap. Under these conditions the widely and long held expectation that for the ion to collisionally cool, the atom must be of lighter mass (i.e. mI > mA ) is overturned. Instead we show ion cooling for mI ⩽ mA in addition to mI > mA , and explain why earlier work establishing mass ratios does not apply to the experiments in hybrid traps. Further, for cooling of an ion A+ by the parent atom A, the mechanism of resonant charge exchange (RCE) allows for extremely efficient cooling of the ion A+. This mechanism is demonstrated by comparing the cooling rate of an ion with a localized ensemble of its parent atoms and with a lighter atomic species, where in the latter case the RCE mechanism does not exist. The difference in measured cooling rates for a given number density of the atoms and the theoretically calculated difference between elastic and RCE cross sections are used to show that the cooling efficiency per collision with RCE is much greater than the cooling by elastic collision. We conclude with some perspectives and prospects of future experiments.
We propose a way for sympathetic cooling of ions in an electromagnetic Paul trap: it implies the use for this purpose of cold buffer atoms in the region of atom-ion confinement-induced resonance (CIR). The problem is that the unavoidable micromotion of the ion and the long-range nature of its interaction with the environment of colder atoms in a hybrid atomic-ion trap prevent its sympathetic cooling. We show that the destructive effect of ion micromotion on its sympathetic cooling can, however, be suppressed in the vicinity of the atom-ion CIR. Here, the resonant blocking of the complete approach of an atom with an ion during a collision also blocks the enhancement of its micromotion. We investigate the effect of sympathetic cooling around CIRs in atom-ion and atom-atom confined collisions within the quasiclassical-quantum approach using the $\mathrm{Li}\ensuremath{-}{\mathrm{Yb}}^{+}$ and Li-Yb confined systems as an example. In this approach, the Schr\"odinger equation for a cold light atom is integrated simultaneously with the classical Hamilton equations for a hotter heavy ion or atom during collision. We have found the region near the atom-ion CIR where the sympathetic cooling of the ion by cold atoms is possible in a hybrid atom-ion trap. We also show that it is possible to improve the efficiency of sympathetic cooling in atomic traps by using atomic CIRs.