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We present and derive analytic expressions for a fundamental limit to thesympathetic cooling of ions in radio-frequency traps using cold atoms. Thelimit arises from the work done by the trap electric field during a long-rangeion-atom collision and applies even to cooling by a zero-temperature atomic gasin a perfectly compensated trap. We conclude that in current experimentalimplementations this collisional heating prevents access to the regimes ofsingle-partial-wave atom-ion interaction or quantized ion motion. We determineconditions on the atom-ion mass ratio and on the trap parameters for reachingthe s-wave collision regime and the trap ground state.

Micromotion-induced Limit to Atom-Ion Sympathetic Cooling in Paul Traps