Rapid laser-free ion cooling by controlled collision

I propose a method to remove the axial motional excitation from an ion qubit within a few oscillation periods of a harmonic trap. The principle is to prepare another coolant ion in its motional ground state, and then apply a phonon beam splitter to swap the motional state between the ions without affecting the internal state. This method requires only the precise control of the trapping potential, thus its performance does not suffer from the limitations of current laser-cooling schemes. With sufficient coolant ions pre-prepared, this method can rapidly re-cool ion qubits during quantum information processing.
Comment: 5 pages, 3 figures. (v2) Substantially re-written with corrected theory and more details