  We theoretically investigate the process of splitting two-ion crystals in
segmented Paul traps, i.e. the structural transition from two ions confined in
a common well to ions confined in separate wells. The precise control of this
process by application of suitable voltage ramps to the trap segments is
non-trivial, as the harmonic confinement transiently vanishes during the
process. This makes the ions strongly susceptible to background electric field
noise, and to static offset fields in the direction of the trap axis. We
analyze the reasons why large energy transfers can occur, which are impulsive
acceleration, the presence of residual background fields and enhanced anomalous
heating. For the impulsive acceleration, we identify the diabatic and adiabatic
regimes, which are characterized by different scaling behavior of the energy
transfer with respect to time. We propose a suitable control scheme based on
experimentally accessible parameters. Simulations are used to verify both the
high sensitivity of the splitting result and the performance of our control
scheme. Finally, we analyze the impact of trap geometry parameters on the
crystal splitting process.
