  We report on a comparative analysis of quenched sideband cooling in trapped
ions. We introduce a theoretical approach for time-efficient simulation of the
temporal cooling characteristics and derive the optimal conditions providing
fast laser cooling into the ion's motional ground state. The simulations were
experimentally benchmarked with a single $^{172}$Yb$^+$ ion confined in a
linear Paul trap. Sideband cooling was carried out on a narrow quadrupole
transition, enhanced with an additional clear-out laser for controlling the
effective linewidth of the cooling transition. Quench cooling was thus for the
first time studied in the resolved sideband, intermediate and semi-classical
regime. We discuss the non-thermal distribution of Fock states during laser
cooling and reveal its impact on time dilation shifts in optical atomic clocks.
