  Conventional theoretical studies on the ground-state laser cooling of a
trapped ion have mostly focused on the weak sideband coupling (WSC) regime,
where the cooling rate is inverse proportional to the linewidth of the excited
state. In a recent work~[New J. Phys. 23, 023018 (2021)], we proposed a
theoretical framework to study the ground state cooling of a trapped ion in the
strong sideband coupling (SSC) regime, under the assumption of a vanishing
carrier transition. Here we extend this analysis to more general situations
with nonvanishing carrier transitions, where we show that by properly tuning
the coupling lasers a cooling rate proportional to the linewidth can be
achieved. Our theoretical predictions closely agree with the corresponding
exact solutions in the SSC regime, which provide an important theoretical
guidance for sideband cooling experiments.
