  We present a joint experimental-theoretical study on the effect of the
carrier-envelope phase (CEP) of a few-cycle pulse on the atomic excitation
process. We focus on the excitation rates of argon as a function of CEP in the
intensity range from 50-300 TW/cm$^2$, which covers the transition between the
multiphoton and tunneling regimes. Through numerical simulations based on
solving the time-dependent Schr\"{o}dinger equation (TDSE), we show that the
resulting bound-state population is highly sensitive to both the intensity and
the CEP. Because the intensity varies over the interaction region, the CEP
effect is considerably reduced in the experiment. Nevertheless, the data
clearly agree with the theoretical prediction, and the results encourage the
use of precisely tailored laser fields to coherently control the strong-field
excitation process. We find a markedly different behavior for the CEP-dependent
bound-state population at low and high intensities with a clear boundary, which
we attribute to the transition from the multiphoton to the tunneling regime.
