We present the results of a study of ionization of Xe atoms by a pair of phase-locked pulses, which is characterized by interference produced by the twin peaks. Two types of interference are considered: ordinary optical interference, which changes the intensity of the composite pulse and thus the ion yield, and a quantum interference, in which the excited electron wave packets interfere. We use the measured Xe+ yield as a function of the temporal delay and/or relative phase between the peaks to monitor the interferences and compare their relative strengths. We model the interference with a pulse intensity function and by calculating the ionization yield with the time-dependent Schrodinger equation. Our results provide insight into optimal control pulses generated with learning algorithms. The results also show that the relative phase between peaks of a control pulse, along with small features such as distortions and imperfections in the wings of an ideal shape, play a significant role in the control process.