Photoionization dynamics of a two level atom interacting with a two-mode laser field

Using an interaction representation, we derive a set of Bloch equations for a two-level atom with a ground state and an excited state interacting with a multi-mode laser field. When the excited state has a constant ionizing rate, the rate equations are obtained from the Bloch equations by using the Wilcox-Lamb approximation. The transition probability in the rate equations consists of two parts; an incoherent part representing the independent contribution of each laser mode and a coherent part representing the interference between laser modes. Using the simple model of a two-mode laser interacting with a two-level atom, we demonstrate that the fluctuation of the relative phases between the modes cancels the interference contribution