Electron-atom ionizing collisions in the presence of a bichromatic laser field

A theory of electron-atom ionizing collisions in the presence of a bichromatic laser field is developed. The incident and scattered electron of high energy is described by Volkov states, the atomic ground state is dressed by the laser field to first order in the electric-field strength, and the atomic continuum state that corresponds to the ejected slow electron is dressed by the laser field to all orders in the field strength, but in an approximate way. It is shown that the dressing of these continuum states is mainly responsible for the different effects that a bichromatic laser field introduces into this process. These effects are more pronounced compared to similar effects recently observed in an analysis of the target dressing in free-free transitions in a bichromatic laser field. The possibility of the coherent phase control is analyzed and it is shown that the triple differential cross section (TDCS) can be changed by almost one order of magnitude by changing the relative phase between the two laser field components. The TDCS as a function of the relative phase, the number of absorbed (emitted) photons, and the laser electric-field strength shows a specific behavior that is mainly determined by the properties of the generalized Bessel functions appearing In our results. It is also shown that these effects are particularly pronounced for rather small scattering angles of the fast electron.