Dependence on relative phase for bichromatically driven atoms

``We consider the interaction of atoms with a pulse of a linearly polarized electric field consisting of two phase-locked frequencies whose ratio omega(H)/omega(L) is the ratio of arbitrary integers h/l, with h > l. If the electric amplitudes vary in time, they do so with the same slow envelope. The relative phase can be used as a control parameter via variation of the phase phi(H) Of omega(H) or phi(L) of omega(L). We derive the physically important ranges of relative phase for total-yield processes as a function of h:1; they depend on whether h, 1 are both odd or only one is odd. We tabulate a variety of relevant phase-dependent results for all h:1 from 2:1 through 8:7. We use calculations and experimental data for helium and hydrogen Rydberg atoms driven by a bichromatic microwave field to confirm the physically important ranges of phi(H) and phi(L) for a few h:l ratios. Two experimental examples taken from the literature for the interactions of atoms with sub-picosecond, bichromatic laser pulses also confirm our conclusions.