  We present the theory of resonance fluorescence from an asymmetric quantum
dot driven by a two-component electromagnetic field with two different
frequencies, polarizations and amplitudes (bichromatic field) in the regime of
strong light-matter coupling. It follows from the elaborated theory that the
broken inversion symmetry of the driven quantum system and the bichromatic
structure of the driving field result in unexpected features of the resonance
fluorescence, including the infinite set of Mollow triplets, the quench of
fluorescence peaks induced by the dressing field, and the oscillating behavior
of the fluorescence intensity as a function of the dressing field amplitude.
These quantum phenomena are of general physical nature and, therefore, can take
place in various double-driven quantum systems with broken inversion symmetry.
