  We show that ultrashort pulses can be focused, in a particular instant, to a
spot size given by the wavelength associated with its spectral width. For
attosecond pulses this spot size is within the nanometer scale. Then we show
that a two-level system can be left excited after interacting with an
ultrashort pulse whose spectral width is larger than the transition frequency,
and that the excitation probability depends not on the field amplitude but on
the field intensity. The latter makes the excitation profile have the same spot
size as the ultrashort pulse. This unusual phenomenon is caused by quantum
electrodynamics in the ultrafast light-matter interaction regime since the
usually neglected counterrotating terms describing the interaction with the
free electromagnetic modes are crucial for making the excitation probability
nonzero and depend on the field intensity. These results suggest that a train
of coherent attosecond pulses could be used to excite fluorescent markers with
nanoscale resolution. The detection of the light emitted after fluorescence -or
any other method used to detect the excitation- could then lead to a new scheme
for far-field light nanoscopy.
