  The possibility to use the ultrashort ion bunches produced by circularly
polarized laser pulses to drive a source of fusion neutrons with sub-optical
cycle duration is discussed. A two-side irradiation of a thin foil deuterated
target produces two countermoving ion bunches, whose collision leads to an
ultrashort neutron burst. Using particle-in-cell simulations and analytical
modeling, it is evaluated that, for intensities of a few $10^{19} W cm^{-2}$,
more than $10^3$ neutrons per Joule may be produced within a time shorter than
one femtosecond. Another scheme based on a layered deuterium-tritium target is
outlined.
