A photon echo in a multilevel quantum medium excited by two extremely
short pulses with durations of less than one period of oscillation of
the light is investigated theoretically. It is shown that Q echo signa
ls (Q is the number of allowed transitions) can form at each frequency
of the allowed transitions, and the number of echo responses for all
the allowed transitions equals Q(2). Of these, Q(Q-1) signals are sepa
rated in both time and space. The other Q echo signals of all the allo
wed frequencies all arise at the time 2 tau(21) (tau(21) is the time i
nter val between application of the first and second pulses to the med
ium) and are collinear with one another. (C) 1998 American institute o
f Physics. [S0021-3640(98)01011-1].