It has been observed experimentally [H.R. Xia, C.Y. Ye, and S.Y. Zhu, Phys.
Rev. Lett. 77, 1032 (1996)] that quantum interference between two molecula
r transitions can lead to a suppression or enhancement of spontaneous emiss
ion. This is manifest in the fluorescent intensity as a function of the det
uning of the driving field from the two-photon resonance condition. Here we
present a theory that explains the observed variation of the number of pea
ks with the mutual polarization of the molecular transition dipole moments.
Using master equation techniques we calculate analytically as well as nume
rically the steady-state fluorescence, and find that the number of peaks de
pends on the excitation process. If the molecule is driven to the upper lev
els by a two-photon process, the fluorescent intensity consists of two peak
s regardless of the mutual polarization of the transition dipole moments. L
f the excitation process is composed of both a two-step, one-photon process
and a one-step, two-photon process, then there are two peaks on transition
s with parallel dipole moments and three peaks on transitions with antipara
llel dipole moments. This latter case is in excellent agreement with the ex
periment.