  The non-resonant interaction between the high-density excitons in a quantum
well and a single mode cavity field is investigated. An analytical expression
for the physical spectrum of the excitons is obtained. The spectral properties
of the excitons, which are initially prepared in the number states or the
superposed states of the two different number states by the resonant
femtosecond pulse pumping experiment, are studied. Numerical study of the
physical spectrum is carried out and a discussion of the detuning effect is
presented.
