We measured the optical transitions due to the internal energy levels of an exciton and biexciton in a CuCl single crystal using pump-probe spectroscopy. The transient absorption bands due to the transitions from the
1s to
2p and from the
1s to
3p exciton states were observed at 3 K, which is consistent with their reported energies. Simultaneously, the transient absorption peak due to the biexciton was observed, which corresponds to a transition from the lowest state (composed of two
1s excitons) to higher states (composed of
1s and
2p excitons). The value of the observed biexciton peak energy was reasonable considering the hydrogen molecule orbitals and the electron-to-hole effective mass ratio. In addition, the transient absorption peaks were broadened at 77 K, because of the increase in the homogeneous width of the
2p exciton state. The transient absorption spectrum was almost completely determined by this width. Our findings are of importance with regard to the optical phenomena in the infrared region related to the quantum coherence of excitons and biexcitons in semiconductors.
The theory of the coherent pairing of Frenkel excitons in the presence of a resonant electromagnetic field is generalized to include the effect of the electron spin. It is shown that at high exciton densities and when the electromagnetic field is at resonance or near resonance, the removal of the spin degeneracy of the exciton pairs results in generating two fields, the singlet and the triplet biexciton fields, respectively. The gap functions ${\ensuremath{\Delta}}_{+}$ and ${\ensuremath{\Delta}}_{\ensuremath{-}}$ due to the singlet and triplet biexciton fields, respectively, are calculated and they are found to be independent of one another only in the limit when the exchange interactions between the charges disappear. In this limit, the energy modes for singlet and triplet biexciton fields have well-defined meaning and propagate through the crystal independently. A dielectric gap is induced by the electromagnetic field, which produces the energy splitting in the singlet biexciton spectrum, and it must be less than that of ${\ensuremath{\Delta}}_{+}$ for the singlet biexciton state. For finite values of the exchange interaction, the gap functions ${\ensuremath{\Delta}}_{+}$ and ${\ensuremath{\Delta}}_{\ensuremath{-}}$ depend strongly on each other and consequently the singlet and triplet biexciton fields are strongly mixed together. Optical transitions to the singlet and triplet biexciton states are considered and the corresponding expressions for the absorption coefficient are derived. The ground-state energy describing the binding energy arising from the singlet and triplet biexciton fields is calculated and discussed. Numerical estimates indicate that at high exciton densities, namely, for exciton concentrations
1018-
1019 ${\mathrm{cm}}^{\ensuremath{-}3}$ and when the ratio of the average exciton-exciton interaction over the average kinetic energy is between 0.7 and 2 (strong-coupling limit), the energy gap due to the singlet biexciton state is in the range 40-650 ${\mathrm{cm}}^{\ensuremath{-}1}$, the corresponding transition temperature is 33-534 \ifmmode^\circ\else\textdegree\fi{}K, while the binding energy is 22-684 ${\mathrm{cm}}^{\ensuremath{-}1}$.