Quantum beat many level

A two-level quantum beating system exhibits one beat frequency. An N-level beating system can exhibit as many as N(N — l)/2 beat frequencies. 

Either two or more molecular levels of a molecule are excited coherently by a spectrally broad, short laser pulse (level-crossing and quantum-beat spectroscopy) or a whole ensemble of many atoms or molecules is coherently excited simultaneously into identical levels (photon-echo spectroscopy). This coherent excitation alters the spatial distribution or the time dependence of the total, emitted, or absorbed radiation amplitude, when compared with incoherent excitation. Whereas methods of incoherent spectroscopy measure only the total intensity, which is proportional to the population density and therefore to the square ir of the wave function iff, the coherent techniques, on the other hand, yield additional information on the amplitudes and phases of ir. 

The energy of the vdW vibrational states w> is approximately 180 cm. The average density of vdW levels with the right symmetry in this energy region is of the order of 1 per cm and therefore we think that the number of interacting states is rather low. Nevertheless we could not observe any oscillatory decay of the fluorescence. The reason for the absence of quantum beats must be that so many rovibronic levels 6a > 0> J,K> are excited in the ensemble of clusters because of the relatively large spectral width... 

---