The effect of photon echo is studied in several multilevel systems with quasi-equidistant spectra. The analysis focuses on the echo schemes that are of interest for femtosecond photon echo experiments involving both fundamental and combination vibrational modes of molecules.
A pair of coherent femtosecond pulse excitations applied to a molecule with strong electron-phonon coupling creates a coherent superposition of a low momentum and a high momentum wavepacket in the vibrational states of both the excited state and the ground state of the coherent transition. As the excited state is accelerated further, interference between the high momentum ground state contribution and the low momentum excited state contribution causes a photon echo. This photon echo is a direct consequence of quantum interference between separate vibrational trajectories and can therefore provide experimental evidence of the non-classical properties of molecular vibrations.
The effect of pulse propagation on the two-dimensional photon echo (2DPE) spectrum of multilevel systems is investigated using a perturbative method. At high optical densities (OD) peak profiles are broadened asymmetrically, in most cases more strongly along the ω2 direction than along the ω1 direction. The amount of broadening is determined both by the OD and by the dynamics of the system. In addition, especially if the different transitions in the system are of unequal strength, the relative intensity of the peaks changes with OD. But even if the transition strengths are the same, the behavior of the cross peaks is different from the diagonal peaks. Since peak shape and relative intensity are important parameters in the interpretation of 2DPE spectra, such OD effects should be taken into account.