Density matrix equation analysis of optical–optical double-resonance multiphoton ionization probability

Abstract An analytical formula of the optical–optical double-resonance multi-photon ionization (OODR-MPI) probability is derived from the time-dependent density-matrix equations that describe the interaction of photon and material. Based on the formula, the variation of the multiphoton ionization (MPI) probability with laser resonance detuning, Rabi frequency, laser pulse duration and ionization rate is investigated theoretically. It is shown that the MPI probability will decrease with the increase of laser resonance detuning, to some extent, to zero. The influence of the pump laser resonance detuning on the ionization probability is more important with respect to the probe laser. It not only influences Rabi frequency for saturation, but also the saturation value of MPI probability. The MPI probability will increase with Rabi frequency, laser pulse duration and ionization rate. It is also found that though the variation of the populations in the ground, the first and the second resonance states is different at the beginning of laser radiation, but they will still decrease to zero as the time goes on. It is then that the ionization probability gets the maximum value. Thus long laser pulse duration and high laser intensity are in favor for improving the MPI probability. These theoretical research results can provide a useful guide for the practical application of OODR-MPI spectroscopy.