Phase conjugation through autoionizing states: a density matrix approach

We present a theoretical study of phase conjugation via degenerate four wave mixing through an autoionizing state (AIS), formulated in terms of a density matrix approach. Within this quite general and flexible formulation the probe field is handled as a perturbation, while the coupling of the pump fields to the atomic system is treated exactly. The AIS is described as an isolated Fano resonance decaying into a single continuum. In the weak-field, steady-state limit it is possible to analytically recover earlier perturbative results for the corresponding nonlinear susceptibility. However, the advantage of this approach is best revealed when applied to the detailed study of realistic examples drawn from such diverse atomic systems as Xe and Mg. Both spectral and temporal features of the produced phase-conjugated (PC) signal are studied quantitatively through the numerical solution of the density matrix equations. Moreover, time-integrated quantities, such as the reflectivity, that are usually employed to measure the PC response, are also calculated. We find that the PC response is determined by the asymmetry of the autoionizing lineshape, the peak intensity of the pump pulses and the interplay between the pump pulse duration and the autoionization lifetime. Moreover, the role of the pump-probe delay in restoring reflectivity to high values under otherwise unfavourable conditions is highlighted. Finally, the impact of pump-induced ionization on the PC response is also studied and conditions to counter its deleterious effect on the reflectivity are determined