Propagation property of ultra-short laser pulses in multi-level quantum system

The propagation property of an ultrashort pulse in multi-level quantum system has been investigated with numerical method. A strong absorption is observed and its degree depends on the characteristic time of quantum system. For rather weak laser field, the self-induced transparency can still be observed with proper pulse area of the input ultrashort laser. When the ultrashort laser pulse becomes stronger, it will be split, and its basic split unit (i.e. the minimum area of a stably propagating laser pulse) A₀ is not the same as that of two-level quantum system, which depends on the number of the excited states and their dipoles. Furthermore, after a rather long propagating distance, there only remains a shorter but more intense sub-pulse with an area of A₀.