  In order to simplify the theoretical description of spasers, a gain medium is
commonly represented by a two-level system. A realistic model, however, should
have four levels. By using the Lindblad equations we develop a description of
such a system and show that depending on ratios of the Rabi frequency and the
rate of relaxation of the polarization, a four-level system may be reduced to
one of two effective two-level systems that reproduce the key properties of a
four-level system.
