  We theoretically investigate the effect of dissipation on multi-photon
excitation of Rydberg atoms. The steady states and the dynamics are compared
via two types of four-level excitation schemes with different dissipative paths
of spontaneous emission. We find that in the case of strong Rydberg-Rydberg
interaction, the schemes will settle in several different non-equilibrium
steady states. The interesting aspect is that there exists the multi-stable
steady states, which reveals the competition between interaction-induced
nonlinearity and dissipation caused by spontaneous emission. A numerical
simulation on the Rydberg population dynamics in the bistable region exhibits
different features existing in the two schemes even with the same initial
conditions, which accounts for the influence of the dissipation on the
dynamics.
