Transient properties of transparency of a quantum system near a plasmonic nanostructure

We study theoretically the time evolution of the susceptibility of a four-level double-V-type quantum system near a plasmonic nanostructure. In the quantum system under study one V-type transition is influenced by the interaction with surface plasmons while the other V-type transition interacts with free-space vacuum. As a plasmonic nanostructure we consider a two-dimensional array of metal-coated dielectric nanospheres. We analyze the case of a linearly polarized weak laser field that couples the lowest state with the upper states in the free-space transitions. We show that the time evolution of the susceptibility of the system is strongly dependent on the distance between the quantum system and the plasmonic nanostructure. For example, while for some distances only transient absorption appears, for others transient gain without inversion is possible.