  We show that transient supersolid quantum states of Rydberg-excitations can
be created dynamically from a Mott insulator of ground state atoms in a 2D
optical-lattices by irradiating it with short laser pulses. The structure of
these supersolids is tunable via the choice of laser parameters. We calculate
first, second and fourth order correlation functions as well as the pressure to
characterize the supersolid states. Our study is based on the development of a
general theoretical tool for obtaining the dynamics of strongly interacting
quantum systems whose initial state is accurately known. We show that this
method allows to accurately approximate the evolution of quantum systems
analytically with a number of operations growing polynomially.
