Dynamical Crystallization in the Dipole Blockade of Ultracold Atoms

We describe a method for controlling many-body states in extended ensembles of Rydberg atoms, forming crystalline structures during laser excitation of a frozen atomic gas. Specifically, we predict the existence of an excitation-number staircase in laser excitation of atomic ensembles into Rydberg states. It is shown that such ordered states can be selectively excited by chirped laser pulses, and, via quantum state transfer from atoms to light, be used to create crystalline photonic states.