  We investigate the quantum melting of one dimensional crystals that are
realized in an atomic lattice in which ground state atoms are laser excited to
two Rydberg states. We focus on a regime where both, intra- and inter-state
density-density interactions as well as coherent exchange interactions
contribute. We determine stable crystalline phases in the classical limit and
explore their melting under quantum fluctuations introduced by the excitation
laser as well as two-body exchange. We find that within a specific parameter
range quantum fluctuations introduced by the laser can give rise to a devil's
staircase structure which one might associate with transitions in the classical
limit. The melting through exchange interactions is shown to also proceed in a
step-like fashion, in case of small crystals, due to the proliferation of
Rydberg spinwaves.
