  We investigate the spectral properties of a finite laser-driven lattice of
ultracold Rydberg atoms exploiting the dipole blockade effect in the frozen
Rydberg gas regime. Uniform one-dimensional lattices as well as lattices with
variable spacings are considered. In the case of a weak laser coupling, we find
a multitude of many-body Rydberg states with well-defined excitation properties
which are adiabatically accessible starting from the ground state. A
comprehensive analysis of the degeneracies of the spectrum as well as of the
single and pair excitations numbers of the eigenstates is performed. In the
strong laser regime, analytical solutions for the pseudo-fermionic eigenmodes
are derived. Perturbative energy corrections for this approximative approach
are provided.
