  Atoms in highly excited (Rydberg) states have a number of unique properties
which make them attractive for applications in quantum information. These are
large dipole moments, lifetimes and polarizabilities, as well as strong
long-range interactions between Rydberg atoms. Experimental methods of laser
cooling and precision spectroscopy enable the trapping and manipulation of
single Rydberg atoms and applying them for practical implementation of quantum
gates over qubits of a quantum computer based on single neutral atoms in
optical traps. In this paper, we give a review of the experimental and
theoretical work performed by the authors at the Rzhanov Institute of
Semiconductor Physics SB RAS and Novosibirsk State University on laser and
microwave spectroscopy of cold Rb Rydberg atoms in a magneto-optical trap and
on their possible applications in quantum information. We also give a brief
review of studies done by other groups in this area.
