Two-Ion System in Paul Trap as Element of Quantum Logic

The results are presented and the future prospects for research are discussed on the practical implementation of the simplest quantum register consisting of two ions trapped and cooled in a linear Paul trap. Physical mechanisms allowing manipulation of systems with high-Q transitions that can be used as new generation optical frequency standards are discussed. Mechanism of a sympathetic cooling for such systems and spectroscopy of highly forbidden “clock” transitions based on quantum logics are presented. Some prospects for the development of a nuclear frequency standard based on optical transition in thorium nucleus allowing increasing frequency uncertainty up to 10-20 ÷ 10-22 are also discussed.