Methods of quantum logic in ion frequency standards, quantum computers, and modern spectroscopy

Today, precise laser control of the quantum states of single ions cooled to low temperatures in traps ensures significant progress in the development of such physical areas as optical and microwave frequency standards, quantum computing, and accurate measurements of transition frequencies to confirm fundamental physical theories. Pioneering ideas about the possibility of using lasers in the development of frequency standards, expressed in the 1960s by the Nobel laureate N G Basov, have enjoyed rapid development: the relative accuracy of frequency standards has reached the 18th decimal place, and the experimentally demonstrated coherence time of narrow optical transitions amounts to tens of seconds. The paper presents a selective review, as well as the results of research at the Lebedev Physical Institute, in the area of using elements of quantum logic in the action of coherent laser pulses on single ions. Also discussed is the use of quantum logic methods in optical clocks based on the $\rm Al^+$ ion and the multiply charged $\rm Al^+$ ion, and also in quantum computers based on $\rm Ca^+$ and $\rm Yb^+$ ions.