Speed-gradient control of cooled atom dynamics in potential of standing wave

Dynamics of cold atoms in laser standing wave is a subject of a great interest, stimulated by the main problem of nano-lithography with cooled atoms: We can obtain the very narrow width of cooled atoms, much less than wavelength of optical radiation, by focusing in standing wave. We consider the possibility to increase the efficiency which means obtaining the very narrow width of atoms by focusing all atoms of an initial atom beam by controlling of an atom dynamics in periodic potential of standing wave. Such control for cooled atom dynamics achieves by using the additional laser field. There are two additional possibilities of atom focusing to comparing with usual focusing without control function. The first, the control function was chosen so that all atoms fall into potential wells of standing wave. In this case we obtain the increasing of atom number in five times (compare with ordinary focusing). At the same time, the width of atom distribution function inside wells is about λ/20. In the second case, the control function was chosen so that all atoms prepare on the hills of the periodical potential. For such unusual focusing we demonstrate that the width of atoms can be done extraordinary narrow 6 nm and an atom number increases in one hundred times.