When applying to a Rydberg atom a weak microwave (MW) field whose frequency nearly matches the classical Kepler frequency of the electron, an electron-probability distribution is localized in space and periodically oscillates synchronized with the MW-field phase for a long time: An “eternal” non-dispersing wave packet is created, which resembles a one-dimensional classical atom, as the wave packet localized nearly along the polarization axis of MW field does not manifest dispersion as time evolves. By exploiting the synchronization of the electron motion in the atom, which can be thought of as a nonlinear phase-locking of electron's radial motion based on the corresponding classical dynamics, we have demonstrated that binding energy of Rydberg atoms can be manipulated by adiabatically increasing or decreasing the MW frequency. In quantum mechanics, this process can be viewed as a ladder-climbing, i.e., population transfer of Rydberg atoms through a sequence of single-photon adiabatic rapid passages (ARPs). We have also found that the same population transfer in the Rydberg ladder can be achieved through a single multi-photon ARP instead of driving transitions via a series of one-photon ARPs. Again, we show that the non-linear phase-locking is responsible for the classical dynamics of the population transfer through the multi-photon ARP.