Wave-packet reconstruction via local dynamics in a parabolic lattice

Abstract

We study the dynamics of a wave packet in a potential formed by the sum of a periodic lattice and a parabolic potential. The dynamics of the wave packet is essentially a superposition of oscillations with frequencies proportional to the local slope of the parabolic potential. The amplitude and the phase of the Fourier transform of a signal characterizing this dynamics then contain information about the amplitude and the phase of the wave packet at a given lattice site. Hence, complete reconstruction of the wave packet in real space can be performed from a study of the dynamics of the system.