Wavepacket reconstruction via local dynamics in a parabolic lattice
Quentin Thommen, Veronique Zehnle, Jean Claude Garreau
Abstract
We study the dynamics of a wavepacket in a potential formed by the sum of a periodic lattice and of a parabolic potential. The dynamics of the wavepacket is essentially a superposition of ``local Bloch oscillations'', whose frequency is proportional to the local slope of the parabolic potential. We show that the amplitude and the phase of the Fourier transform of a signal characterizing this dynamics contains information about the amplitude and the phase of the wavepacket at a given lattice site. Hence, complete reconstruction of the the wavepacket in the real space can be performed from the study of the dynamics of the system.
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