Coherent manipulations of atomic wavefunctions in optical lattices

We report on the realization of dynamical control of transport for ultra-cold $^{88}$Sr atoms loaded in accelerated and amplitude-modulated optical lattices. Cold atoms trapped in vertical optical lattices give rise to localized states, the Wannier-Stark states. Delocalization can be recovered by introducing a resonant coupling among neighboring lattice sites. We demonstrated this by applying a modulation either to the phase or the amplitude of the lattice potential. Atomic samples loaded into modulated vertical optical-lattice potentials exhibit a resonant delocalization dynamics arising from intraband transitions among Wannier-Stark levels [1]. We demonstrate the coherent control of the spatial extent of atomic wavefunctions by reversibly stretching and shrinking the wavefunctions over a distance of more than one millimeter [2]. Furthermore we tailor the dispersion law of atomic traveling wave-packets and show the ability to reversibly switch between localization regime and tunneling one. From this a novel atom mirror in optical lattices is demonstrated by reversing the group velocity of the atoms. \\[4pt] [1] V. V. Ivanov \textit{et al.,} Phys. Rev. Lett. \textbf{100}, 043602 (2008) \\[0pt] [2] A. Alberti, V. V. Ivanov, G. M. Tino and G. Ferrari, Nature Physics \textbf{5}, 547 (2009)