We report on the first direct observation of coherent control of single-particle tunneling in a strongly driven double-well potential. In our setup atoms propagate in a periodic arrangement of double wells allowing the full control of the driving parameters such as frequency, amplitude, and even the space-time symmetry. Our experimental findings are in quantitative agreement with the predictions of the corresponding Floquet theory and are also compared to the predictions of a simple two mode model. Our experiments reveal directly the critical dependence of coherent destruction of tunneling on the generalized parity symmetry.

We propose and experimentally demonstrate a method to prepare a nonspreading atomic wave packet. Our technique relies on a spatially modulated absorption constantly chiseling away from an initially broad de Broglie wave. The resulting contraction is balanced by dispersion due to Heisenberg's uncertainty principle. This quantum evolution results in the formation of a nonspreading wave packet of Gaussian form with a spatially quadratic phase. Experimentally, we confirm these predictions by observing the evolution of the momentum distribution. Moreover, by employing interferometric techniques, we measure the predicted quadratic phase across the wave packet. Nonspreading wave packets of this kind also exist in two space dimensions and we can control their amplitude and phase using optical elements.PACS numbers: 03.75. Be, 42.50.Vk, 03.75.Dg Nonspreading wave packets have attracted interest since the early days of quantum mechanics. Already in 1926 Schrödinger [1] found that the displaced Gaussian ground state of a harmonic oscillator experiences conformal evolution because a classical force prevents the wave packet from spreading. Even in free space the correlations between position and momentum stored in an initially Airy-function-shaped wave packet can prevent spreading [2]. Here we propose and experimentally observe the formation and propagation of nondispersive atomic wave packets in an imaginary (absorptive) potential accessible in atom optics [3,4,5]. Although there is no classical force, there are correlations continuously imposed by Heisenberg's uncertainty relation resulting in the stabilization of the wave packet.Localized wave packets due to stabilization are well known in the context of periodically driven quantum systems [6] and studied with increasing interest for electronic wave packets in Rydberg atoms [7,8,9,10]. Our approach to create nondispersive atomic wave packets relies on three ingredients: (i) an absorption process [11] cuts away the unwanted parts of a broad wave creating a packet that is continuously contracting in position space, (ii) this process leads due to Heisenberg's uncertainty relation to a broadening in momentum space and consequently to a faster spreading in real space, and (iii) the absorptive narrowing and the quantum spreading are balanced, leading to a nonspreading wave packet. In the following we will refer to such a wave packet as Michelangelo packet [12].Complex potentials for matter waves [13] emerge from the interaction of near resonant light with an open twolevel system shown in Fig. 1(a). For a standing light wave tuned exactly on resonance an array of purely imaginary harmonic potentials arises. When the Rabi frequency Ω 0 is of the order of the excited state linewidth Γ the local saturation parameter |Ω 0 sin(kx)/Γ|, and thus the upper level population, is of the order of unity except in a small vicinity of the field nodes. Consequently, our system decays approximately with the rate Γ. Therefore, in the time domain t ≫ 1/Γ the atomic wave function vanishes almost...

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