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The quantum dynamics of two distant H atoms excited by ultrashort andspatially shaped laser pulses is studied by the numerical solution of thenon-Born-Oppenheimer time-dependent Schr\"odinger equation within athree-dimensional (3D) model, including the internuclear distance R and the twoz coordinates of the electrons, z1 and z2. The two 1D hydrogen atoms, A and B,are assumed to be initially in their ground states with a large (but otherwisearbitrary) internuclear separation of R = 100 a.u. (5.29 nm). Two types of aspatial envelope of a laser field linearly po- larized along the z-axis areconsidered: (i) a broad Gaussian envelope, such that atom A is excited by thelaser field predominantly, and (ii) a narrow envelope, such that practicallyonly atom A is excited by the laser field. With the laser carrier frequency{\omega} = 1.0 a.u. and the pulse duration tp = 5 fs, in both cases anefficient energy transfer from atom A to atom B has been found. The ionizationof atom B achieved mostly after the end of the laser pulse is close to or evenhigher than that of atom A. It is shown that with a narrow spatial envelope ofthe laser field, the underlying mechanisms of the energy transfer from A to Band the ionization of B are the Coulomb attraction of the laser driven electronby the proton of atom B and a short-range Coulomb repulsion of the twoelectrons when their wave functions significantly overlap in the domain of atomB. In the case of a broad Gaussian spatial envelope of the laser field, theopposite process also occurs, but with smaller probability: the energy istransferred from the weakly excited atom B to atom A, and the ionization ofatom A is also induced by the electron-electron repulsion in the domain of atomA due to a strong overlap of the electronic wave functions.

Energy transfer among distant quantum systems in spatially shaped laser fields: Two H atoms with the internuclear separation of 5.29 nm (100 a.u.)