We study atoms in optical lattices whose electronic ground state is off-resonantly coupled to a highly excited state with strong binary interactions. We present a time-dependent treatment of the resulting quantum dynamics, which -contrary to recent predictions [Phys. Rev. Lett. 110, 213005 (2013)] -proves that the strong repulsion between the weakly admixed Rydberg states does not lead to atomic trap-loss. This finding provides an important basis for creating and manipulating coherent long-range interactions in optical lattice experiments.PACS numbers: 32.80. Ee, 32.80.Rm, 37.10.De By virtue of their strong interactions, laser-excitation of high-lying Rydberg states in cold atomic gases has recently enabled numerous experimental breakthroughs in quantum information science [1][2][3], quantum nonlinear optics [4][5][6][7][8][9] and investigations of long-range interacting quantum many-body systems [10][11][12]. Most of these applications rely on the ability to manipulate atoms coherently on timescales below the radiative lifetime of the excited states, during which atoms remain essentially frozen in space. However, it was shown [13,14] that off-resonant excitation of Rydberg states can extend this timescale limitation beyond this frozen gas regime. Recent experiments have demonstrated coherent Rydberg excitation in a Bose-Einstein condensate [15], and observed long-time effects of molecular interactions [16][17][18][19][20] between Rydberg and ground state atoms. Theory predicts that this approach also yields a unique type of longrange interactions between Rydberg-dressed ground state atoms, that would enable the observation of interesting nonlinear wave dynamics [21][22][23][24] and exotic many-body phenomena, such as supersolidity [13,14,[25][26][27][28][29][30][31][32], in degenerate quantum gases.Extending this scheme to atomic lattices promises a number of intriguing perspectives, e.g., for quantum transport problems [33], applications in quantum computation [34], quantum simulations of lattice models [35], and spin squeezing in optical lattice clocks [36]. However, in a recent work [37] it was predicted that atomic motion together with the strong repulsion between the excited atoms induces large trap losses that would inevitably preclude the applicability of Rydberg dressing in optical lattices. Here, we present a time-dependent treatment of this problem and show that such trap losses (i ) are negligibly small under the approximations used in [37] and (ii ) are strictly absent if a more accurate description of the Rydberg-Rydberg atom interactions is employed.Rydberg dressing in free space -Let us first consider an ensemble of atoms in free space [13,14], whose ground state |g is off-resonantly coupled to a high-lying Rydberg state |e with a Rabi frequency Ω and a laser detuning ∆ Ω. The excited atoms feature greatly enhanced van der Waals (vdW) interactions V ee = C 6 /x 6 . Owing to the strong scaling of the vdW coefficient C 6 ∼ n 11 with the atom's principal quantum number n, V ee exceeds the groun...