We study the expansion of bosonic Mott insulators in the presence of an optical lattice after switching off a confining potential. We use the Gutzwiller mean-field approximation and consider two different setups. In the first one, the expansion is restricted to one direction. We show that this leads to the emergence of two condensates with well defined momenta, and argue that such a construct can be used to create atom lasers in optical lattices. In the second setup, we study Mott insulators that are allowed to expand in all directions in the lattice. In this case, a simple condensate is seen to develop within the mean-field approximation. However, its constituent bosons are found to populate many nonzero momentum modes. An analytic understanding of both phenomena in terms of the exact dispersion relation in the hard-core limit is presented.Comment: 11 pages, 9 figures. Figures 2,3,4 correcte

Section IV of the article was devoted to the study of the expansion of initial states that were confined only along the x direction (nonzero V x and V y = 0), while open boundary conditions were applied in the y direction (a box trap in the y direction). The expansion followed after turning off the confining potential along x, i.e., setting V x = 0. We have found that, due to an error in the input files, the reported numerical calculations correspond to initial states prepared as explained, but expanding in the presence of periodic (not open) boundary conditions in the y direction. The figures below are corrected versions of Figs. 2, 3, and 4 in the paper, when open boundary conditions are applied during the expansion.Results for the density during the expansion are depicted in Fig. 2. The corresponding momentum distributions are presented in Fig. 3. The effect of having open boundary conditions during the expansion is apparent mainly in the density profiles, where a sort of lensing effect can be seen. Otherwise, the behavior of both the density and the momentum distribution functions is qualitatively the same as the one reported in the paper. From the new calculations, we extract the dependence of the location of the peaks versus η, for three values of U/J x . The results are reported in Fig. 4. They are also qualitatively the same (and quantitatively very close) to the ones reported in the original paper. Hence, no significant changes occur in the overall behavior of the observables studied and the conclusions remain unchanged. −100 0 100 x −20 0 20 y 0 1 −20 0 20 y 0 1 −20 0 20 y 0 1 −20 0 20 y 0 1 n U/J=25 −20 0 20 y 0 1 −100 0 100 x −20 0 20 0 1 −20 0 20 0 1 −20 0 20 0 1 −20 0 20 0 1 n U/J=60 −20 0 20 0 1 FIG. 2. (Color online) Comparison between the time evolution of the density profile across the trap of systems with U/J x = 25 (left) and U/J x = 60 (right), at t = 0, 10, 20, 30, and 40 (from top to bottom) following the release from traps with V x /J x = 0.03 and V x /J x = 0.08, respectively. η = 0.3 and the time is reported in units ofh/J x . 069905-1 1050-2947/2012/85(6)/069905(2)