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The necessity to go beyond Gross-Pitaevskii to properly describe
strongly-interacting cold bosonic atoms, and even weakly-interacting atoms in double- and multi-well traps has by now became well-accepted by the community.
Starting from the problem of attractive condensates on a ring and ending with that of repulsive bosons in general traps, we present two new theoretical and computational approaches going beyond standard mean-field. These have enabled us to predict new physical phenomena. I discuss fragmentation of attractive and repulsive condensates, a zoo of Mott-insulator phases in optical lattices [thereby going beyond Bose-Hubbard model], and the pathway to fermionizion/crystallization of trapped cold bosonic systems. |
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