Many-body effects in fragmented, depleted, and condensed bosonic systems in traps and optical cavities by MCTDHB and MCTDH-X

The many-body physics of trapped Bose-Einstein condensates (BECs) is very rich and demanding. During the past year of the MCTDHB project at the HLRS we continued to shed further light on it with the help of the MultiConfigurational Time-Dependent Hartree for Bosons (MCTDHB) method and using the MCTDHB and MCTDH-X software packages. Indeed, our results on which we report below span a realm of many-body effects in fragmented, depleted, and even in fully condensed BECs. Our findings include: (1) fragmented superradiance of a BEC trapped in an optical cavity; (2) properties of phantom (fragmented) vortices in trapped BECs; (3) dynamics of a two-dimensional trapped BEC described by the Bose-Hubbard Hamiltonian with MCTDH-X; (4) overlap of exact and Gross-Pitaevskii wave-functions in trapped BECs; (5) properties of the uncertainty product of an out-of-equilibrium trapped BEC; (6) many-body excitations and de-excitations in trapped BECs and relation to variance; and (7) many-body effects in the excitation spectrum of weakly-interacting BECs in finite one-dimensional optical lattices. These are all appealing and fundamental many-body results made through the kind allocation of computer resources by the HLRS to the MCTDHB project. Finally, we put forward some future developments and research plans, as well as further many-body perspectives.