MCTDHB Physics and Technologies: Excitations and Vorticity, Single-Shot Detection, Measurement of Fragmentation, and Optimal Control in Correlated Ultra-Cold Bosonic Many-Body Systems

Here we report on further applications, developments, expansion, and proliferation of the Multi-Configurational Time-Dependent Hartree for Bosons (MCTDHB) method in the context of ultra-cold atomic systems. In this year we put our main efforts to understanding and generalizing vortices—two-dimensional (2D) and three-dimensional (3D) quantum objects carrying angular momentum—from the perspective of the many-body physics. We have studied static properties and quantum dynamics of vortices confined in simple parabolic traps and in circular traps. Particular emphasis has been put on the loss of coherence and build-up of the fragmentation. Complimentary, we continue to develop the MCTDHB method spanning several directions of the theoretical and computational physics as well as optimal-control theory: (a) the linear-response on-top of the MCTDHB method (LR-MCTDHB) has been reformulated in a compact block form, expanded for general inter-particle interactions, and benchmarked against the exactly-solvable harmonic-interaction model; (b) a new analysis tool capable of simulating the outcomes of typical shots generated in the experimental detection of ultra-cold atomic systems has been invented, tested, and applied; (c) a novel algorithm offering a direct quantitative measurement of the possible fragmentation in bosonic systems has been proposed and applied; (d) the optimal-control Chopped RAndom Basis (CRAB) algorithm has been merged with the MCTDHB package and applied to manipulate quantum systems. Implications and further perspectives and future research plans are briefly discussed and addressed.