Many-boson quantum states and highly non-equilibrium quantum dynamics of low-dimensional attractive Bose systems

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A major goal of this project is to understand the quantum dynamics and explore the wealth of physical phenomena of low-dimensional attractive Bose systems, on the manybody level. The Gross-Pitaevskii theory is one of the widely accepted mean-field tools dealing with static and dynamical properties of ultracold low-dimensional attractive Bose gases. It predicts the existence of dynamically-stable coherent one-dimensional (1D) objects - solitons and soliton trains. Recently, we studied the dynamics of 1D attractive Bose gases on the many-body level by utilizing our multiconfigurational time-dependent.Hartree for bosons (MCTDHB) method and found a substantially richer physics that what was previously known. In particular, we have discovered new dynamically-stable fragmented objects - termed catons and fragmentons. These fragmented objects are distinct from and generally are lower in energy than the soliton trains. The proposed project is aimed at:(1) Studying the phenomenology and mechanisms of formation of the new dynamically-stable objects catons and fragmentons.(2) Studying the collisional properties of solitons on the many-body level, searching and checking for the emergence of many-body physics during these collisions.(3) Developing and benchmarking the MCTDHB method in 2D, and exploring - what is expected to be very rich - the many-body dynamics of attractive Bose gases in 2D.