Study of quasi-conserved quantities in atomic BEC and dilute quantum gases

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We studied adiabaticity and nonlinear dynamics in the context of the manipulation and control of the Bose-Einstein condensate (BEC) made of an atomic gas. We conducted a pilot study of the mechanism for the unanticipated creation of quantum vorticies in an experiment pertaining to the construction of a beam-splitter in a BEC-interferometer. Since the numerical techniques and the computer codes required for the analysis of BEC have much in common with those for the ultra-short laser pulses and their application to atomic physics, we observed a new development by applying the techniques to the ionization of atoms in ultra-intense laser fields and to the high-harmonics generation.With a view to the representation of two-body interactions, we employed a computation scheme based on theoretical chemistry, and evaluated the mobility of an ion in a low-temperature gas of helium, thereby carrying out a dynamical analysis of the mobility and comparing it with experimental results. Quite unexpectedly, we pinned down the cause of the hitherto unsolved polarization-limit problem.In addition to such discoveries, there emerged new challenges. For instance, the transformation of an atomic pair into a molecule at ultra-low temperatures constitutes a nonlinear STIRAP problem, which is an important issue under the present theme and is all the more applicable to related problems because of the universal mathematical nature of the nonlinear STIRAP problem. We expect more challenges will appear in relation to the adiabaticity and nonlinear dynamics in many-body physics at low temperatures. A new experimental development is equally likely in the field of ultra-short laser pulses and their interactions with atoms. We look forward to contributing to further progress.