Quantum many-body dynamics of bright matter-wave solitons : a thesis presented in partial fulfilment of the requirements for the degree of Doctor of Philosophy at Massey University, Albany, New Zealand

T. Ernst

Published Jan 1, 2011• 0 citations

Abstract

The interplay of particle and resonant wave scattering including nonlinear effects \ncreates systems of diverse and interesting quantum many-body physics. A better \nunderstanding of the physics in these systems could lead to new and exiting \napplication exploiting their quantum nature. \nAs an example, in this thesis we investigate the scattering of bright matter-wave \nsolitons in ultracold gases on a square well in one spatial dimension. For this, solutions \nof the mean-field Gross-Pitaevskii approximation and a full quantum manybody \nmethod, the so-called multiconfigurational time-dependent Hartree approach \n(MCTDH), are compared. \nThe MCTDH method is based on a finite basis set expansion, which naturally \nleads to errors in system properties, such as energies and densities, when compared \nto exact results. In this thesis, we propose an efficient solution to this problem \nby rescaling the interaction strength between the particles. Even for very large \ninteractions in the Tonks-Girardeau limit, the rescaling leads to significant improvements. \nThis is validated by successfully applying the rescaling to problems \nin ring systems as well as external confinements, such as a harmonic well and a \ndouble-well. \nThe MCTDH method is then applied to the soliton scattering problem and \ncompared to results from mean-field calculations. The latter verify that solitons, \nwhen scattered on a well, show quantum effects, such as reflection. For the first \ntime, we show that a soliton can be additionally permanently trapped by the well \ndue to resonances with bound states. \nFor this thesis, to extend these results to a full many-body approach, we developed \nQiwiB. It is a program package implementing the MCTDHB method, \nwhich is a derivative of the MCTDH method, but optimised for bosonic systems. \nLimits for the validity of the MCTDHB approach are addressed by convergence \nstudies on the soliton scattering problem. Furthermore, we demonstrate that the \nscattering on the well enables the creation of macroscopic binary quantum superposition \nstates, i.e. NOON states. Novel NOON states corresponding to a \nsuperposition of a reflected soliton and a trapped soliton are observed. These \nstates are shown to exist for a large range of initial conditions, and a possible \nexperimental realisation is discussed.

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