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 - Ernst, Thomas (Massey University, 2011)
The interplay of particle and resonant wave scattering including nonlinear effects creates systems of diverse and interesting quantum many-body physics. A better understanding of the physics in these systems could lead to new and exiting application exploiting their quantum nature. As an example, in this thesis we investigate the scattering of bright matter-wave solitons in ultracold gases on a square well in one spatial dimension. For this, solutions of the mean-field Gross-Pitaevskii approximation and a full quantum manybody method, the so-called multiconfigurational time-dependent Hartree approach (MCTDH), are compared. The MCTDH method is based on a finite basis set expansion, which naturally leads to errors in system properties, such as energies and densities, when compared to exact results. In this thesis, we propose an efficient solution to this problem by rescaling the interaction strength between the particles. Even for very large interactions in the Tonks-Girardeau limit, the rescaling leads to significant improvements. This is validated by successfully applying the rescaling to problems in ring systems as well as external confinements, such as a harmonic well and a double-well. The MCTDH method is then applied to the soliton scattering problem and compared to results from mean-field calculations. The latter verify that solitons, when scattered on a well, show quantum effects, such as reflection. For the first time, we show that a soliton can be additionally permanently trapped by the well due to resonances with bound states. For this thesis, to extend these results to a full many-body approach, we developed QiwiB. It is a program package implementing the MCTDHB method, which is a derivative of the MCTDH method, but optimised for bosonic systems. Limits for the validity of the MCTDHB approach are addressed by convergence studies on the soliton scattering problem. Furthermore, we demonstrate that the scattering on the well enables the creation of macroscopic binary quantum superposition states, i.e. NOON states. Novel NOON states corresponding to a superposition of a reflected soliton and a trapped soliton are observed. These states are shown to exist for a large range of initial conditions, and a possible experimental realisation is discussed.
Keywords: Solitons; Quantum theory