Nonlinear dynamics of a matter-wave soliton in driven potentials

Abstract

In this thesis we study, analytically and numerically, the dynamics of a bright matter-wave soliton formed from a Bose-Einstein condensate with attractive interatomic interactions, confined by a one dimensional harmonic or double-well trapping potential, and subject to weak periodic driving. Such systems have potential applications in metrology, specifically in the use of atom interferometers for high precision inertial and gravitational field sensing. The localised and dynamically robust nature of matter-wave solitons may help overcome limitations such as wavepacket spreading in current atom interferometry experiments. A typical matter-wave interferometer involves a condensate trapped in a double-well potential. Being able to manipulate the tunnelling behaviour of a matter-wave soliton in potentials such as a double-well would thus give greater control in setting up these experiments. This also has a bearing upon the broader problem of transport of matter-wave solitons across potential barriers. These are questions which are largely unanswered in the current literature. We understand the tunnelling behaviour of a matter-wave soliton in a driven double well potential by first studying the fundamental mechanisms by which energy is transferred to a soliton in a driven harmonic potential. In this way our work also contributes more generally to the problem of transport in driven potentials. Within the mean field approximation, we show that efficient energy transfer to the soliton occurs in two frequency regimes: on resonance with the trapping frequency and on resonance with the internal mode frequency of the soliton. The former regime is well described by modelling the soliton effectively as a rigid particle, and in this regime energy transfer occurs due to parametric driving. In the latter regime, the extended nature of the soliton is important and energy transfer occurs due to internal mode coupling: a coupling between the width oscillations of the soliton and its translational motion. We find that in this internal mode coupling regime the soliton is unstable to decay. We thus show that effective particle regime is the more promising for efficiently exciting a bright matter-wave soliton to tunnel across a potential barrier, while preserving its form.