Chiral matter-wave solitons in a density-dependent gauge theory

Abstract

In this thesis, we study the properties of one-dimensional chiral matter-wave solitons described by a density-dependent gauge theory. We begin, by first detailing the origin of the physical model, in which a synthetic density-dependent gauge potential is optically engineered in an ultracold bosonic gas. The resulting equation of motion for the condensate, which takes the form of a ‘chiral nonlinear Schr¨odinger equation’, will then be the main focus of this work, as the prose of the thesis changes from the field of condensed matter physics to that of nonlinear dynamics. In particular, we will demonstrate how the introduction of the density-dependent gauge potential leads to the breakdown of integrability, Galilean invariance, and chiral symmetry in the model and show how these properties, in part, lead to the emergence of both dark and bright chiral soliton solutions. From this, we will derive the principle conservation laws of the model using variational techniques and illustrate the semiclassical behaviour of the solitons in the context of the density-dependent gauge theory. The majority and remainder of this thesis, will then be devoted to two of the traditional problems in nonlinear physics for the bright chiral soliton: the stability in response to a linear perturbation and the collision dynamics between pairs of solitons. Here, we will find that the gauge theory features near-integrable dynamics in the case of a single-soliton, but is dominated by non-integrable dynamics in the two-soliton case. This result demonstrates the role and importance of nonintegrability in the description of nonlinear models, while potentially offering new possibilities for the coherent control of solitons in the ultracold setting.