"Solitary Matter Waves in Combined Linear and Nonlinear Potentials: Detection, Stability, and Dynamics"

One of my papers came out in its final published form today. Here are the details.

Title: Solitary matter waves in combined linear and nonlinear potentials: Detection, stability, and dynamics

Authors: Scott Holmes, Mason A. Porter, Peter Krüger, and Panayotis G. Kevrekidis

Abstract: We study statically homogeneous Bose-Einstein condensates with spatially inhomogeneous interactions and outline an experimental realization of compensating linear and nonlinear potentials that can yield constant-density solutions. We illustrate how the presence of a step in the nonlinearity coefficient can only be revealed dynamically and examine how to reveal it by exploiting the inhomogeneity of the sound speed with a defect-dragging experiment. We conduct computational experiments and observe the spontaneous emergence of dark solitary waves. We use effective-potential theory to perform a detailed analytical investigation of the existence and stability of solitary waves in this setting, and we corroborate these results computationally using a Bogoliubov–de Gennes linear stability analysis. We find that dark solitary waves are unstable for all step widths, whereas bright solitary waves can become stable through a symmetry-breaking bifurcation as one varies the step width. Using phase-plane analysis, we illustrate the scenarios that permit this bifurcation and explore the dynamical outcomes of the interaction between the solitary wave and the step.


As an additional note, there have been a couple of hundred theoretical/computational papers on BECs with spatially inhomogeneous nonlinearities, but (to my knowledge) there has been only a single experimental paper on the topic, and that paper's basic point was essentially just that one can actually make these things in the laboratory. The challenge is thus to do something interesting in the laboratory, and this paper includes some experimental designs to try to do that (and, indeed, it includes an experimentalist as one of the authors). So here's hoping that we'll see some of these things or other phenomena soon in spatially inhomogeneous BECs studied in laboratories...