Variational determination of approximate bright matter-wave soliton solutions in anisotropic traps

G. Herring, P. G. Kevrekidis, R. Carretero-González +3 more

Bettina Gertjerenken, Timothy P. Wiles, Christoph Weiß

T. P. Billam, Steven A. Wrathmall, S. A. Gardiner

We consider the ground state of an attractively interacting atomic Bose-Einstein condensate in a prolate, cylindrically symmetric harmonic trap. If a true quasi-one-dimensional limit is realized, then for sufficiently weak axial trapping this ground state takes the form of a bright soliton solution of the nonlinear Schr\"odinger equation. Using analytic variational and highly accurate numerical solutions of the Gross-Pitaevskii equation, we systematically and quantitatively assess how solitonlike this ground state is, over a wide range of trap and interaction strengths. Our analysis reveals that the regime in which the ground state is highly solitonlike is significantly restricted and occurs only for experimentally challenging trap anisotropies. This result and our broader identification of regimes in which the ground state is well approximated by our simple analytic variational solution are relevant to a range of potential experiments involving attractively interacting Bose-Einstein condensates.

Paul Dyke, Sidong Lei, S. E. Pollack +2 more

Tangyou Huang, Jia Zhang, Jing Li +1 more

Motivated by recent experiments, we present the time-optimal variational control of a bright matter-wave soliton trapped in the harmonic trap by manipulating the atomic interaction through Feshbach resonances. More specifically, we first apply the variational technique to derive the motion equation for capturing the soliton's shape and, second, combine an inverse-engineering method with optimal control theory to design the scatter length for implementing time-optimal decompression. Since the minimum-time solution is of the ``bang-bang'' type, the smooth regularization is further adopted to smooth the on-off controller out, thus avoiding the heating and atom loss induced from the magnetic field ramp across a Feshbach resonance, in practice.

Paul Dyke, Sidong Lei, Randall G. Hulet