Numerical method for evolving the dipolar projected Gross-Pitaevskii equation

Details Numerical method for evolving the dipolar projected Gross-Pitaevskii equation Numerical method for evolving the dipolar projected Gross-Pitaevskii equation

2009-04-22

arxiv.org/abs/0904.3440v2

Phys. Rev. E 80, 016703 (2009)

Physics

Condensed Matter

Quantum Gases

16 pages, 6 figures. Updated to published version

Scientific paper

10.1103/PhysRevE.80.016703

We describe a method for evolving the projected Gross-Pitaevskii equation (PGPE) for an interacting Bose gas in a harmonic oscillator potential, with the inclusion of a long-range dipolar interaction. The central difficulty in solving this equation is the requirement that the field is restricted to a small set of prescribed modes that constitute the low energy c-field region of the system. We present a scheme, using a Hermite-polynomial based spectral representation, that precisely implements this mode restriction and allows an efficient and accurate solution of the dipolar PGPE. We introduce a set of auxiliary oscillator states to perform a Fourier transform necessary to evaluate the dipolar interaction in reciprocal space. We extensively characterize the accuracy of our approach, and derive Ehrenfest equations for the evolution of the angular momentum.

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