Numerical method for evolving the dipolar projected Gross-Pitaevskii equation

Abstract

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.

16 pages, 6 figures. Updated to published version

References in corpus (11)

• A High Phase-Space-Density Gas of Polar Molecules
• Dynamics and statistical mechanics of ultra-cold Bose gases using c-field techniques
• Strong dipolar effects in a quantum ferrofluid
• Observation of dipole-dipole interaction in a degenerate quantum gas
• d-wave collapse and explosion of a dipolar Bose-Einstein condensate
• Can Spinor Dipolar Effects be Observed in Bose-Einstein Condensates?
• Spectral method for the time-dependent Gross-Pitaevskii equation with a harmonic trap
• Effect of quantum fluctuations on the dipolar motion of Bose-Einstein condensates in optical lattices
• Trapping of ultracold polar molecules with a Thin Wire Electrostatic Trap
• Numerical method for evolving the Projected Gross-Pitaevskii equation
• Two point correlations of a trapped interacting Bose gas at finite temperature