Numerical method for evolving the dipolar projected Gross-Pitaevskii equation.
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, which 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.
Blakie
P B
PB
Department of Physics, Jack Dodd Centre for Quantum Technology, University of Otago, Dunedin 9016, New Zealand.
Ticknor
C
C
Bradley
A S
AS
Martin
A M
AM
Davis
M J
MJ
Kawaguchi
Y
Y