Efficient and accurate methods for solving the time-dependent spin-1 Gross-Pitaevskii equation.
We develop a numerical method for solving the spin-1 Gross-Pitaevskii equation. The basis of our work is a two-way splitting of the spin-1 evolution equation that leads to two exactly solvable flows. We use this to implement a second-order and a fourth-order symplectic integration method. These are the first fully symplectic methods for evolving spin-1 condensates. We develop two nontrivial numerical tests to compare our methods against two other approaches.
Quantum Science Otago, Dodd-Walls Centre for Photonic and Quantum Technologies, Department of Physics, University of Otago, Dunedin 9016, New Zealand.
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Symes
Institute of Fundamental Sciences, Massey University, Palmerston North 4474, New Zealand.
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McLachlan
Quantum Science Otago, Dodd-Walls Centre for Photonic and Quantum Technologies, Department of Physics, University of Otago, Dunedin 9016, New Zealand.
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Blakie